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DR. COLLINS PCAT – INORGANIC CHEMISTRY

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atomic number (Z)
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number of protons in the nucleus
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mass number (A)
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number of protons + number of neutrons
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how to calculate the number of neutrons
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mass number (A) – atomic number (Z) for a neutral atom: Z = number of protons = number of electrons
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isotopes
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-are atoms of the same element that differ in mass number (i.e. isotopes differ in the number of neutrons that they possess) -the chemical properties of the isotopes of an element are almost identical since those properties depend almost exclusively on the atomic number (number of protons) -hydrogen is an exception to this rule because its 3 isotopes vary slightly in their properties, and thus they have different names (H-1 is hydrogen, H-2 is deuterium, and H-3 is tritium) -when occurring naturally, the proportions (percent abundancies) of the various isotopes are always the same
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atomic weight
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the weighted average of all the naturally occurring isotopes for that element
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symbolism: 2 representations of an atom (E)
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1. mass number (A) over atomic number (Z) followed by the element symbol (E) 2. element symbol (E) – mass number (A)
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ions
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ions are charged atoms formed by gaining or losing electrons
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cation
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a positive ion formed by the LOSS of one or more electrons
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anion
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a negative ion formed by the GAIN of one or more electrons
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essential ion charges
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-IA: Na1+, K1+ -2A: Mg2+, Ca2+, Ba2+ -B group ions: Fe2+ or Fe3+, Co2+ or Co3+, Ni2+, Zn2+, Ag1+ -3A: Al3+ -4A: O2- -5A: F1-, Cl1-, Br1-, I1-
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common polyatomic ions (note: the -ite anion always has ONE LESS oxygen than the corresponding -ate anion)
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-hydroxide OH1- -cyanide CN1- -sulfate SO4^2- -phosphate PO4^3- -nitrate NO3^1- -carbonate CO3^2- -bicarbonate HCO3^1- -peroxide O2^2- -permanganate MnO4^1- -ammonium NH4^1+ -perchlorate ClO4^1- -chlorate ClO3^1- -chlorite ClO2^1- -hypochlorite ClO1-
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ionic compound formula
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-the formula for an ionic compound always gives the simplest whole number ratio of the ions that yields electrical neutrality
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ionic compound naming
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a. use a two word name – the first word for the cation, second word for the anion b. for monatomic cations, simply give the element’s name (e.g. Na1+ is sodium) c. for monatomic anions, affix an -ide ending to the stem of the element’s name (e.g. Cl1- is chloride) d. use the unadjusted given name for polyatomic ions e. for cations that exhibit more than one common ion charge, indicate the charge with a roman numeral after the element’s name (e.g. Fe2+ is iron (II) and Fe3+ is iron (III)) -alternately use -ous and -ic endings to differentiate the two ions (e.g. Co2+ is cobaltous and Co3+ is cobaltic; Fe2+ is ferrous and Fe3+ is ferric)
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quantum numbers
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-use the 4 quantum numbers to characterize each electron in the atom -*n*: indicates the SHELL the electron is in -*l*: indicates the SUBSHELL the electron is in -*ml*: indicates the ORBITAL the electron is in -*ms*: indicates the electron spin’s ORIENTATION
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allowed values of the quantum numbers
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-shell: first (n=1), subshell: 1s (l=0), # of orbitals: one (m1=0) -shell: second (n=2), subshell: 2s (l=0) 2p (l=1). # of orbitals: one (m1=0) three (m1=-1,0,+1) -shell: third (n=3), subshell: 3s (l=0) 3p (l=1) 3d (l=2), # of orbitals: one (m1=0) three (m1=-1,0,+1) five (m1=-2,-1,0,+1,+2) -shell: fourth (n=4), subshell: 4s (l=0) 4p (l=1) 4d (l=2) 4f (l=3), # of orbitals: one (m1=0) three (m1=-1,0,+1) five (m1=-2,-1,0,+1,+2) seven (m1=-3,-2,-1,0,+1,+2,+3)
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note that for each allowed m1, the spin quantum number could be either +1/2 or -1/2; thus 2 electrons per orbital
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-subshell: s (l=0), # of orbitals: one (m1=0), max electrons: 2 -subshell: p (l=1), # of orbitals: three (m1=-1,0,+1), max electrons: 6 -subshell: d (l=2), # of orbitals: five (m1=-2,-1,0,+1,+2), max electrons: 10 -subshell: f (l=3), # of orbitals: seven (m1=-3,-2,-1,0,+1,+2,+3), max electrons: 14
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pauli exclusion principle
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no two electrons in the same atom can have the same set of 4 quantum numbers
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note that the maximum number of electrons per shell is 2n^2
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fill the subtle in left to right diagonal order: 1s,2s,2p,3s,3p,4s,3d,4p,5s…
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predicting subshell energy separations
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-the energy difference between two subshells that are in different shells is GREATER than the energy difference between two subshells that are in the same shell -thus the energy difference between 2s and 4p is GREATER than the energy difference beween 4s and 4d
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predicting ion charges
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-many elements form ions with either EIGHT or ZERO valence electrons (electrons in the outer shell – i.e. shell with the largest n value) i.e. sulfur (3s)^2 (3p)^4 will add 2e- to give (3s)^2 (3p)^6 β†’ six to eight valence electrons i.e. aluminum (3s)^2 (3p)^1 will lose 3e- to give (3s)^0 (3p)0 β†’ three to zero valence electrons
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diamagnetic
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-an element, ion, or molecule that has TWO electrons in all of its occupied orbitals -is repelled by an external magnetic field
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paramagnetic
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-an element, ion, or molecule that has at least one orbital with only ONE electron in it -is attracted by an external magnetic field
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counting the number of unpaired electrons
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-an unpaired electron (upe) is an electron that is the sole occupant of an orbital β†’ thus an orbital with one electron in it counts as an upe –diamagnetic substances have zero upe’s ex: calcium is diamagnetic because has zero upe’s (1s)^2 (2s)^2 (2p)^6 (3s)^2 (3p)^6 (4s)^2 ex: oxygen is paramagnetic because 2p is not fully filled – has two upe’s (1s)^2 (2s)^2 (2p)^4 –to count the upe represent the three p orbitals as boxes and add electrons one by one |↑↑|↑|↑|
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the periodic table
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1. the maximum number of electrons per row is given by 2n^2 (same as max per shell) 2. elements in a column (called family or group) have the same number of valence electrons 3. elements in a row (called period or series) have their outermost valence electrons in the same shell 4. remember that halogens ranged from lightest to heaviest are: fluorine to chlorine to bromine to iodine 5. remember that the noble gases ranged from lightest to heaviest are: helium to neon to argon to krypton to xenon to radon
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ideal gas law
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*PV=nRT* P = pressure in atm V = volume in L n = number of moles R = 0.082 L atm/mole K T = absolute temperature in Kelvin -parameters that are on the OPPOSITE sides of the equal sign are DIRECTLY proportional to each other -parameters that are on the SAME side of the equal sign are INVERSELY proportional to each other
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quantitative calculations with the ideal gas law
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-always convert C to K by: adding 273 to the C temp -must convert mmHg or torr to atm by: dividing the mmHg or torr pressure by 760; make sure volume is in L
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avogadro’s law
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-equal volumes of different gases, if measured at the same temp and pressure, contain equal numbers of gas molecules -therefore you can do stoichiometry (ratio) calculations based on a balanced equation in volume units as long as the gases are measured at the same temp and pressure
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dalton’s law of partial pressures
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-the total pressure of a gas is a SUM of the partial pressures of the individual gases that are present in the gas mixture -note: for a gas collected “over water” (collected wet) one must SUBTRACT the vapor pressure of the water from the total pressure to get the pressure of the gas
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molar volume
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-at STP (0 C and one atm) one mole of a gas would occupy a volume of 22.4 L thus 1 mole = 22.4 L at STP
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postulates of the kinetic-molecular model
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1. gases consist of individual molecules or atoms that are widely dispersed 2. gas molecules travel in random, straight-line motion 3. the average kinetic energy of the gas molecules is directly proportional to the absolute temperature of the gas 4. collisions that the gas molecules experience are perfectly elastic (i.e. result in no net loss of momentum) 5. the pressure of a gas is due to collisions between the gas molecules and the walls of the gas’s container 6. gas molecules do NOT attract each other 7. the volume actually occupied by the gas molecules is negligible relative to the total volume of the gas’s container
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non-ideal behavior for gases
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gases tend to deviate from ideal behavior at low temperatures and/or high pressures
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intermolecular attractions
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intermolecular means BETWEEN molecules; whereas intramolecular means WITHIN a molecule
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electronegativity (EN)
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-EN is a measure of the capacity of the atoms of an element to attract bonded electrons note: 1. the non-metals have GREATER EN than do the metals 2. fluorine has the greatest EN (4), oxygen the second greatest EN (3.5), and cesium has the least EN (0.7) 3. the larger the EN difference between the bonded atoms, the more polar (or more ionic) the bond
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can use the EN difference to characterize the nature of the bond:
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-EN 1.9 = ionic bond
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polar vs non-polar molecules
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-symmetric molecules are NON-POLAR -non-symmetric molecules are POLAR (if the bonds are polar!)
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intermolecular attractions for neutral molecules (3)
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1. *london forces* (van der waal’s forces): the means by which neutral, non-polar molecules attract each other – the weakest intermolecular attraction 2. *dipole-dipole attraction*: polar molecules attract each other strongly (partial charges) 3. *hydrogen bonding*: a very strong dipole-dipole attraction that involves a polar molecule containing H bonded to either F, O, or N -common H-bonders: H2O, NH3, HF, alcohols (R-OH), amines (R-NH2), and carboxylic acids (R-COOH)
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what is the weakest intermolecular attraction?
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london forces (van der waal’s forces)
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what is the strongest intermolecular attraction?
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ionic compounds
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diatomics
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-all X2 type molecules are NON-POLAR (i.e. H2, O2, N2, F2, Cl2, Br2, I2) -all AX type molecules are POLAR (i.e. CO, HCl, NO, HBr)
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common neutral molecules (pg 9)
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-water = bent and polar (an H-bonder) -carbon dioxide = linear and non-polar -sulfur dioxide = bent and polar -sulfur trioxide = trigonal planar and non-polar -ammonia = pyramidal and polar (an H-bonder) -methane (CH4) = tetrahedral and non-polar -sulfur hexafluoride (SF6) = octahedral and non-polar
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ionic compounds – recognize by:
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1. presence of a metal/non-metal combination (e.g. NaCl, MgO) 2. presence of common polyatomic ions (e.g. NH4NO3, NH4Cl) -the attraction between the ions in an ionic compound is the strongest possible intermolecular force
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relative strengths of the intermolecular forces
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from strongest to weakest: ion-ion > H-bonding > dipole-dipole > london
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effect of intermolecular attractions on boiling and melting points
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-the stronger the intermolecular attraction, the higher the MP and BP will be note: size has a significant effect on intermolecular attractions -for neutral, non-polar molecules β†’ the larger the molecule, the stronger the attraction -for polar molecules and ions β†’ the smaller the molecule, the stronger the attraction
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predicting bond polarity
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-a non-polar bond results when two atoms of the same element form a bond or when two atoms of different elements but with the same EN form a bond -the greater the EN difference between the atoms in a bond, the more polar the bond will be -if the EN difference between the two atoms in a bond is very large (greater than 1.9) the bond will be ionic
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types of formulas
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1. *empirical (simplest) formula*: gives the SIMPLEST whole number ratio of atoms present in the compound 2. *molecular formula*: gives the ACTUAL number of atoms of each element that are present in the compound -thus the molecular formula may be the same as or a multiple of the empirical formula
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formula weight (FW)
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-aka molecular weight (MW) and molar mass -the mass of one mole of a compound based on the compound’s formula
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FW can be used as a conversion factor for what?
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between grams and moles
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percent composition by mass
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1. calculation of percent composition from the formula -ex: NaCl FW = 1(23.0) + 1(35.5) = 58.5 g/mol %Na = 1(23.0)/58.5 x 100 = 39.3% %Cl = 1(35.5)/58.5 x 100 = 60.7% 2. determining empirical formula from percent composition – change % to grams, find moles, divide by least moles
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density
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-density = mass/volume note: -1 mL = 1 cm^3 -1 L = 1000 mL = 1000 cm^3
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specific gravity (SG)
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-SG of X = (d of X)/(d of water); with both densities measured at the same temperature note: -SG has no units -at temperatures where water is a liquid (0-100C) SG is numerically equal to density -objects with a SG greater than one will sink in water whereas objects with a SG less than one will float in water
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solutions
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-definition: a homogenous (completely uniform) mixture with a variable concentration (e.g. sugar dissolved in water) -the solution can be viewed as being composed of one or more *solutes* (that which is dissolved) and a *solvent* (that which does the dissolving) -the solute is usually the lesser part of the solution, but regardless the solution always takes on the physical state of the solvent -LIKE DISSOLVES LIKE: a polar solvent (like water or ammonia) tends to be a good solvent for other polar substances and ionic compounds; while a non-polar solvent (like carbon tetrachloride or hydrocarbon) tends to be a good solvent for other non-polar, non-ionic substances
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concentration
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concentration = (quantity of solute)/(quantity of solvent or solution as a whole)
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types of concentration
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1. *molarity (M)* M = (# moles of solute)/(V of solution in L) M x VL = # of moles or M x VmL = # of mmoles 2. *percent* -by mass = %w/w = (mass of solute x 100)/(mass of solution) -by mass/volume = %w/v = (mass of solute in g x 100)/(V of solution in mL) 3. *molality (m)* m = (# moles of solute)/(mass of solvent in kg) 4. *mole fraction (Xi)* Xi = (# moles of i)/(total # of moles)
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colligative properties
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-a property whose value depends on the NUMBER of solute molecules that are present, not on the nature of the solute molecules
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type of colligative property – raoult’s law
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-dissolving a non-volatile solute in a volatile solvent has the effect of LOWERING the vapor pressure of the resultant solution, relative to that of the pure solvent -thus P (solution) < P^0 (solvent alone) -*P = (Xsolvent)(P^0)* where Xsolvent is the mole fraction of the solvent, P is the vapor pressure of the solution, and P^0 is the vapor pressure of the solvent
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type of colligative property – boiling point (BP) elevation
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-dissolving a non-volatile solute in a volatile solvent has the effect of RAISING the BP of the solution, relative to that of the pure solvent -*deltaTB = (kB)(m)* -where deltaTB is how much the BP is elevated, m is the molality of the solute, and kB is a constant characteristic of the solvent (kB indicates how much the BP is elevated per unit molality of solute for a particular solvent)
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type of colligative property – freezing point (FP) depression
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-dissolving a solute in a solvent has the effect of LOWERING the FP of the solution, relative to that of the pure solvent -*deltaTF = (kF)(m)* -where deltaTF is how much the FP is lowered, m is the molality of the solute, and kF is a constant characteristic of the solvent (kF indicates how much the FP is lowered per unit molality of solute for a particular solvent)
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osmosis
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the flow of SOLVENT through a semi-permeable membrane, in an effort to equalize concentrations
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dialysis
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in contrast to osmosis, the flow of SOLUTE through a semi-permeable membrane
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osmotic pressure
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the pressure that must be exerted on the surface of a solution to stop the the flow of osmosis into that solution -osmotic pressure is proportional to the solute concentration
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non-quantitative colligative property questions
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-you may be asked to determine which solution, among the 4 possible choices, will have the greatest colligative effect β†’ it is always the solution with the *largest solute concentration that will yield the greatest colligative effect* (lowest vapor pressure, highest BP, lowest FP, largest osmotic pressure) -in determining the solute concentration remember that, other things being equal, ionic solutes (electrolytes) will have a greater concentration than non-ionic solutes (non-electrolytes); also strong electrolytes will yield a higher effective concentration than will weak electrolytes
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common strong electrolytes
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1. water soluble strong acids (HCl, HNO3, H2SO4) 2. water soluble strong bases (NaOH, KOH) 3. water soluble salts (NaCl, KNO3, K2SO4)
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common weak electrolytes
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1. water soluble weak acids (CH3COOH) 2. water soluble weak bases (NH3)
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common non-electrolyte solutes
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1. water soluble sugars like glucose (C6H12O6) and sucrose (C12H22O11) 2. water soluble alcohols like methanol (CH3OH) and ethanol (C2H5OH)
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dilutions
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-adding more solvent to a solution (diluting it) does NOT change the amount of solute present in the solution *Mi x Vi = Mf x Vf* and *(%)i x Vi = (%)f x Vf* where i indicates the initial conditions and f indicates the final conditions after dilution
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basic stoichiometric calculations
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1. obtain the moles of the specified starting species 2. use the ratio from the balanced equation to convert from the specified starting material to the target material 3. convert from the calculated moles of the target material to the desired final unit (usually grams or volume)
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the law of combining volumes
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recall that for gases measured at the same T and P, the ratio from the balanced equation is valid in volume units as well as in mole units (see page 16)
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limiting reactant problems
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-in a limiting reactant problem, quantities of all reactants are specified so that it is not obvious which reactant the calculation of the product should be based on -the easiest way to do a limiting reactant problem is to separately calculate for each reactant the quantity of product expected -the right answer will then be the LEAST quantity of calculated product as that must correspond to the reactant that RAN OUT first
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common properties of acids
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1. taste sour 2. turn litmus red 3. leave phenolphthalein colorless 4. yield pH’s less than 7
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common properties of bases
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1. taste bitter and have a slippery feel 2. turn litmus blue 3. leave phenolphthalein pink 4. yield pH’s greater than 7
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arrhenius definition
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-an acid generates hydronium ions (H3O^1+ or H^1+) when dissolved in water, whereas a base yields hydroxide ions (OH^1-) when dissolved in water note: on the PCAT the hydronium ion may simply be referred to as the hydrogen ion
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bronsted-lowry definition
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-an acid is a proton (H^1+) donor -a base is proton acceptor
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lewis definition
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-an acid is an electron pair acceptor -a base is an electron pair donor
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“strong”
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undergoes the rxn in question completely
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“weak”
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undergoes the rxn only partially (incompletely)
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common strong acids
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-hydrochloric acid = HCl -nitric acid = HNO3 -sulfuric acid = H2SO4 -perchloric acid = HClO4
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common weak acids
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-acetic acid = HC2H3O2 or CH3COOH -carbonic acid = H2CO3 -hydrofluoric acid = HF -phosphoric acid = H3PO4
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common strong bases
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the IA and IIA hydroxide salts are strong bases (e.g. NaOH, KOH, Ca(OH)2, Ba(OH)2)
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common weak bases
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ammonia = NH3
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conjugate base anions
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-an anion obtained by the removal of a proton (H^1+) from a weak acid is itself a weak base; however the anion obtained by the removal of a proton from a strong acid is NOT a base EX: -thus HF (a weak acid) yields F^1- which is a weak base = basic -thus HCl (a strong acid) yields Cl^1- which is NOT a base = acidic -similarly protonating a weak base yields a cation that is a weak acid; protonating a strong base however yields a cation that is NOT an acid EX: -thus NH3 (a weak base) yields NH4^1+ which is a weak acid = acidic -thus NaOH (a strong base) yields Na^1+ which is NOT an acid = basic
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conjugate pairs
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-two molecules are conjugates of each other if their structures differ by a *single H^1+* -the molecule that has the extra H^1+ is called the conjugate acid while the molecules that lacks the H^1+ is called the conjugate base *HA + H2O β†’ A- + H3O+* acid + base β†’ conjugate base + conjugate acid *B + H2O β†’ HB+ + OH-* base + acid β†’ conjugate acid + conjugate base
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pH
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pH = -log[H+] [H+]= in log(-pH)
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pOH
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pOH= -log[OH-] [OH-]= in log(-pOH)
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[ ]
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denotes molarity
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self-ionization of water
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-pure water ionizes to a very limited extent yielding the following equilibrium: H2O + H2O β†’ H3O+ + OH- -at 25C: [H3O+] = [OH-] = 1×10^-7 -the equilibrium expression is: Kw = [H3O+][OH-] = 1×10^-14 which also yields pH + pOH = 14
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buffer
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a combination of a weak acid and a weak base that resists changes in pH
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short-cut approach to acid/base stoich calculations (pg 21)
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*nA x MA x VA = nB x MB x VB* -nA: acid’s capacity to donate protons per molecule of acid -nB: base’s capacity to accept protons per molecule of base -thus for HCl nA = 1; for H2SO4 nA = 2, for H3PO4 nA = 3, etc. -thus for NaOH nB = 1; for Ca(OH)2 nB=2; for NH3 nB = 1
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redox reactions: assigning oxidation numbers (oxidation states)
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-for the elemental, uncombined state the oxidation number (ON) is zero (e.g. N in N2 is zero) for compounds and ions: 1. F is always -1 2. the IA elements (Li, Na, K, Rb, Cs) are always +1 3. the IIA elements (Be, Mg, Ca, Sr, Ba) are always +2 4. Al is always +3 5. H is +1 when bonded to a NON-METAL; H is -1 when bonded to a METAL 6. O is usually -2 7. Cl, Br, and I are usually -1 8. assign other oxidation numbers consistent with these rules and consistent with the charge on the molecule
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For a redox reaction, at least one element will undergo a change in oxidation number. consider:
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Au3+ + Fe2+ β†’ Au1+ + Fe3+ -reduction half reaction: (Au3+ + 2e- β†’ Au+) x1 -oxidation half reaction: (Fe2+ β†’ Fe3+ + 1e-) x2 -balanced equation: 1 Au3+ + 2 Fe2+ β†’ 1 Au+ + 2 Fe3+
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electronic equations
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-a minimal half-rxn showing only the element that is undergoing a change in oxidation number (ON) -for any redox equation there will always be TWO electronic equations, one for oxidation and one for reduction -to identify the electronic equations, note the two elements that are undergoing a change in ON -for each, assign the electrons as needed to accomplish the ON change and you will have the electronic equations
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combustion reaction
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-consists of the burning of a substance in air β†’ thus a combustion rxn is a rapid rxn with oxygen -most commonly, the substance combusted is a hydrocarbon or one of its derivatives -the ideal products for the combustion of a hydrocarbon are: *carbon dioxide and water*
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energy units
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-the most common energy units: the calorie (cal) and joule (J) -*1 calorie* is defined as the energy needed to raise the temperature of 1 gram of liquid water by one degree celsius -the *joule* is the SI unit of energy and is defined as: *1 J = 1 kg m^2/sec^2* -*1 cal = 4.18J*
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specific heat (SH)
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-the heat needed to raise the temperature of 1 gram of the substance by one degree celsius -*SH of H2O (l) = 1.00 cal/g C = 4.18 J/g C*
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heat calculations involving no change in physical state
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heat (q) = mass x SH x deltaT
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heat of fusion (qFUS)
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-the amount of heat needed to convert 1 gram of solid to liquid at the substance’s melting point -qFUS of H2O = 80 cal/g = 334 J/g
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heat of evaporation (qVAP)
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-the amount of heat needed to convert 1 gram of liquid to vapor at the liquid’s boiling point -qVAP of H2O = 540 cal/g = 2260 J/g
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the first law of thermodynamics (the law of conservation)
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-in the physical universe, the sum total of mass and energy never changes -for non-nuclear reactions, it is approximately true that mass is conserved as mass, and energy is conserved as energy
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the second law of thermodynamics (the law of disorder)
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-entropy (S) = the energy equivalent of disorder -a spontaneous reaction is favored by an increase in disorder (entropy); or whenever a spontaneous process occurs, there is a net increase in the entropy (disorder) of the universe
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the third law of thermodynamics
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-a pure, perfect crystalline solid at absolute zero (0 K) temperature would have zero entropy (disorder)
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entropy (S)
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-the energy equivalent of the extent disorder present in a system -NO material can have negative entropy as that would imply greater order than perfect order -however an *entropy change* (deltaS), could be either positive (disorder increases) or negative (disorder decreases) -*entropy change (deltaS) = (S of products) – (S of reactants)* note: other things being equal, entropy increases from a solid to a liquid to a gas
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enthalpy (H)
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-the heat change for a reaction, if measured at constant temp and pressure, is called *enthalpy change* (deltaH) -a reaction that evolves heat is said to be *exothermic*; has a deltaH that is NEGATIVE -a reaction that absorbs heat is said to be *endothermic*; has a deltaH that is POSITIVE
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gibb’s free energy (G)
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-G is the total energy parameter (i.e. deltaG takes all energy interactions into account) -thus the change in the gibb’s free energy for a reaction will determine whether or not the reaction is spontaneous -*deltaG = deltaH – (T in Kelvin)(deltaS)* -if total energy is liberated, deltaG is negative and the reaction is spontaneous -if total energy must be consumed, deltaG is positive and the reaction is non-spontaneous -if deltaG is zero, the system has reached its energy minimum and said to be at “equilibrium”
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summary of sign conventions
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-DeltaH is (-): reaction is exothermic; favors spontaneity -DeltaH is (+): reaction is endothermic; favors non- spontaneity -DeltaS is (+): disorder is increased; favors spontaneity -DeltaS is (-): disorder is decreased; favors non-spontaneity -DeltaG is (-): available energy is produced; reaction spontaneous -DeltaG is (+): available energy is consumed; reaction non-spontaneous -DeltaG is (0): no available energy; reaction is at equilibrium
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kinetics
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the study of the rate of a reaction
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the rate law
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-gives the rel’ship of the rate of the reaction to the concentrations of the reactants -for a reaction: *aA + bB + cC β†’ products* -rate law will be of the form: *rate = k[A]^x[B]^y[C]^z* where x, y, z are the individual orders, x+y+z=overall order (n), k is the rate constant, [ ] indicates the concentration in molarity notes: -the individual orders (the exponents of the concentrations in the rate law) are not necessarily the same as the respective balancing coefficients -the individual orders are usually either 0, 1, or 2 but may take on any value -the individual orders are determined by selectively varying the concentrations of the reactants and seeing how the rate is affected -k is characteristic of the reaction in question and is dependent on temperature –although k is not directly proportional to temperature, an increase in temperature will cause an increase in k and a decrease in temperature will cause a decrease in k –the larger the value of k, the faster the reaction
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rate theories: the collision theory
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-for molecules to react, they must collide -for a collision to be effective in producing a reaction: 1. the molecules must collide with enough FORCE to break the old (reactant molecule) bonds 2. the molecules must collide with the proper ORIENTATION to form the new (product molecule) bonds note: as a consequence of the above, an increase in temperature must inevitably lead to an increase in the rate of a reaction
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rate theories: the transition state theory
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-the reactants must pass through a short-lived, maximum energy state (known as the *transition state*) before forming products -the energy needed to boost the reactant molecules to the transition state is called the *activation energy (EA)* -EA is always positive as it is the energy that must be ADDED to reach the maximum energy transition state -the larger the value of EA, the slower the reaction will be
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energy diagrams
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-EA (forward) = (E of transition state) – (E of reactants) -EA (reverse) = (E of transition state) – (E of products) -overall deltaG = (E of products) – (E of reactants) -spontaneous reactions: R β†’ P + deltaG (deltaG is negative) -nonspontaneous reactions: R + deltaG β†’ P (deltaG is positive) -equilibrium reactions: R β†’ P (deltaG = zero) note: at equilibrium, the rate of the forward reaction is EQUAL to the rate of the reverse reaction
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mechanisms
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-the mechanism for a reaction: the series of steps (called the pathway) by which the reactant molecules are converted into product molecules -the sum of the steps of the mechanisms yields the overall equation for the reaction -invariably one step in the mechanism occurs much more slowly than the other steps, and hence determines by itself the RATE of the reaction (the slow step is called the *rate determining step* ex: NO2 + CO β†’ NO + CO2 step 1 – 2 NO2 β†’ NO + NO3 SLOW step 2 – NO3 + CO β†’ NO2 + CO2 FAST the rate law would be: rate = k[NO2]^2 which derives entirely from the reactants in the slow step!
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catalysts
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-speeds up a reaction but is left unchanged by the reaction -operates by altering the mechanism of the reaction, leading to a lower energy transition state -thus the catalyst LOWERS the activation energy for the reaction
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equilibrium
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-at equilibrium, the rates of the forward and reverse reactions are the same β†’ think of an equilibrium as opposite processes occurring at the same rate
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the equilibrium constant (K)
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-the appropriate ratio of products to reactants that yields equilibrium is given by the *equilibrium expression* -consider: 3A + B β†’ 2C; K=[C]^2/[A]^3[B] -*K is the equilibrium constant* for the reaction; the larger the value of K, the more complete the reaction will be -generally the equilibrium expression concentrations are expressed in molarity units; at times however pressure units may be more convenient (in this case, constant is denoted as KP) notes: -the exponents for the reactants and products in the equilibrium expression are always the same as the respective balancing coefficients from the overall equation -the equilibrium expression is always a ratio of products to reactants -pure solids, pure liquids, and water when it is acting as the solvent for a dilute solution are NOT included in the equilibrium expression
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le chatelier’s principle
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-any system at equilibrium will respond in such a way as to relieve any stress applied to the system -the response will be either to speed up the forward or the reverse reaction until equilibrium is reestablished
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le chatelier’s principle – changes in concentration
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1. add reactant = favor forward reaction (shift to right) 2. remove reactant = favor reverse reaction (shift to left) 3. add product = favor reverse reaction (shift to left) 4. remove product = favor forward reaction (shift to right)
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le chatelier’s principle – changes in pressure (volume)
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consider any change in pressure to be due to the appropriate change in volume. thus: -a decrease in pressure must arise from an increase in volume, this will cause equilibrium to shift toward the side with MORE moles of gas -an increase in pressure must arise from a decrease in volume, this will cause equilibrium to shift toward the side with LESS moles of gas
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le chatelier’s principle – changes in temperature
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-for an endothermic reaction view heat as a reactant as: R + deltaH β†’ P -for an exothermic reaction view heat as a product as: R β†’ P + deltaH -then view an increase in temperature as the addition of heat & a decrease in temperature as the removal of heat -thus a temperature change is treated as a change in the concentration of heat (a reactant for an endothermic reaction or a product for an exothermic reaction)
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catalysts and equilibrium
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-the addition of a catalyst to a system at equilibrium has NO net effect on the position of equilibrium (i.e. the ratio of products to reactants at equilibrium) -by lowering the energy of the transition state, the catalyst would increase the rate of both the forward reaction and reverse reaction, but by the same proportional factor
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nuclear chemistry
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-some isotopes have stable nucleii, other isotopes have unstable nucleii -isotopes with unstable nucleii are said to be naturally radioactive and are called *radioisotopes* -radioisotopes usually decay by emitting *radiation* note: elements whose atomic number is greater than 82 have NO stable isotopes
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what are radioisotopes?
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isotopes with unstable nucleii, naturally radioactive
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balancing nuclear equations
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criteria: 1. balance mass number (exponents) as a sum 2. balance atomic number (subscripts) as a sum
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nuclear fission
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-in a nuclear fission reaction, a heavy radioisotope SPLITS into two lighter isoptopes -this reaction (which may be caused by a collision with a neutron) evolves an enormous amount of energy and two or more neutrons as a side product
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nuclear fusion
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-in a fusion reaction, two light isotopes UNITE (fuse) to form one heavier isotope -fusion reactions require a very high initiation temperature and evolve enormous amounts of energy (more than fission reaction)
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anhydride
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-an anhydride is formed by the removal of one H2O from a molecule ex: H2SO4 β†’ SO3 + H2O; thus SO3 is the anhydride of H2SO4 -if the original molecule only contains one hydrogen, use two of the molecules in the formation of the anhydride ex: 2 HNO3 β†’ H2N2O6 β†’ N2O5 + H2O
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phase diagram
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-a phase diagram indicates the physical state that a substance will take on at a particular combination of pressure and temperature -point A is the *triple point* β†’ the triple point for a substance is the combination of pressure and temperature at which the three physical states can coexist –helium is the only substance that does NOT have a triple point (no solid state) -point B signifies the critical temperature and critical pressure –the *critical temperature* is the temperature above which a gas cannot be liquefied by an increase in pressure note: the direct conversion from solid to gas is called *sublimation*; the direct conversion from gas to solid is called *deposition*
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solubility product equilibrium
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-a salt (e.g. MX) establishes the following equilibrium when dissolved in water: MX (s) β†’ M^n+ (aq) + X^n- (aq) -equilibrium is reached when the solution is saturated with ions from the salt note: due to this equilibrium, no salt has unlimited solubility in water nor is any salt completely insoluble in water -the equilibrium expression (called *solubility product expression*) for the above reaction is: KSP = [M^n+][X^n-]; the equilibrium constant is called *solubility product constant* -for salts of an analogous formula (e.g. both MX or both MX2) the SMALLER the value of KSP, the LESS soluble the salt will be! ex: Ag2S Ksp= [Ag^1+]^2[S^2-]
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calculating solubility
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-for simple one to one salts (formula of MX) we can easily calculate the solubility from the KSP value ex: AgCl with KSP = 1.8 x 10^-10 AgCl (s) β†’ Ag^1+ (aq) + Cl^1- (aq) at equilibrium let x x so KSP = [Ag^1+][Cl^1-] = 1.8 x 10^-10 = x^2 x = 1.3 x 10^-5 -thus for a one to one salt dissolving in pure water we have: *x = solubility = sqrt(KSP)* -if an ion that is common to the salt is initially present in solution, the solubility of the salt in that solution will be significantly LESS than its solubility in pure water (called the *common ion effect*)
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cell potentials
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-in an electrochemical cell: oxidation occurs at the anode; reduction occurs at the cathode -in a *galvanic (voltaic) cell*, a spontaneous redox reaction generates a flow of electricity -in an *electrolytic cell*, an external source of electricity is used to cause a non-spontaneous redox reaction to occur
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sign conventions
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-if the cell potential (E) is positive, the reaction will be spontaneous; whereas if the cell potential (E) is negative, the reaction will be non-spontaneous
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half-cell potentials
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-though half-cell potentials (E1/2) can never be measured as absolute numbers, they are assigned relative values -the reduction in the Standard Hydrogen Electrode (below) is assigned a half-cell potential of zero: 2H^1+ + 2e- –> H2 has E1/2 of 0V -all other half-cell potentials are determined relative to this arbitrary standard note: -half-cell potentials are invariably tabulated as reduction potentials -thus to obtain an oxidation potential, must change the sign of the half-cell potential relative to its value in a reduction table -to obtain the overall cell potential, ADD the oxidation potential to the reduction potential
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non-ideal behavior: the van der waal’s constants
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-gases tend to deviate from ideal behavior at very low temperatures (i.e. proximity to the condensation point) and very high pressures -the van der waal’s equation adjusts the Ideal Gas Law for non-ideal conditions: (P + n^2a/V^2)(V – nb) = nRT -on PCAT, will be asked to demonstrate understanding of the two constants: a and b, which are characteristic of the gas in question
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van der waal’s constant a
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*constant a*: reflects the attractive forces between the gas molecules -the stronger the attractions between the gas molecules, the more likely the molecules will aggregate and eventually condense -relative values of a depend on polarity with the MORE POLAR molecules having the stronger attractions and the larger value of a -size plays an important role in determining the magnitude of intermolecular attractions with LARGE molecules being much stronger attractors than small molecules
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van der waal’s constant b
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*constant b*: reflects the physical space occupied by one mole of gas molecules -thus by substracting nb from V (the volume of the container that the gas is constrained in) one obtains the free space available to all the gas molecules in the sample -the units for constant b are L/mole
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graham’s law of effusion
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-*effusion rate of a gas*: the rate the gas will escape through a tiny opening in its container -what determines the rate of effusion? the velocity of the gas particles -many factors, such as temperature and pressure, obviously effect the rate of effusion but we will focus on the role of the mass of the molecules plays in determining the effusion rate -other things being equal (T and P) LIGHTER molecules have greater average velocities than do heavier molecules and will effuse at a GREATER rate -to obtain the quantitative form of graham’s law we set, at the same T and P, the average kinetic energy of two gases (A and B) equal and solve for the velocity ratio (which is also the effusion ratio): (1/2)mA VA^2 = (1/2) mB VB^2; solving yields VA/VB = sqrt[(MW of B)/(MW of A)] which also gives the relative effusion rate note: 1. lighter molecules effuse (move) more rapidly than do heavier molecules at the same T and P 2. the relative factor by which the lighter gas effuses more rapidly than the heavier gas at the same T and P is given by: sqrt of the inverse of their molecular weights