(1)Physical Chemistry Chapter 2: Basic Concepts

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Isobaric Calorimeter
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Calorimeter for studying a process at a constant pressure.
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Enthalpy
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H = U + pV
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Thermodynamics
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Study of transformations of energy
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System
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Part of the world where we have a special interest (eg. Reaction vessel, an engine, electrochemical cell)
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Surroundings
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Comprise the region outside the system and are where we make our measurements.
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Open System
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Can exchange matter and energy with surroundings
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Closed System
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Can exchange energy with its surroundings, but not matter.
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Isolated System
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Cannot exchange energy or matter with its surroundings.
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Work
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Achieving motion against an opposing force. Work = -F (distance)
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Energy
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A system’s capacity to do work. Note: When the system does work, the system’s energy is reduced, then it does less work than before.
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Heat
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Energy transfer resulting from the temperature difference of the system and the surroundings.
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Diathermic
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Boundaries that permit the transfer of energy as heat.
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Adiabatic
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Boundaries that don’t permit the transfer of energy as heat.
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Exothermic Process
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Releases heat into surroundings (eg. Combustion reaction)
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What happens when an endothermic process occurs in an adiabatic system?
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The temperature falls
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What happens when an exothermic process occurs in an adiabatic system?
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The temperature rises
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Endothermic Process
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Process where energy required from surroundings as heat. (eg. Vaporization of water)
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What happens when an endothermic process occurs in a diathermic container?
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Energy enters as heat from surroundings, system remains at the same temperature.
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What happens when an exothermic process occurs in a diathermic container?
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Energy leaves as heat, and the process is isothermal.
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Thermal Motion
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Disorderly motion of molecules.
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Internal energy (U)
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Total energy of a system, the total kinetic and potential energy of molecules in the system. Note: it’s a state function
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Molar Internal Energy (Um)
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Internal energy divided by the amount of substance in a system. U/n
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Equipartition Theorem
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In a sample at temperature T, all quadratic contributions to the total energy have the same mean value, (1/2kT)
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What’s the average energy contribution of each mode of freedom?
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1/2kT
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How many quadratic contributions to the kinetic energy are there?
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3, a molecule can move along the x,y, or z planes. Therefore the total average KE for a molecule to move on 3D is (3/2kT)
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Energy for a monatomic gas with only translation motion.
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Um (T) = Um(0) + 3/2RT
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How much energy does translational motion contribute?
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4 kJ/mol, translational motion is the motion of a molecule of its center of mass through space.
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How many modes of motion does a linear molecule have?
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2, NO2 and CO2 can rotate around two axes perpendicular to the line of the atoms.
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Energy for linear molecule with only translational and rotational motion
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Um (T) = Um(0) + 5/2 RT
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Energy for non-linear molecule with only translational and rotational motion
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Um(T) = Um (0) + 3RT
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True/False Molecules vibrate significantly at room temperature?
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False, The contribution of molecular vibrations to the internal energy is negligible, except for very large molecules (eg. Polymers)
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True/False The internal energy of a perfect gas is independent of the volume it occupies?
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True, Internal energy is dependent on temperature not volume.
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The First Law of Thermodynamics
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The internal energy of an isolated system is constant. (delta)U = q + w
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Equation for infinitesimal changes in energy
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dU = dq + dw
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Expansion Work
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Work arising from a change in volume. It’s the work done by a gas as it expands and drives back the atmosphere.
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Expansion Work Derived
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dw = -Fdz F = pA dw = -pAdz dw= – pdV
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Free Expansion
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Expansion against zero opposing force, w = 0 (eg. When gas expands in a vacuum)
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Reversible Change in Thermodynamics
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A change that can be reversed by an infinitesimal modification of a variable. Note: systems at equilibrium are poised to undergo reversible change.
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Expansion against constant pressure
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w = – p(ex) (delta)V
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Change in Internal Energy of a System
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dU = dq + dw(exp) + dw(e) dw(e) –> extra work (eg. electrical)
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Calorimetry
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The study of heat transfer during physical and chemical processes.
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Calorimeter
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A device for measuring energy transferred as heat.
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Heat Capacity
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Slope of the tangent to the curve at any temperature on a graph of internal energy (U) vs Temperature (T)
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Specific Heat
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Heat capacity of a substance divided by the mass.
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Will the increase in temperature be large or small for a sample with a large heat capacity?
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The increase will be small.
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dH = dq
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When a system is subjected to constant pressure and only expansion work can occur, the change in enthalpy is equal to the energy supplied as heat. (eg. If we supply 36 kJ of energy through an electric heater immersed in an open beaker of water, then the enthalpy of the water increases by 36 kJ, and we write (delta)H =+36kJ.
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Enthalpy of a Perfect gas (H)
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H = U + pV = U + nRT
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Change of enthalpy in a reaction that produces or consumes gas
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(delta)H = (delta)U + (delta)n(g)RT (delta)n(g) is the change in the amount of gas molecules in the reaction.
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Change in Enthalpy at a constant pressure
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(delta)H = q(p)
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Change in internal energy at a constant volume
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(delta)U = q(v) This equation world because a system at constant volume can do no expansion work.
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Equation for energy supplied as heat
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q = C(delta)T C = calorimeter constant q = It(delta) (potential difference)
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Heat Capacity at Constant Pressure
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Slope of the tangent to a plot of enthalpy against temperature at constant pressure. It’s an extensive property Cp = (dH/dT)p
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Molar heat capacity at constant pressure
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Heat capacity per mole of material. It’s an intensive property. dH = CpdT (infinitesimal change of temperature) (delta)H = Cp(delta)T (measurable change of temperature)
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q(p) = Cp(delta)T
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This equation shows how enthalpy (H) can be equated with the energy supplied as heat (q) at a constant pressure.
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How does one measure the heat capacity of a sample?
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A measured quantity of energy is supplied as heat (under conditions of constant pressure) and the temperature rise is measured.
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What’s an example of constant pressure?
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A sample is exposed to the atmosphere and is free to expand.
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Equation for the variation of heat capacity with temperature.
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Cp,m = a + bT + c/T^2 a,b, and c are empirical parameters and are independent of temperature.
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True/False Most systems expand when heated at constant pressure.
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True, Such systems do work on the surroundings and therefore some of the energy supplied to them as heat escapes back to the surroundings. Result: the temperature of the system rises less than when heating at constant volume.
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What’s the Molar heat capacity of a perfect gas?
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8 J/K • mol
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What’s the heat capacity at constant volume of a monatomic gas?
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12 J/K • mol
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Equation relating heat capacities of a perfect gas.
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Cp – Cv = nR
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Differential (in Chemistry)
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The behavior of the sample is compared to that of a reference material that does not undergo a physical/chemical change during the analysis. (eg. differential scanning calorimeter, DSC)
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Scanning (in chemistry)
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The temperature of the sample and reference material are increased (or scanned) during the analysis.
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Amphiphilic
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Both water and hydrocarbon attracting
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What happens when a perfect gas expands adiabatically?
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Temperature decreases Work done, but no heat enters the system Internal energy decreases Kinetic energy falls as work done, so the average speed of the molecules decreases.
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The change in internal energy and volume of a perfect gas
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(delta)U = Cv ( Tf -Ti) = Cv(delta)T This is a two-step process. In the first step only the volume changes, and the temperature is held constant. The overall change in internal energy (internal energy of molecules is independent of the volume the molecules occupy) arises solely from the second step. (The heat capacity must be independent of the temperature change)
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Work done on an adiabatic expansion
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Wad = Cv(delta)T
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Equation for initial and final temperature of a perfect gas that undergoes reversible adiabatic expansion.
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Tf = Ti (Vi/Vf)^(1/c) c = Cv,m /R Another form of equation Vi Ti^c = Vf Tf^c
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Why does an adiabat fall more steeply than an isotherm?
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In isothermal expansion energy flows into a system as heat and maintains the temperature. The pressure doesn’t fall as much in an adiabatic expansion.

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