Chemistry 467 – Flashcards
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| What do we call the system when a reacting system has fully equilibrated? |
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| Equilibrium |
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| What is the heat of mixing for an ideal mixture? |
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| Zero |
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| If DeltaVmix is negative, what does that tell you about the interactions between the components of the mixture? |
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| They are generally favorable (attractive) |
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| Write the mathematical expression for chemical potential for a component in an ideal mixture |
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| mu=mu* + RT ln(x) |
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| If a mixture follows Raoult's Law, describe the interactions between the different molecules |
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| They are the same as between themselves (behaving as though pure) |
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| What happens to the boiling point of a mixture compared to the pure solvent (nonvolatile solute)? |
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| Rises |
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| Write the definition of chemical potential |
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| mu=(dG/dn)T,p,n |
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| At a given temperature and pressure, which phase is thermodynamically preferred? |
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| The one with the lowest chemical potential |
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| Write the fundamental equation of chemical thermodynamics |
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| dG=-SdT+VdP+sum(mudni) |
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| As pressure is increased, what happens to the boiling point of a liquid? |
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| It increases |
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| What property drives mixing for an ideal mixture? |
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| Entropy |
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| Does the Gibbs energy increase or decrease with an increase in pressure? |
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| Increases, because (dG/dP)T=V and V is positive |
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| If a reaction is exothermic, what happens to DeltarG if the temperature increases? Think Le Chatelier |
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| DeltarG will increase |
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| Why do we need fugacity |
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| To account for the behavior of real gases (attractions, repulsions) |
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| Under what conditions are two phases in equilibrium? |
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| When they have the same chemical potential (or molar Gibbs energy) |
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| What is the maximum number of phases that can coexist at a particular temperature and pressure? |
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| 3 |
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| Write the fundamental equation of thermodynamics |
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| dU=TdS-pdV |
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| Write the Gibbs equation (derived from the fundamental equation) for the Gibbs energy |
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| dG=-SdT+VdP |
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| What are the natural variables of the Gibbs energy? |
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| temperature and pressure |
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| Why is the Gibbs energy a useful quantity? |
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| It tells us the maximum non-expansion work a process can produce; how much of the energy is 'useful' |
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| Does the Gibbs energy increase or decreases as the temperature increases? |
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| Decreases, because dG/dT,p=-S |
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| How o you maximize the efficiency of a Carnot engine? |
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| Create the largest temperature difference between the hot and cold parts of the engine |
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| What is DeltaSuniverse fora phase transition at its normal transition temperature? |
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| 0 |
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| Briefly explain why all processes are treated as reversible for the surroundings |
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| Because the surroundings are infinitely massive compared to the system. |
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| Is DeltaSuniverse for a spontaneous, irreversible adiabatic expansion positive, negative, or zero? |
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| positive, the process is spontaneous |
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| Write the definition of Gibbs energy |
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| G=H-TS |
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| What is the sign of DeltavapH for any material? |
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| Positive, it takes an input of energy to vaporize something |
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| Write the thermodynamic definition of entropy |
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| dS=dqrev/T |
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| What makes a process spontaneous? |
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| DeltaSuniverse increases |
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| True or False: the entropy of the system can spontaneously decrease |
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| True |
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| True or False: the entropy of all substances is zero at zero Kelvin |
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| False |
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| What is DeltaU for any isothermal process involving ideal gas? |
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| Zero |
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| What is DeltaU for any cyclic process? |
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| Zero |
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| What do we mean when we say an expansion process is reversible? |
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| p=p,ex throughout the process, no net work for the process and its opposite |
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| Which process produces more work? reversible isothermal expansion of ideal gas or reversible adiabatic expansion of ideal gas? |
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| Reversible isothermal expansion of ideal gas produces more work |
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| When two objects are at different temperatures and then placed in thermal contact, in which direction does heat flow? |
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| from the hot to the cold |
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| On what variables does the internal energy of an ideal gas depend? |
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| Only on Temperature |
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| Write the total differential of internal energy as a function of temperature and volume, U(T,V) |
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| dU=(dU/dV),T*dV+(dU/dT),V*dT |
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| Write the definition of the constant volume heat capacity |
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| C,v=(dU/dT)v |
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| Write the definition of enthalpy |
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| H=U+pV |
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| What is meant by an adiabatic process? |
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| One in which no heat flows between system and surroundings. |
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| What cna a closed system exchange with the surroundings? |
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| Energy but not matter |
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| The Zeroth Law of Thermodynamics helps us to define what kind of Equilibrium? |
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| Thermal Equilibrium |
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| Generally speaking, what physical quantity is the First Law of Thermodynamics Concerned with? |
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| Energy, or internal energy |
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| Provide a brief explanation of the difference between heat and work at the molecular level? |
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| Work involves organized motion of the molecules; heat involved random motion |
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| Write the mathematical definition of expansion work |
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| dwexp=-pexdV |
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| Write the general expression for the chemical potential as a function of conditions. |
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| mu=mu^not+RTln(a) |
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| Write the general form of the reaction quotient, Q |
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| Q=product(a^nu) |
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| Write the relation between the equilibrium constant and the standard reaction Gibbs energy, DeltaGreaction |
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| DeltaGreaction^not=-RTln(K) |
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| What is the value of the reaction Gibbs energy when the reacting system is at equilibrium? |
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| DeltaGreaction=0 |
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| If a reaction is exothermic, in what direction will it shift with an increase in temperature? |
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| Toward the reactants. |
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| True or False: The equilibrium composition of a gas phase reaction can change when the vessel is compressed at constant temperature. |
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| True |
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| True or False: The equilibrium constant of a gas phase reaction can change when the vessel is compressed at constant temperature. |
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| False |
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| True or False: The equilibrium constant of a reaction generally changes with temperature. |
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| True |
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| Write the general expression for the reaction Gibbs energy as a function of conditions |
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| DeltaGrxn=DeltaGrxn.not+RTln(Q) |
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| What is the key difference between standard conditions and standard biological conditions? |
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| Standard biological conditions are at pH 7, [H+]=1*10^-7 molar, 1 molar |
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| True or False: A transition state is a stable molecular configuration that can be isolated and studied |
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| False |
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| Is the mathematical shape of the transition state a maximum, minimum, or saddle point on the potential energy surface? |
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| Saddle Point |
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| To spectroscopically probe a transition state, what time scale of pulses do we need? |
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| Femtosecond |
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| What is the sign of DeltaS(doubledagger)? |
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| Negative |
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| What is the sign of DeltaG(doubledagger)? |
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| Positive |
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| List three state variables that we use to describe the physical properties of a gas? |
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| T,p,V and n |
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| The Zeroth Law of Thermodynamics defines what type of equilibrium? |
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| Thermal Equilibrium |
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| Name one of the scientists whose work led to the development of the ideal gas law? |
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| Boyle, Charles, Gay-Lussac, Avogadro |
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| Under what conditions of temperature and pressure do the ideal gas law hold true? |
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| Low pressure and high temperature |
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| Upon what was the development of the Ideal Gas Law based? |
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| Experimental observation and proposed principles |
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| What happens to the width of a probability distribution as the number of trials increases? |
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| The width narrows |
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| How do we calculate the average of a property described by a continuous probability density function? |
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| h_bar=integral(h*f(h)dh)= |
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| Define what is meant by an ensemble? |
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| A collection of individual items such as molecules |
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| Consider placing balls in boxes. We put 2 balls in the first box, 1 in the second, and 1 in the third. Assuming all the balls are identical, and the order doesn't matter, what is the statistical weight of this arrangement? |
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| W=4!/(2!1!1!)=12 |
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| What is the statistical weight if all four balls are in the first box (of three)? |
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| W=4!/(4!0!0!)=1 |
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| According to the principle of equal a priori probabilities, which of these two arrangements (all balls in one box or some in all three) is preferred? |
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| Neither is preferred |
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| State one of the constraints of the Boltzmann distribution |
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| Fixed number of molecules in the system; fixed total energy in the system |
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| State the two constraints that lead to the Boltzmann distribution |
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| Fixed number of molecules; fixed total energy in the system |
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| Write the mathematical expression of the partition function |
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| q=sum(e^-E_i/kT) |
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| Write the Boltzmann expression for entropy in terms of statistical weight |
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| S=kln(W) |
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| What does it mean when two states are said to be 'degenerate'? |
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| They have the same energy |
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| Consider a container of Ar gas. What happens to the average speed of the Ar atoms as the temperature increaseS? |
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| The average speed increases. |
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| At a molecular level, what is the source of the pressure of a gas? |
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| Collisions between the gas molecules and the walls of the container |
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| Consider two samples of gas, He and Ar, at the same temperature. In which sample are the atoms, on average, moving faster? |
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| He, the average speed increases as the mass decreases. |
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| State one of the assumptions in the kinetic molecular theory of gases, as we treated it. |
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| Molecules are in ceaseless, random motion; gas molecules have no size; all collisions are elastic. |
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| Describe what is meant by the term "mean free path" |
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| The average distance a molecule travels before experiencing a collision. |
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| What term do we use to describe the transfer of matter through another medium (such as a gas)? |
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| Diffusion |
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| If the pressure decreases, but the temperature stays the same, what happens to the collision density? |
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| The collision density decreases; there are fewer collisions. |
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| If there is a sharp change of concentration with distance, in what direction will diffusion occur? |
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| In the direction of the region with lower concentration. |
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| Name one other property besides diffusion that is correctly predicted by the kinetic molecular theory of gases: |
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| Viscosity, thermal conductivity |
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| What must phsyically happen between two molecules in order for a reaction to take place? |
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| Collision |
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| A reaction is found to have the rate law v=k[A]^2. What is the order of the reaction? |
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| Second order |
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| True or False: The rate of a reaction can be either positive or negative. |
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| False, reaction rates are always positive. |
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| At a molecular level, what does the activation energy represent? |
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| The minimum energy required for a collision to lead to reaction. |
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| True or False: If I know the overall reaction, I can write down the rate law? |
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| False, rate laws MUST be determined experimentally. |
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| What is meant by the term "half life"? |
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| The time it takes for the concentration of a reactant to drop by half the initial value. |
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| IF a reaction follows first order kinetic, how should I plot the data to determine the rate constant? |
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| As ln[A] vs. t |
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| If a reaction takes place through a bi-molecular mechanism, what order will the rate law be? |
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| Second order, of the form v=k[A][B] |
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| If we have a branching reaction that is under kinetic control, which product is more likely to be formed? |
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| The one with the larger rate constant. |
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| If we have a branching reaction that is under thermodynamic control, which product is more likely to be formed? |
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| The one with the larger equilibrium constant. |
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| In the steady state approximation, what do we assume about the concentration of an intermediate? |
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| The concentration does not change with time: d[I]/dt=0 |
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| Briefly describe how a catalyst speeds up a reaction |
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| By lowering the activation energy, or providing an environment that allows the reactants to interact in a way that favors production of product. |
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| What step(s) generally determine the rate of reaction, fast or slow? |
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| Slow |
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| What kind of chemical species is commonly involved in chain reaction mechanisms? |
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| Free radicals |
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| In the Langmuir model, how deep can a surface be covered? |
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| One monolayer |
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| What is one of the two types of energy we have from Newtonian mechanics? |
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| Kinetic, potential |
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| Name one type of molecular motion that contributes to the heat capacity. |
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| Translational, vibrational, rotational. |
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| How much does each rotational degree of freedom contributes to the heat capacity? |
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| 1/2R |
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| How many degrees of freedom does NH3 have? |
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| 3N=12 |
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| How many vibrational degrees of freedom does NH3 have? |
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| 3N-6=6 |
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| What quantity do we use as our 'energy ruler' in determining whether an energy state is high or low |
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| The quantity k.bT (or RT in molar units) |
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| Name or describe one phenomenon that led to the development of quantum mechanics? |
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| Blackbody radiation, heat capacity of solids, photoelectric effect, electron diffraction |
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| What did Einstein's explanation of the photoelectric effect tell us about light? |
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| Light can act like a particle, or the energy is quantized. |
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| What was de Broglie's hypothesis about the behavior of particles? |
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| Particles should behave like waves to some degree |
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| Name an experiment that proved de Broglie correct? |
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| Electron diffraction, two-slit experiment |
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| How do we mathematically describe the behavior of a particle in quantum mechanics? |
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| With a wavefunction |
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| What does the Hamiltonian operator account for? |
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| Total energy, kinetic plus potential |
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| What does the quantity psi*psi tell us about? |
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| The probability of finding the particle between x and x+dx |
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| State one of the requirement of a wavefunction? |
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| Continuous, continuous first derivative, square integrable, single valued, finite |
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| If we have a free particle (no forces acting on it) that is described by a single value of momentum, where is the particle located? |
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| It has no location, it is delocalized over all space |
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| In the formalism of quantum mechanics, how do we represent a physically measurable quantity? |
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| With the corresponding quantum mechanical operator. |
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| How do we determine the expectation value of a physically observable quantity? |
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| Evaluate |
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| If a wavefunction is not an eigenfunction of a given operator, how should I write it? |
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| As a linear combination of eigenfunctions of that operator. |
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| If a wavefunction is a linear combination of two eigenfunctions of the Hamiltonian, what values of energy can we measure? |
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| We can only measure one of the two eigenvalues. |
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| True or False: Before an individual measurement on the wavefunction (in this case, a linear combination of two eigenfunctions of the Hamiltonian), I can predict the energy I will measure. |
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| False: I can predict the probability of each measurement, but not individual measurements. |
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| After measuring the energy of the wavefunction in question 2, what happens to the wavefunction? |
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| The wavefunction 'collapses' to the eigenfunction corresponding to the measured energy. |
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| What does it mean to say that two operators do not commute? |
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| The result of the measurements will be different depending on the order in which the measurements are performed. |
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| What is a postulate? |
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| Something we assume to be true and use for further reasoning. |
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| For the particle in a box, what happens to the energy as the size of the box decreases? |
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| Energy increases. |
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| For the n=1 state of the particle in a box, what is probability of finding the right particle right next to the wall of the box? |
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| Zero |
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| True or False: A particle confined to a box can have zero energy |
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| False; if the energy is zero, there is no particle in the box. |
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| If I want to cause a transition between two energy states, what must the frequency of the incident light be? |
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| v=DeltaE/h; the incident light has to match the difference in energy of the two states. |
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| What are the two conditions that must be met for a spectroscopic transition to occur? |
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| The energy of the photon must match the energy difference between the states. The transition dipole moment must be non-zero; the transition must be allowed. |
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| In the classical limit, what does the probability density function look like for the particle in a box? |
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| Uniform probability of finding the particle anywhere in the box. |
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| Why don't we worry about quantum effects when talking about an ideal gas? |
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| The size of the container is so large that the energy levels can be treated as a continuum; or the molecules are so far apart that they don't have any quantum interactions. |
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| State one practical application of tunneling |
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| Schottky or tunneling diode; proton transfer; nuclear fusion; electron microscopy |
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| Which are more likely to tunnel through a barrier, electrons or protons? |
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| Electrons, because of their smaller mass. |
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| True or false: After tunneling through a barrier, a particle has less kinetic energy |
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| False; the energy is unchanged. The amplitude of the wavefunction, or the probability of being on the other side of the barrier, is reduced. |
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| If we isotopically substitute deuterium for hydrogen, and the rate of reaction decreases, what does that tell us about the rate limiting step? |
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| It likely involves proton transfer, or proton tunneling. |
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| In a 3-D situation, what aspect of the system leads to degenerate states? |
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| Symmetry |
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| In addition to energy, the rigid rotor illustrates that what physical quantity is also quantized? |
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| Angular momentum |
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| In what region of the electromagnetic spectrum do rotational transitions take place? |
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| The microwave region |
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| How can we break the degeneracy of rotational states? |
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| With an external field, magnetic or electric. |
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| TRue or False: Compared to k.bT, rotational levels are close together? |
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| True |
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| Name one type of spectroscopy that allows us to measure vibrational transitions. |
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| IR or Raman spectroscopy |
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| How many vibrational normal modes does H2O have? |
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| 3n-6=3 |
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| True or False: a molecule can have no vibrational energy? |
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| False, there is always zero point energy of 1/2 h*nu |
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| In what region of the electromagnetic spectrum do vibrational transitions take place? |
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| Infrared |
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| True or False: Compared to k.bT, vibrational levels are very close together? |
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| False |
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| True or False: Electrons circle the nucleus just like planets orbit the sun. |
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| False |
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| Name one atom for which we have solve the Schrodinger equation exactly. |
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| Hydrogen (it's the only one) |
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| What do we call solutions to the Schrodinger equation for the hydrogen atom? |
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| Atomic orbitals |
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| In what range of the electromagnetic spectrum do we observe transitions between the electronic states of an atom? |
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| Visible to UV |
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| What do we take as our zero of potential energy for a hydrogen atom? |
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| Infinite separation of the proton and electron |
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| When constructing molecular orbitals from atomic orbitals, h ow many molecular orbitals will we have? |
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| The same as the number of atomic orbitals. |
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| We generally talk about two types of molecular orbitals. Name one. |
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| sigma and pi |
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| Why doesn't He form a diatomic molecule? |
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| The energy would have higher than for two unbonded atoms. |
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| True or False: All molecular orbitals are localized along particular bonds |
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| False: Most molecular orbitals are delocalized over the whole molecule. |
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| How does the Born-Oppenheimer approximation treat motion of the nuclei? |
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| Nuclei move much more slowly than the electrons. |
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| True or False: If a molecule has a bound ground electronic state, all excited states are also bound. |
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| False: Excited states can be unbound. The molecule will dissociate if it is excited to such a state. |
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| Name one process by which an electronically excited molecule relaxes and emits a photon. |
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| Fluorescence, phosphorescence, chemiluminescence. |
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| What has a longer lifetime, fluorescence or phosphorescence? |
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| Phosphorescence |
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| Why are the lifetimes different for fluorescence and phosphorescence? |
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| Because phosphorescence involves a forbidden transition. |
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| What term do we use to describe breaking chemical bonds with light? |
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| Photolysis or photodissociation |
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| Will fluorescence occur at longer or shorter wavelengths than the excitation? |
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| Longer wavelengths, or lower energy |
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| What quantum mechanical model do we use for translations of molecules when building the partition function? |
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| Particle in a box |
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| identify one of the key components of a laser: |
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| Gain medium, pump source, resonator cavity |
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| True or False: at room temperature, we can reasonable assume that rotational levels are close together |
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| True: the rotational temperature is many times less than T |
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| At the molecular level, what conditions are required for ideal behavior? |
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| No interactions (except for collisions) |
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| What do we call a collection of individual microsystems? |
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| An ensemble |
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| Given our collection of microsystems, how do we determine bulk properties? |
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| By taking the ensemble average of that property: M_bar=sum(M_j*P_J)=(sum(M_j*e^(-E_j/kT)))/Q |
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| What thermodynamic properties do we keep constant in the canonical ensemble? |
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| N,V, and T |
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| What is the interaction potential for an ideal gas? |
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| E_p=0 (or V=o) |
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| What do we call the temperature below which a gas can condense? |
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| The critical temperature |
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| Write the definition of the reduced temperature. |
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| T_r=T/T_c |
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| Name one equation of state for real gases |
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| van der Waals, virial (Berthelot, Dieterici, Redlich-Kwong) |
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| What happens when a real gas is compressed at a temperature below the critical temperature? |
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| It condenses |
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| What do the two parameters in the van der Waals equation account for? |
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| Finite volume of the gas molecules and attractive interactions |
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| For a particular gas at ambient in the van der Waals equation account for? |
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| Attractive interactions |
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| According to the principle of corresponding states, how do we best compare the behavior of different gases? |
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| By comparing the reduced variables |
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| In terms of molecular order, what characterizes the structure of a liquid at short and long distances? |
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| Short-range order, long range disorder |
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| What can a closed system exchange with its surroundings? |
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| Energy, but not matter |
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| The zeroth law of thermodynamics helps us to define what kind of equilibrium? |
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| Thermal |
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| Generally speaking, what physical quantity is the First Law of Thermodyamics concerned with? |
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| Energy, or internal energy |
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| Provide a brief explanation of the difference between heat and work at the molecular level? |
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| Work involves organized motion of the molecules, heat involves unorganized motion. |
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| Give the mathematical definition of expansion work? |
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| delW_exp=-p_ex*dV |
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| On what variables does the internal energy of an ideal gas depend? |
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| Only T |
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| Write the total differential of internal energy as a function of temperature and volume U(T,V) |
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| dU=(dU/dV)_T*dV+(dU/dT)_v*dT |
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| Write the definition of constant volume heat capacity |
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| C_v=(dU/dT)_v |
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| Write the definition of enthalpy |
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| H=U+pV |
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| What is meant by an adiabatic process |
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| One in which no heat flows between system and surroundings. |
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