Physical Chemistry Exam 3

Indicate the correct units for entropy, heat capacities, compressibility factor, and chemical potential, respectively. (a) J·K-1, J·K-1, unitless, J·mol-1. (b) J, J, unitless, J. (c) J·K-1, J, unitless, J. (d) J·K-1, J·K-1, atm, J·mol-1. (e) J, J, atm, J.

(a) J·K-1, J·K-1, unitless, J·mol-1.

Which chemical reaction favors the product (a) Kpo = 2.4 x 10^4 (b) Kpo = 2.4 x 10^-4 (c) Kpo = 1 (d) Kpo = -2.4 x 10^4 (e) Kpo = -2.4 x 10^-4

(a) Kpo = 2.4 x 10^4

Is a process showing ∆𝑯>𝟎 and ∆𝑺<𝟎 spontaneous? (a) No. (b) Yes. (c) The process would be spontaneous only if ∆𝐻 <0 and ∆𝑆<0. (d) The process would be spontaneous only if ∆𝐻 <0 and ∆𝑆>0. (e) Holy cow, I have no idea!

(a) No.

Consider the same process described in the previous question to determine the change in Gibbs free energy. (a) ∆𝑡𝑟𝑎𝑛𝑠𝐺̅[298.15 𝐾]=+2.866 𝑘𝐽∙𝑚𝑜𝑙−1 (b) ∆𝑡𝑟𝑎𝑛𝑠𝐺̅[298.15 𝐾]=−2.866 𝑘𝐽∙𝑚𝑜𝑙−1 (c) ∆𝑡𝑟𝑎𝑛𝑠𝐺̅[298.15 𝐾]=0 𝑘𝐽∙𝑚𝑜𝑙−1 (d) ∆𝑡𝑟𝑎𝑛𝑠𝐺̅[298.15 𝐾]=+3.866 𝑘𝐽∙𝑚𝑜𝑙−1 (e) ∆𝑡𝑟𝑎𝑛𝑠𝐺̅[298.15 𝐾]=−3.866 𝑘𝐽∙𝑚𝑜𝑙−1

(a) ∆𝑡𝑟𝑎𝑛𝑠𝐺̅[298.15 𝐾]=+2.866 𝑘𝐽∙𝑚𝑜𝑙−1

A given amount of substance undergoes a transition from phase 1 to phase 2. Indicate the correct expression/statement that describes (at least partially) such a process. (a) −𝑑𝑛phase1 = +𝑑𝑛phase2 (b) +𝑑𝑛phase1 = −𝑑𝑛phase2 (c) −𝜇phase1 = +𝜇phase2 (d) Answers (a) and (c) are both correct. (e) Answers (b) and (c) are both correct.

(a) −𝑑𝑛phase1 = +𝑑𝑛phase2

Which of the following thermodynamic conditions would cause the Gibbs free energy for an ideal gas to remain constant? (a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

(a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

Which of the following thermodynamic conditions would cause the Helmholtz free energy for an ideal gas to remain constant? (a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

(a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

Which of the following statements about changes in Gibbs free energy is correct? (a) 𝛥𝐺 is a monotone and continuous decreasing function of the temperature. (b) 𝛥𝐺 is a monotone and continuous increasing function of the temperature. (c) (𝛥𝐺)𝑃,𝑇 >0 is the spontaneous condition for the Gibbs free energy. (d) Since both 𝛥𝐻 and 𝛥𝑆 show discontinuities at phase transitions, 𝛥𝐺 will also be a non-continuous function of the temperature. (e) All the previous statements are correct.

(a) 𝛥𝐺 is a monotone and continuous decreasing function of the temperature.

Calculate the molar enthalpy of combustion for the reaction C6H12O6 (s) + 6 O2 (g) → 6 CO2 (g) + 6 H2O (l) using the following values for the molar enthalpies of formation: C6H12O6 (s): 𝜟𝒇𝑯̅ =−1275 kJ/mol CO2 (g): 𝜟𝒇𝑯̅ =−393.5 kJ/mol H2O (l): 𝜟𝒇𝑯̅ =−285.8 kJ/mol (a) 𝛥𝑐𝐻̅ ≅−2800 kJ/mol. (b) 𝛥𝑐𝐻̅ ≅+2800 kJ/mol. (c) 𝛥𝑐𝐻̅ = 0 kJ/mol. (d) 𝛥𝑐𝐻̅ ≅+600 kJ/mol. (e) 𝛥𝑐𝐻̅ ≅−600 kJ/mol.

(a) 𝛥𝑐𝐻̅ ≅−2800 kJ/mol.

Determine (𝝏𝑽/𝝏𝑺)𝑻 for a gas that obeys the equation of state 𝑷(𝑽−𝒏𝒃)=𝒏𝑹𝑻. (a) (𝜕𝑉/𝜕𝑆)𝑇 = 𝑛𝑅/𝑉−𝑛𝑏. (b) (𝜕𝑉/𝜕𝑆)𝑇 =𝑉−𝑛𝑏/𝑛𝑅 . (c) (𝜕𝑉/𝜕𝑆)𝑇 =1−𝑛𝑏/𝑛𝑅𝑇 . (d) (𝜕𝑉/𝜕𝑆)𝑇 =−𝑅/𝑏. (e) (𝜕𝑉/𝜕𝑆)𝑇 =−𝑏/𝑅.

(b) (𝜕𝑉/𝜕𝑆)𝑇 =𝑉−𝑛𝑏/𝑛𝑅 .

Determine (𝝏𝑷/𝝏𝑺)𝑻 for an ideal gas. (a) (𝝏𝑷/𝝏𝑺)𝑻 = P/nR (b) (𝝏𝑷/𝝏𝑺)𝑻 = − P/nR (c) (𝝏𝑷/𝝏𝑺)𝑻 = nR/P . (d) (𝝏𝑷/𝝏𝑺)𝑻 = − nR/P. (e) (𝝏𝑷/𝝏𝑺)𝑻 = 0.

(b) (𝝏𝑷/𝝏𝑺)𝑻 = − P/nR

Consider the phase transition graphite ⇄ diamond occurring at room temperature. For such process, ∆𝒕𝒓𝒂𝒏𝒔𝑯̅[𝟐𝟗𝟖.𝟏𝟓 𝑲]=+𝟏.𝟖𝟗𝟔 𝒌𝑱∙𝒎𝒐𝒍−𝟏 and ∆𝒕𝒓𝒂𝒏𝒔𝑺̅[𝟐𝟗𝟖.𝟏𝟓 𝑲]=−𝟑.𝟐𝟓𝟓 𝑱∙𝑲−𝟏 ∙𝒎𝒐𝒍−𝟏. Which kind of process are we investigating? (a) A spontaneous process. (b) A non-spontaneous process. (c) This is a tricky one! (d) Oh man, I missed that class! (e) One does not simply pay attention in CH3510...

(b) A non-spontaneous process.

A given amount of liquid water condenses into ice. Indicate, among the following, the correct expression or statement that describes (at least partially) such a phase transition. (a) Entropy will increase. (b) Entropy will decrease. (c) 𝑇𝑤𝑎𝑡𝑒𝑟 >𝑇𝑖𝑐𝑒. (d) 𝑃𝑖𝑐𝑒 >𝑃𝑤𝑎𝑡𝑒𝑟. (e) The Gibbs free energy will increase.

(b) Entropy will decrease.

Which of the following statements describes correctly the graph reported in the figure? (a) The curves represent the Boyle's law. Each curve refers to a different amount of substance. (b) The curves represent the Boyle's law. Each curve refers to a different temperature. (c) The curves represent the Boyle's law. Each curve refers to a different temperature and a different amount of substance. (d) The curves represent the Charles' law. (e) None. The above descriptions are all wrong!

(b) The curves represent the Boyle's law. Each curve refers to a different temperature.

Which of the following is a correct statement of the 3rd law of thermodynamics? (a) limT→0K S(T)=0 when a substance undergoes a phase transition. (b) limT→0K S(T)=0 for a perfect crystalline system. (c) limT→0K S(T)=0 when equilibrium conditions are established. (d) limT→0°C S(T)=0 for a perfect crystalline system. (e) limT→298.15 K S(T)=0 for a perfect crystalline system.

(b) limT→0K S(T)=0 for a perfect crystalline system.

For an ideal gas undergoing an isothermal reversible process it can be shown that ∆𝑺=𝒏𝑹𝐥𝐧(𝑷𝒊/𝑷𝒇) . Which of the following expressions is also true? (a) ∆𝑆=𝑛𝑅ln(𝑉𝑖/𝑉𝑓) . (b) ∆𝑆=−𝑛𝑅ln(𝑉𝑖/𝑉𝑓). (c) ∆𝑆=−𝑛𝑅ln(𝑇𝑖/𝑇𝑓) . (d) ∆𝑆=−𝑛𝑅ln(𝑉𝑓/𝑉𝑖) . (e) ∆𝑆=𝑛𝑅ln(𝑇𝑖/𝑇𝑓) .

(b) ∆𝑆=−𝑛𝑅ln(𝑉𝑖/𝑉𝑓).

At standard pressure and 353 K, liquid benzene undergoes a phase transition and vaporizes. Which of the following statements referring to such a process is correct? (a) +𝑑𝑛𝑙𝑖𝑞𝑢𝑖𝑑 =−𝑑𝑛𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (b) −𝑑𝑛𝑙𝑖𝑞𝑢𝑖𝑑 =+𝑑𝑛𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (c) 𝑑𝑛𝑙𝑖𝑞𝑢𝑖𝑑 =𝑑𝑛𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (d) 𝑃𝑙𝑖𝑞𝑢𝑖𝑑 ≫𝑃𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (e) 𝑃𝑙𝑖𝑞𝑢𝑖𝑑 ≪𝑃𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas.

(b) −𝑑𝑛𝑙𝑖𝑞𝑢𝑖𝑑 =+𝑑𝑛𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas.

Which of the following thermodynamic conditions would cause the Helmholtz free energy for a real gas to remain constant? (a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

(b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡.

Consider the Helmholtz free energy and a mechanically reversible process. Which of the following expressions is correct? (a) 𝑑𝐴=(𝜕𝐴𝜕𝑉)𝑆 𝑑𝑉+(𝜕𝐴𝜕𝑆)𝑉 𝑑𝑆. (b) 𝑑𝐴=−𝑃𝑑𝑉−𝑆𝑑𝑇. (c) 𝑑𝐴=−𝑃𝑑𝑉+𝑆𝑑𝑇. (d) (𝑑𝐴)𝑃,𝑇 =0 is the equilibrium condition. (e) Answers (c) and (d) are both correct.

(b) 𝑑𝐴=−𝑃𝑑𝑉−𝑆𝑑𝑇.

Consider an isolated system. Which of the following is the correct expression for the entropy of an irreversible process? (a) 𝑑𝑆 =0. (b) 𝑑𝑆 >0. (c) 𝑑𝑆 <𝛿𝑞𝑇 . (d) 𝑑𝑆 >𝛿𝑞𝑇 . (e) 𝑑𝑆 =𝛿𝑞𝑇 .

(b) 𝑑𝑆 >0.

A given amount of ideal gas compresses isothermally (from 12.0 L to 3.0 L) due to an external pressure of 1.0 atm. Indicate the correct answer referring to the change in internal energy experienced by the system. (a) 𝛥𝑈 = +912 J. (b) 𝛥𝑈 = 0 J. (c) 𝛥𝑈 = -912 J. (d) I cannot tell because the change in internal energy will depend upon the exchange of heat between system and surroundings, which is not provided. (e) I cannot tell because the change in internal energy will depend upon the amount of substance, which is not provided.

(b) 𝛥𝑈 = 0 J.

Given the definition of "extent of reaction" which of the following statements is wrong? (a) At the beginning of a reaction 𝜉 =0. (b) 𝜉 is a unitless coefficient. (c) 𝜉 is expressed in units of moles. (d) 𝜉 measures the progress of a chemical reaction. (e) 𝜉 is proportional to the change in the number of moles during a reaction.

(b) 𝜉 is a unitless coefficient.

Consider the concept of equilibrium constant; which of the following statements is wrong? (a) For a reaction at equilibrium, the reaction quotient is called equilibrium constant. (b) At equilibrium, the following expression is valid: ∆𝑟𝐺o =−𝑅𝑇ln𝐾𝑃. (c) The equilibrium constant can be negative. (d) Large values of 𝐾𝑃 indicate that, at equilibrium, the products of a chemical reaction are favored with respect to the reactants. (e) Small values of 𝐾𝑃 indicate that, at equilibrium, the reactants of a chemical reaction are favored with respect to the products.

(c) The equilibrium constant can be negative.

Which of the following statements is correct? (a) The virial equation is less accurate than the ideal gas law equation of state. (b) The van der Waals equation of state is less accurate than the ideal gas equation of state. (c) The four Maxwell relationships allow us to find changes in entropy through changes in state variables; this aspect is extremely useful in practical applications. (d) Statements (a) and (c) are both correct. (e) Statements (b) and (c) are both correct.

(c) The four Maxwell relationships allow us to find changes in entropy through changes in state variables; this aspect is extremely useful in practical applications.

For and ideal gas undergoing an isothermal process, indicate the correct expression for the change in entropy in terms of the initial and final pressure of the system. (a) ∆𝑆 = 𝑛𝑅 ln (Pf/Pi). (b) ∆𝑆 = −𝑛𝑅 ln (Pi/Pf). (c) ∆𝑆 = −𝑛𝑅 ln (Pf/Pi). (d) ∆𝑆 = 0 because we are dealing with an ideal gas undergoing an isothermal process. (e) Answers (a) and (b) are both correct.

(c) ∆𝑆 = −𝑛𝑅 ln (Pf/Pi).

Consider the concept of natural independent variables; which of the following thermodynamic conditions would cause the internal energy of a liquid substance to remain constant? (a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇 =𝑐𝑜𝑛𝑠𝑡. (e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞 =0.

(c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

Which of the following statements is wrong? (a) 𝑑𝐻 =𝑇𝑑𝑆+𝑉𝑑𝑃 for a mechanically reversible process. (b) 𝑑𝐻 =𝑃𝑑𝑉+𝑉𝑑𝑃 for an adiabatic expansion against vacuum. (c) 𝑑𝐺 =−𝑆𝑑𝑇 for an isobaric process. (d) 𝑑𝑈 <0 for a mechanically irreversible adiabatic process. (e) None. They are all correct.

(c) 𝑑𝐺 =−𝑆𝑑𝑇 for an isobaric process.

At standard pressure and 353 K, liquid benzene undergoes a phase transition and vaporizes. What is the change in Gibbs free energy during such a process? (a) I cannot tell because no information about the amount of substance is given. (b) 𝛥𝐺 <0. (c) 𝛥𝐺 =0. (d) 𝛥𝐺 >0. (e) I cannot tell because I missed that class, and I didn't watch the corresponding video.

(c) 𝛥𝐺 =0.

Consider solid ice and liquid water as a closed system at equilibrium. Which of the following expressions does represent the equilibrium condition satisfied by the system? (a) 𝑑𝑛𝑖𝑐𝑒 =𝑑𝑛𝑤𝑎𝑡𝑒𝑟. (b) ±𝜇𝑖𝑐𝑒 =∓𝜇𝑤𝑎𝑡𝑒𝑟. (c) 𝜇𝑖𝑐𝑒 =𝜇𝑤𝑎𝑡𝑒𝑟. (d) 𝜇𝑖𝑐𝑒 ≫𝜇𝑤𝑎𝑡𝑒𝑟. (e) ( 𝜕𝐺/𝜕𝑛𝑡𝑜𝑡)𝑇,𝑃=𝜇𝑤𝑎𝑡𝑒𝑟/𝜇𝑖𝑐𝑒.

(c) 𝜇𝑖𝑐𝑒 =𝜇𝑤𝑎𝑡𝑒𝑟.

At standard pressure and 353 K, liquid benzene undergoes a phase transition and vaporizes. Which of the following statements referring to such a process is correct? (a) +𝜇𝑙𝑖𝑞𝑢𝑖𝑑 =−𝜇𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (b) −𝜇𝑙𝑖𝑞𝑢𝑖𝑑 =+𝜇𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (c) 𝜇𝑙𝑖𝑞𝑢𝑖𝑑 =𝜇𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (d) 𝜇𝑙𝑖𝑞𝑢𝑖𝑑 >𝜇𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas. (e) 𝜇𝑙𝑖𝑞𝑢𝑖𝑑 <𝜇𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas.

(c) 𝜇𝑙𝑖𝑞𝑢𝑖𝑑 =𝜇𝑔𝑎𝑠 until all the amount of liquid benzene is converted into gas.

Which of the following statements about the equilibrium constant is correct? (a) 𝐾po is always unitless. (b) 𝐾po for the reverse reaction is the reciprocal of 𝐾BC for the forward reaction. (c) 𝐾po for the reserve reaction is the negative of 𝐾BC for the forward reaction. (d) Answers (a) and (b) are both correct. (e) Answers (a) and (c) are both correct.

(d) Answers (a) and (b) are both correct.

Consider an ideal gas that, when at a certain temperature, expands. What will be the value of the ratio PiVi/PfVf ? (a) I cannot tell because I do not have any information about the amount of substance. (b) I cannot tell because I do not have any information about 𝑃𝑖,𝑉𝑖,𝑃𝑓, and 𝑉𝑓. (c) I cannot tell because I do not have any information about 𝑛,𝑃𝑖,𝑉𝑖,𝑃𝑓, and 𝑉𝑓. (d) PiVi/PfVf =1. (e) PiVi/PfVf =𝑇.

(d) PiVi/PfVf =1.

For a certain chemical reaction, it is found that 𝑲𝑷𝒐 = 𝟏. What does this mean? (a) The reaction is spontaneous. (b) The products are favored. (c) The reactants are favored. (d) The equilibrium condition for the enthalpy is satisfied. (e) Nothing, because the van't Hoff equation is a pure theoretical statement that has no reference to real-world scenarios.

(d) The equilibrium condition for the enthalpy is satisfied.

Which of the following physical chemical properties can never be negative? (a) The change in Gibbs free energy for a given reaction. (b) The change in Gibbs free energy for a formation reaction. (c) The change in chemical potential for a stirring solution. (d) The equilibrium constant. (e) All of the above.

(d) The equilibrium constant.

Consider the chemical potential; which of the following statements is wrong? (a) The chemical potential indicates how much a substance wants to undergo a chemical change. (b) In multi-component systems, substances with different chemical potentials will try to find a common chemical potential. (c) The previous statement is equivalent of saying that the system will try to reach chemical equilibrium. (d) We can define the chemical potential for a single-component system as the partial derivative of each energetic state function we have encountered in the course (internal, enthalpy, Helmholtz, Gibbs) with respect to the volume. (e) We can define the chemical potential for a single component system as the partial derivative of each energetic state function we have encountered in the course (internal, enthalpy, Helmholtz, Gibbs) with respect to the amount of substance.

(d) We can define the chemical potential for a single-component system as the partial derivative of each energetic state function we have encountered in the course (internal, enthalpy, Helmholtz, Gibbs) with respect to the volume.

Which of the following thermodynamic conditions would cause the Gibbs free energy for a real gas to remain constant? (a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

(d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡.

Which of the following expressions represents the change in entropy for an isolated system that undergoes a reversible process? (a) 𝑑 𝑆 >0. (b) 𝑑 𝑆 <0. (c) 𝑑 𝑆 =𝛿𝑞𝑇 . (d) 𝑑 𝑆 =0. (e) 𝑑 𝑆 >𝛿𝑞𝑇 .

(d) 𝑑 𝑆 =0.

Consider a closed system behaving as an ideal gas and undergoing an isothermal reversible process. Indicate, among the following, the wrong expression for the Helmholtz energy. (a) 𝑑𝐴=−𝑇𝑑𝑆. (b) 𝑑𝐴=𝛿𝑤𝑟𝑒𝑣. (c) 𝑑𝐴=−𝑃𝑑𝑉. (d) 𝑑𝐴=𝛿𝑞. (e) None. They are all correct.

(d) 𝑑𝐴=𝛿𝑞.

Consider the Carnot engine and its overall thermodynamic cycle. Indicate the correct set of expressions among the following. (a) 𝑑𝑆 >0,𝑑𝐻 =0,𝑑𝐺 =0. (b) 𝑑𝑆 =0,𝑑𝐻 >0,𝑑𝐺 =0. (c) 𝑑𝑆 =0,𝛿𝑤>0,𝛿𝑞 <0. (d) 𝑑𝐺 =0,𝛿𝑤<0,𝛿𝑞>0. (e) None, the previous answers are all wrong!

(d) 𝑑𝐺 =0,𝛿𝑤<0,𝛿𝑞>0.

Consider an ideal gas as a closed system that expands due to a reversible and adiabatic process. Which of the following thermodynamic conditions is wrong? (a) 𝛿𝑞=0. (b) 𝛿𝑤𝑟𝑒𝑣 <0. (c) 𝑑𝑈 <0. (d) 𝑑𝑆 >0. (e) Given the lack of information provided, the trend for 𝑑𝑈 cannot be established.

(d) 𝑑𝑆 >0.

Which of the following statements about the change in Gibbs free energy is wrong? (a) 𝛥𝐺 decreases when the temperature increases. (b) From a physical-chemical standpoint, 𝛥𝐺 is a continuous function of the temperature. (c) The previous statements imply that 𝛥𝐺 is a monotone decreasing function with respect to 𝑇 and that it does not show physical-chemical discontinuities at phase transitions. (d) 𝛥𝐺 >0 is the spontaneous condition for the Gibbs free energy. (e) 𝛥𝐺 =0 is the equilibrium condition for the Gibbs free energy.

(d) 𝛥𝐺 >0 is the spontaneous condition for the Gibbs free energy.

Which of the following statements is wrong? "The extent of reaction... (a) ...is a measure of the progress of a chemical reaction." (b) ...is proportional to the change in the number of moles during a reaction." (c) ...has the dimension of mole." (d) ...can be easily related to the Gibbs free energy because both depend on the change in number of moles." (e) ...can take different values according to the chemical species present in a given chemical reaction."

(e) ...can take different values according to the chemical species present in a given chemical reaction."

Indicate the correct statement among the following. (a) 𝛥𝑇 =0 during phase transitions. (b) 𝛥𝐴<0 for an irreversible process occurring at constant 𝑇 and 𝑃. (c) 𝛥𝑇 =0 for every isothermal process. (d) Answers (a) and (b) are both correct. (e) Answers (a) and (c) are both correct.

(e) Answers (a) and (c) are both correct.

Which of the following expressions or statements does not apply to an ideal gas? (a) 𝐶𝑃-𝐶𝑉 =𝑛𝑅. (b) 𝑍=1. (c) ∆𝐴=∆𝐺 =𝛿𝑤 for isothermal processes. (d) ∆𝐴=∆𝐺 =−𝛿𝑞 for isothermal processes. (e) None, they are all correct.

(e) None, they are all correct.

Which of the following statements is correct? (a) For an ideal gas, one can prove that 𝑈 ≡𝑈(𝑇,𝑉) and 𝐻 ≡𝐻(𝑇,𝑉). (b) For an ideal gas, one can prove that 𝑈 ≡𝑈(𝑇,𝑃) and 𝐻 ≡(𝑇,𝑃). (c) For an ideal gas, one can prove that 𝐴≡𝐴(𝑇) and 𝐺 ≡𝐺(𝑇). (d) For a real gas, the expressions 𝑑𝑈 =𝐶𝑉𝑑𝑇 and 𝑑𝐻 =𝐶𝑃𝑑𝑇 are always verified. (e) None. All the previous statements are wrong.

(e) None. All the previous statements are wrong.

Which of the following statements does not apply to the definition of an ideal gas mixture? (a) Intermolecular interactions are negligible. (b) 𝑈 ≡𝑈(𝑇) and 𝐻 ≡𝐻(𝑇). (c) 𝜇 ≡𝜇(𝑇,𝑃). (d) For isobaric reversible processes, ∆𝐻 =𝑞𝑃. (e) None. The previous answers are all correct.

(e) None. The previous answers are all correct.

Consider the Carnot engine and its overall thermodynamic cycle. Indicate the correct expression among the following. (a) 𝑑𝐴=0,𝑤 =0. (b) 𝑑𝐴=0,−𝛿𝑞=+𝛿𝑤. (c) 𝑑𝑆 >0,𝑑𝐺 =0. (d) 𝑑𝑆 =0,𝑑𝐺 >0. (e) None. The previous expressions are all wrong.

(e) None. The previous expressions are all wrong.

Which of the following statements is correct? (a) The chemical potential can be defined only with respect to the Gibbs free energy. (b) 𝛥𝐺 can be studied only for isobaric and isothermal processes. (c) For ideal gases, one can prove that 𝑑𝐴=𝑑𝐺. (d) Answers (a) and (b) are both correct. (e) None. The previous statements are all wrong.

(e) None. The previous statements are all wrong.

Consider an ideal gas behaving as a closed system. Choose the wrong expression for the Gibbs free energy. (a) 𝑑𝐺 =𝑑𝐻-𝑇𝑑𝑆-𝑆𝑑𝑇. (b) 𝑑𝐺 =𝑑𝐴+𝑑(𝑃𝑉). (c) 𝑑𝐺 =𝑑𝑈+𝑑(𝑃𝑉)-𝑑(𝑇𝑆). (d) 𝑑𝐺 =𝑑𝐻-𝑑𝑈+𝑑𝐴. (e) None. They are all correct.

(e) None. They are all correct.

Which of the following expressions or statements for the Gibbs free energy is wrong? (a) 𝑑𝐺 =(𝜕𝐺𝜕𝑃)𝑇,𝑛 𝑑𝑃+(𝜕𝐺𝜕𝑇)𝑃,𝑛𝑑𝑇+∑ (𝜕𝐺𝜕𝑛𝑖)𝑇,𝑃,𝑛𝑗(𝑗≠𝑖)𝑑𝑛𝑖𝑖 . (b) 𝑑𝐺 =−𝑆𝑑𝑇+𝑉𝑑𝑃+∑ 𝜇𝑖𝑑𝑛𝑖𝑖 . (c) 𝑑𝐺 =(𝜕𝐺𝜕𝑃)𝑇,𝑛 𝑑𝑃+(𝜕𝐺𝜕𝑇)𝑃,𝑛𝑑𝑇+∑ 𝜇𝑖𝜐𝑖𝑑𝜉𝑖𝑖 . (d) 𝑑𝐺 <0 is the spontaneous condition. (e) None. They are all correct.

(e) None. They are all correct.

Which of the following statements referring to single-component systems undergoing phase transitions is wrong? (a) Phase transitions usually occur at constant pressure and constant temperature. (b) During a phase transition the amount of one phase decreases to compensate the increase in amount of the other phase. (c) Phase transitions are isothermal processes; therefore heat will act changing the temperature of the system only when all the amount of one phase has completely changed into the other. (d) ∆𝑡𝑟𝑎𝑛𝑠𝑆 =∆𝑡𝑟𝑎𝑛𝑠𝐻𝑇𝑡𝑟𝑎𝑛𝑠 for phase transitions occurring under isothermal and isobaric conditions. (e) None. They are all correct.

(e) None. They are all correct.

Which of the following expression referring to an ideal gas is wrong? (a) 𝑈 ≡𝑈(𝑇) and 𝐻 ≡𝐻(𝑇). (b) 𝑑𝐻 =0 for isothermal processes. (c) 𝑑𝐴<0 for isothermal expansions. (d) 𝑑𝐴=𝑑𝐺 for isothermal processes. (e) None. They previous expressions are all correct.

(e) None. They previous expressions are all correct.

Consider the concept of natural independent variables; which of the following thermodynamic conditions would cause the enthalpy for a solid substance to remain constant? (a) 𝑇=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (b) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (c) 𝑉 =𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0. (d) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝑇=𝑐𝑜𝑛𝑠𝑡. (e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

(e) 𝑃=𝑐𝑜𝑛𝑠𝑡,𝛿𝑞=0.

For an ideal gas behaving as a closed system and undergoing an adiabatic process, which of the following expressions is wrong? (a) 𝐻 ≡ 𝐻(𝑇). (b) 𝑑𝐻 = 𝛿𝑤 + 𝑛𝑅𝑑𝑇. (c) 𝑈 = 𝑐𝑜𝑛𝑠𝑡 when the process is also isothermal. (d) 𝑑𝐴 = 𝑑𝐺 when the process is also isothermal. (e) 𝑑𝐺 = −𝑇𝑑𝑆 when the process is also isothermal.

(e) 𝑑𝐺 = −𝑇𝑑𝑆 when the process is also isothermal.

At standard pressure and 353 K liquid benzene experiences a phase transition and vaporizes. Which of the following statements referring to the Gibbs free energy is correct? a) The Gibbs free energy remains constant until all the amount of liquid benzene is converted into gas. b) The Gibbs free energy decreases until all the amount of liquid benzene is converted into gas. c) The Gibbs free energy increases until all the amount of liquid benzene is converted into gas. d) I cannot tell because no information about entropy is provided. e) I cannot tell because no information about the amount of substance is provided.

a) The Gibbs free energy remains constant until all the amount of liquid benzene is converted into gas.

At 0°C ice melts, and H2O solid and liquid phases coexist. Given the absolute molar entropies reported in the table, indicate the change in molar entropy that the system experience during the melting process. Phase 𝑺̅ (𝑱∙𝑲−𝟏 ∙𝒎𝒐𝒍−𝟏) solid 37.95 liquid 59.94 a) ∆𝑓𝑢𝑠𝑆̅ = +21.99 J·K-1·mol-1. b) ∆𝑓𝑢𝑠𝑆̅ = -21.99 J·K-1·mol-1. c) ∆𝑓𝑢𝑠𝑆̅ = 0. d) ∆𝑓𝑢𝑠𝑆̅ = +10.99 J·K-1·mol-1. e) ∆𝑓𝑢𝑠𝑆̅ = -10.99 J·K-1·mol-1.

a) ∆𝑓𝑢𝑠𝑆̅ = +21.99 J·K-1·mol-1.

Determine the equilibrium constant for a chemical reaction for which 𝜟𝒓𝑮̅°= +20.2 kJ/mol. a) 𝐾𝑃𝑜 ≅ = 2.9 x 10^-4. b) 𝐾𝑃𝑜 ≅ 3.5 x 10^3. c) 𝐾𝑃𝑜 ≅ -2.9 x 10^-4. d) 𝐾𝑃𝑜 ≅ -3.5 x 10^3. e) 𝐾𝑃𝑜 ≅ 0.

a) 𝐾𝑃𝑜 ≅ = 2.9 x 10^-4.

Indicate the infinitesimal change in temperature registered by 1 L of liquid water during the transition to ice when the process occurs at constant pressure. a) 𝑑𝑇 = 0. b) 𝑑𝑇 > 0. c) 𝑑𝑇 < 0. d) This question violates the second law of thermodynamics. e) I don't have enough information to tell because I never came to class and I never watched a single video on Canvas.

a) 𝑑𝑇 = 0.

Which of the following statements about the entropy of mixing is wrong? a) The mixing of two or more miscible liquids is driven by entropy. b) The mixing of two or more gases is driven by the entropy. c) In an isolated system, the mixing of two or more gases is a spontaneous process. d) The previous answers are consequences of the second law of thermodynamics. e) The entropy of mixing always assumes negative values.

e) The entropy of mixing always assumes negative values.

What is the change in entropy for 2 moles of an ideal gas when the volume doubles and the system does not experience any change in temperature? a) I cannot tell because I do not have any information to determine the heat exchanged between the system and the surroundings. b) I cannot tell because I do not have any information about the temperature at which the process is occurring. c) 𝛥𝑆 < 0. d) 𝛥𝑆 = 0. e) 𝛥𝑆 > 0.

e) 𝛥𝑆 > 0.

Which of the following processes would cause the Helmholtz free energy to remain constant? a) A reversible isochoric and isobaric process. b) A reversible isochoric and isothermal process. c) A reversible isothermal and isobaric process. d) A generic reversible process. e) A generic irreversible process.

b) A reversible isochoric and isothermal process.

Indicate the correct trend for the entropy for a substance undergoing phase transitions from solid to liquid to gas. a) S(s) = 0, S(l) < 𝑆(g). b) S(s) < 𝑆(l) < 𝑆(g). c) S(s) > 𝑆(l) > 𝑆(g). d) S(s) ≅ S(l) ≅ S(g). e) S(s) = S(l) = S(g) = 0.

b) S(s) < 𝑆(l) < 𝑆(g).

When a Carnot engine works with a high-temperature reservoir at 110°C, its efficiency is 17%. Which is the temperature of the low-temperature reservoir? a) 𝑇𝑙𝑜𝑤 = 91°C. b) 𝑇𝑙𝑜𝑤 = 45°C. c) 𝑇𝑙𝑜𝑤 = 120 K. d) 𝑇𝑙𝑜𝑤 = 263 K. e) 𝑇𝑙𝑜𝑤 = 10°C.

b) 𝑇𝑙𝑜𝑤 = 45°C.

Which is the correct expression for the change in enthalpy for a system undergoing an isochoric and adiabatic process? a) 𝑑𝐻 =0. b) 𝑑𝐻 =𝑉𝑑𝑃. c) 𝑑𝐻 =𝛿𝑤+𝑉𝑑𝑃. d) 𝑑𝐻 =𝑇𝑑𝑆+𝑉𝑑𝑃. e) I do not have enough information to tell.

b) 𝑑𝐻 =𝑉𝑑𝑃.

Which is the slope of the straight line representing the behavior of one of the van't Hoff equations reported in the figure? a) 𝑠𝑙𝑜𝑝𝑒=−∆𝑟𝐻°/𝑅 b) 𝑠𝑙𝑜𝑝𝑒=+∆𝑟𝐻°/𝑅 c) 𝑠𝑙𝑜𝑝𝑒=+∆𝑟𝐻° d) 𝑠𝑙𝑜𝑝𝑒=−∆𝑟𝐻° e) 𝑠𝑙𝑜𝑝𝑒=+1/𝑅

b) 𝑠𝑙𝑜𝑝𝑒=+∆𝑟𝐻°/𝑅

Why the entropies of vaporization are larger than the entropies of fusion? a) Because it is more difficult to control the behavior of gases than the behavior of liquids. Consequently, systematic experimental errors occur in the measurements of the entropy of the former translating into larger values. b) This is not generally true: entropies of vaporization are larger than entropies of fusion only for spontaneous processes. c) Because gases are more disordered than liquids. d) Because gases are less disordered than liquids. e) This is not generally true: entropies of vaporization are larger than entropies of fusion only for processes occurring in closed systems.

c) Because gases are more disordered than liquids.

Consider Helmholtz and Gibbs free energies. Which of the following statements is correct? a) Both of them can be mathematically represented by inexact differentials. b) Both of them are path-dependent functions. c) For a thermodynamic cycle: ∆𝐴 = ∆𝐺 = 0. d) For a thermodynamic cycle: ∆𝐴 > 0, ∆𝐺 > 0. e) None, the previous statements are all wrong.

c) For a thermodynamic cycle: ∆𝐴 = ∆𝐺 = 0.

Which of the following expressions does not represent an infinitesimal change in the Helmholtz energy? a) 𝑑𝐴=𝑑𝑈-𝑇𝑑𝑆-𝑆𝑑𝑇. b) 𝑑𝐴=𝑑𝑈-𝑑(𝑇𝑆). c) 𝑑𝐴=𝛿𝑤-𝑇𝑑𝑆-𝑆𝑑𝑇. d) 𝑑𝐴=𝑑𝐺−𝑑(𝑃𝑉). e) 𝑑𝐴=−𝑃𝑑𝑉-𝑆𝑑𝑇.

c) 𝑑𝐴=𝛿𝑤-𝑇𝑑𝑆-𝑆𝑑𝑇.

Given 𝑪𝒑(𝑻)=𝒂𝑻 where 𝒂=𝟏𝟓.𝟑 𝐉∙𝐊−𝟐 determine the value for the change in entropy when 𝑻 increases from 15°C to 30°C. a) 𝛥𝑆 = +77.6 J·K-1. b) 𝛥𝑆 = -229.5 J·K-1. c) 𝛥𝑆 = +229.5 J·K-1. d) 𝛥𝑆 = -77.6 J·K-1. e) 𝛥𝑆 = 0 J·K-1.

c) 𝛥𝑆 = +229.5 J·K-1.

Which is the correct expression for the change in internal energy for a gas undergoing an isochoric and adiabatic process? a) 𝛥𝑈 =𝑤. b) 𝛥𝑈 =𝑇𝛥𝑆. c) 𝛥𝑈 =0. d) 𝛥𝑈 =−𝑃𝛥𝑉+𝑇𝛥𝑆. e) I do not have enough information to tell.

c) 𝛥𝑈 =0.

Which is the main cause for the increasing of entropy in the reaction Br2(l) + Cl2(g) → 2BrCl(g) ? a) The temperature. b) The heat. c) The ratio between heat and temperature. d) The amount of substance. e) I do not have enough information to tell.

d) The amount of substance.

Which of the following statements about the change in the Gibbs free energy is wrong? a) 𝛥𝐺 decreases when the temperature increases. b) 𝛥𝐺 =0 is the equilibrium condition for the Gibbs free energy. c) 𝛥𝐺 <0 is the spontaneous condition for the Gibbs free energy. d) 𝛥𝐺 >0 is the spontaneous condition for the Gibbs free energy. e) Gibbs' free energy natural independent variables are pressure and temperature.

d) 𝛥𝐺 >0 is the spontaneous condition for the Gibbs free energy.

What is the change in enthalpy for 2 moles of an ideal gas when the volume doubles and the system does not experience any change in temperature? a) I cannot tell because I do not have any information to determine the work done by the system on the surroundings. b) I cannot tell because I do not have any information about the internal energy. c) 𝛥𝐻 < 0. d) 𝛥𝐻 = 0. e) 𝛥𝐻 > 0.

d) 𝛥𝐻 = 0.

Consider solid ice and liquid water during a phase transition. Not knowing if heat is absorbed or realized, which of the following expressions is correct? a) ±𝑑𝑛𝑖𝑐𝑒 =∓𝑑𝑛𝑤𝑎𝑡𝑒𝑟. b) ±𝜇𝑖𝑐𝑒 =∓𝜇𝑤𝑎𝑡𝑒𝑟. c) 𝜇𝑖𝑐𝑒 =𝜇𝑤𝑎𝑡𝑒𝑟. d) Answers (a) and (b) are both correct. e) Answers (a) and (c) are both correct.

e) Answers (a) and (c) are both correct.

Consider the van't Hoff equation. Indicate the correct trend for the equilibrium constant with respect to the change in temperature for an endothermic process. a) 𝐾𝑃𝑜 decreases when 𝑇 increases. b) 𝐾𝑃𝑜 decreases when 𝑇 decreases. c) 𝐾𝑃𝑜 increases when 𝑇 increases. d) Answers (a) and (b) are both correct. e) Answers (b) and (c) are both correct.

e) Answers (b) and (c) are both correct.

Which of the following statements is wrong? a) 𝑑𝐻 = 𝑇𝑑𝑆 + 𝑉𝑑𝑃 for a mechanically reversible process. b) 𝑑𝐻 = 𝑃𝑑𝑉 + 𝑉𝑑𝑃 for an adiabatic expansion against vacuum. c) 𝑑𝐴 = −𝑆𝑑𝑇 for an expansion against vacuum. d) 𝑑𝐴 = 0 for an isothermal adiabatic process involving an ideal gas. e) None. They are all correct.

e) None. They are all correct.