Chapter 17 3 The entropy change associated with the expansion of one mole

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4) For which process is the sign of ΔS negative in the system?

A) 2 H2(g) + O2(g) → 2 H2O(g)

B) 2 H2O(l) + 2 Rb(s) → 2 Rb+(aq) +2 OH–(aq) + H2(g)

C) H2O(l) → H2O(g)

D) 2 H2O(g) → 2 H2(g) + O2(g)

5) Predict the sign of ΔS of the system for both of the following.

I. 2 C(graphite) + O2(g) → 2 CO(g)

II. C4H10(g) → C4H10(l)

A) ΔS should be negative for I and negative for II.

B) ΔS should be negative for I and positive for II.

C) ΔS should be positive for I and negative for II.

D) ΔS should be positive for I and positive for II.

6) The entropy change associated with the expansion of one mole of an ideal gas from an initial volume of

Vi to a final volume of Vf at constant temperature is given by the equation, ΔS = R ln (Vf/Vi). What is the

entropy change associated with the expansion of five moles of an ideal gas from an initial volume of Vi to

a final volume of Vf at constant temperature?

A) ΔS = R ln (Vf/Vi)

B) ΔS = 5 mol × R ln (Vf/Vi)

C) ΔS = R ln (Vf × 23/Vi)

D) ΔS = R ln (Vf × 5!/Vi)

7) What is the entropy change associated with the expansion of one mole of an ideal gas from an initial

volume of V to a final volume of 2.50V at constant temperature?

A) ΔS = 2.50 R ln (Vf/Vi)

B) ΔS = -2.50 R ln (Vf/Vi)

C) ΔS = R ln 2.50

D) ΔS = –R ln 2.50

8) Predict the sign of ΔS for each of the following systems, which occur at constant temperature.

I. The volume of 2.0 moles of Ne

(g) increases from 54 L to 62 L.

II. The pressure of 2.0 moles of Ne

(g) increases from 0.90 atm to 1.0 atm.

A) I: ΔS = negative; II: ΔS = negative

B) I: ΔS = negative; II: ΔS = positive

C) I: ΔS = positive; II: ΔS = negative

D) I: ΔS = positive; II: ΔS = positive

9) Which electron on an atom of palladium would have the highest value of W in the Boltzmann formula?

A) 3s

B) 4d

C) 4s

D) 3p

10) Under which of the following conditions would one mole of Kr have the highest entropy, S?

A) 47°C and 45 L

B) 157°C and 45 L

C) 47°C and 55 L

D) 157°C and 55 L

11) Which has the lowest entropy?

A) CH3OH(s, -26°C)

B) CH3OH(s, -13°C)

C) CH3OH(l, 16°C)

D) CH3OH(l, 30°C)

12) Which has the highest entropy in each set?

I. H2O(s), H2O(l), H2O(g) at 0.1°C, 4.40 atm

II. H2O(l) at 0°C, H2O(l) at 23°C, H2O(l) at 100°C (all at 1.0 atm pressure)

A) H2O(l) in set I and H2O(l) at 0°C in set II

B) H2O(s) in set I and H2O(l) at 100°C in set II

C) H2O(g) in set I and H2O(l) at 0°C in set II

D) H2O(g) in set I and H2O(l) at 100°C in set II

13) Which provides the greatest increase in entropy?

A) H2O (s, 0°C) → H2O (l, 0°C)

B) H2O (l, 0°C) → H2O (l, 20°C)

C) H2O (g, 0.4°C) → H2O (s, 0.4°C)

D) H2O (l, 101°C) → H2O (g, 101°C)

14) Under which of the following conditions would one mole of Ne have the highest entropy, S?

A) 29°C and 26 L

B) 135°C and 26 L

C) 29°C and 34 L

D) 135°C and 34 L

15) Which one of the following would be expected to have the lowest standard molar entropy, S°, at

25°C?

A) C

H4(g)

B) C3H6(g)

C) C3H8(g)

D) C4 H10OH(g)

16) Which has the highest standard molar entropy at 25°C?

A) P(s)

B) P(l)

C) P(g)

D) All three should have a standard molar entropy of zero.

17) Which has the highest standard molar entropy at 25°C?

A) F2(g)

B) N2(g)

C) Cl2(g)

D) I2(g)

18) Which of the following straight chain molecules has the greatest standard molar entropy at 25°C?

A) C2H2

B) C2H4

C) C2H6

D) All have the same entropy.

19) Which substance has the highest standard molar entropy at 25°C?

A) C(graphite)

B) C2H4(g)

C) CH3OCH3(l)

D) BaCO3(s)

20) Which of the three laws of thermodynamics states the criterion for spontaneity?

A) the first law of thermodynamics

B) the second law of thermodynamics

C) the third law of thermodynamics

D) both the second and third laws of thermodynamics

21) Which of the following is a criterion for spontaneity that holds for any process?

A) ΔG < 0

B) ΔG > 0

C) ΔStotal < 0

D) ΔStotal > 0

22) According to the second law of thermodynamics, all reactions proceed spontaneously in the direction

that increases the entropy of the

A) surroundings.

B) surroundings x system.

C) system – surroundings.

D) system + surroundings.

23) Which one of the following has the lowest standard molar entropy, S°, at 25°C?

A) C5H12(s)

B) C9H20(l)

C) C12H26(s)

D) C18H38(l)

24) Other than only PV work, what reaction conditions must be satisfied for the sign of ΔG to be used as a

criterion for spontaneity?

A) constant volume and temperature

B) constant temperature and pressure

C) constant temperature, volume, and pressure

D) constant temperature only

25) For a particular process ΔG is less than ΔH. Therefore

A) ΔS is positive.

B) ΔS is negative.

C) ΔS is zero.

D) ΔS is negative if ΔH is positive and ΔS is positive if ΔH is negative.

26) For a particular process, ΔG = ΔH at a given temperature and pressure. Therefore,

A) ΔS is positive if ΔH is negative and negative is ΔH is positive.

B) ΔS is negative if ΔG is positive and positive if ΔG is positive.

C) ΔS is zero.

D) ΔS = ΔG/T.

27) Which statement is true concerning the standard states of F2(g) and C12H22O11(aq)?

A) The standard state for F2(g) is the pure gas at 1 atm and for C12H22O11(aq) is the pure solid at 1 atm.

B) The standard state for F2(g) is the pure gas at 1 mol/L and for C12H22O11(aq) is the pure solid at 1 atm.

C) The standard state for F2(g) is the pure gas at 1 atm and for C12H22O11(aq) is the solution at a

concentration of 1 mol/L.

D) The standard state for F2(g) is the pure gas at 1 mol/L and for C12H22O11(aq) is the solution at a

concentration of 1 mol/L.

28) Which of the following is zero at 25°C?

A) ΔG°f for O2(g)

B) ΔG°f for H2Se (l)

C) S° for O2 (g)

D) S° for H2S (l)

29) In general, as a reaction goes to equilibrium

A) ΔG decreases.

B) ΔG°f decreases.

C) ΔG goes to zero.

D) ΔG° decreases.

30) What is K if ΔG° = -19.0 kJ for a reaction at 25°?

A) 2.10 × 103

B) 2.80 × 102

C) 1.80 × 10-3

D) 5.30 × 10-4

31) The synthesis of ethanol from ethylene and water proceeds using the following reaction.

C2H4(g) + H2O(l) C2H5OH(l) ΔGºrxn = -116.6 kJ/mol

Determine the Gibbs free energy if the pressure of the vessel is 325 atm at 570 K.

A) -27526 kJ/mole

B) -89 kJ/mole

C) -144.0 kJ/mole

D) none of these

17.3 Short Answer Questions

1) Chemical and physical changes can be classified as spontaneous or nonspontaneous. At 25°C and 1 atm

pressure the decomposition of water into hydrogen and oxygen is classified as ________, and the melting

of snow is classified as ________.

2) The sign (+ or –) of ΔH is ________ and the sign (+ or –) of ΔS is ________ for the evaporation of water.

3) What is the entropy of 12 molecules in a system of 100 boxes?

4) What is the entropy of 50 molecules in a system of 1000 boxes?

5) By what factor does the entropy increase for a collection of 100 molecules from a system of 1 × 105

boxes to 1 × 106 boxes?

6) If the entropy of a collection of molecules in 5000 boxes is 1.76 × 10–20 J/K, how many molecules are

there?

7) A 1.8 mole sample of gas at STP has a ________ entropy than 1.8 mole of gas at 273 K and 835 mm Hg.

8) The entropy of water at 30° is ________ than the entropy of water at 37°C.

9) Standard molar entropies, S°, in J/K∙mol, are given below each reactant and product in the reaction

shown below. The standard entropy of reaction, ΔS°, for this reaction is ________ J/K.

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l)

186.2 205.0 213.6 69.9

10) Standard molar entropies, S°, in J/Kmol, are given below each reactant and product in the reaction

shown below. The standard entropy of reaction, ΔS°, for this reaction is ________ J/K.

S(s, rhombic) + O2(g) → SO2(g)

31.8 205.0 248.1

11) Standard molar entropies, S°, in J/Kmol, are given below each reactant and product in the reaction

shown below. The standard entropy of reaction, ΔS°, for this reaction is ________ J/K.

2 SO2(g)+ O2(g) → 2 SO3(g)

248.1 205.0 256.6

12) The most commonly used white pigment is titanium white, which is titanium(IV) oxide, TiO2.

Titanium white can be formed from TiCl4 as shown in the reaction below.

TiCl4(l) + 2 H2O(l) → TiO2(s) + 4 HCl(g)

If ΔH° = 61.9 kJ/mol and ΔS° = 405.4 J/K, what are ΔSsurr and ΔStotal for this reaction at 25°C?

13) The most common white pigment until the 1880s was lead white, sometimes called basic lead

carbonate: (PbCO3)2Pb(OH)2. Paintings containing lead white turned black in the presence of moist H2S

from natural sources and polluted air due to the formation of PbS. The PbCO3 portion of this reaction is

shown below.

PbCO3(s) + H2S(aq) → PbS(s) + H2CO3(aq)

If ΔH° = –60.9 kJ/mol and ΔS° = 26.6 J/K, what are ΔSsurr and ΔStotal for this reaction at 25°C?

14) For the reaction N2(g) + O2(g) → 2 NO(g), ΔH° = 180.4 kJ/mol and ΔS° = 24.9 J/K. ΔStotal for this

reaction is ________ J/K, and the reaction is ________ (spontaneous, nonspontaneous) at 25°C.

15) For the reaction N2(g) +2 O2(g) → 2 NO2(g), ΔH° = 66.4 kJ/mol and ΔS° = –121.5 J/K. ΔStotal for this

reaction is ________ J/K, and the reaction is ________ (spontaneous, nonspontaneous) at 25°C.

16) A reaction for which ΔH° = + 98.8 kJ and ΔS° = + 141.5 J/K is ________ (spontaneous or

nonspontaneous) at low temperatures and ________ (spontaneous or nonspontaneous) at high

temperatures.

17) A reaction has ΔG° = + 21.5 kJ/mol, ΔH° = + 25.0 kJ/mol, and ΔS° = + 15.0 J/mol∙K can become

spontaneous at a temperature of ________ K.

18) For the reaction N2(g) + O2(g) → 2NO(g), ΔH° = 180.4 kJ/mol and ΔS° = 24.9 J/K. Is there a temperature

at which the spontaneity of this reaction be changed, either from spontaneous to nonspontaneous or

nonspontaneous to spontaneous? If so, estimate the temperature.

19) For the reaction N2(g) + 2 O2(g) → 2 NO2(g), ΔH° = 66.4 kJ/mol and ΔS° = -121.5 J/K. Is there a

temperature at which the spontaneity of this reaction be changed, either from spontaneous to

nonspontaneous or nonspontaneous to spontaneous? If so, estimate the temperature.

20) Acetylene, C2H2, has a standard enthalpy of formation, ΔH° = 226.7 kJ/mol, and a standard entropy

change for its formation from its elements, ΔS° = 58.8 J/K∙mol. The standard free energy of formation of

acetylene is ________ kJ/mol.

21) Standard free energies of formation, ΔG°, in kJ/mol, are given below each reactant and product in the

reaction shown below. The standard free energy of reaction, ΔG°, for this reaction is ________ kJ.

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l)

-50.8 0 -394.4 -237.2

22) The standard free energy for a reaction is ΔG° = –33.0 kJ. At 25°C the equilibrium constant for this

reaction, Kp = ________.

23) For the reaction N2(g) + 2 O2(g) → 2 NO2(g), ΔG° = 102.6 kJ. At 25°C the equilibrium constant Kp =

________.

24) The reaction 2 H2(g) + O2(g) → 2 H2O(g) is spontaneous at 25°C. The addition of a catalyst will

________ (decrease, increase, not change) the rate of reaction and ________ (decrease, increase, not

change) the spontaneity of the reaction.

25) The reaction 2 H2O(g) + CO2(g) → CH4(g) + 2 CO2(g) is nonspontaneous at 25°C. The addition of a

catalyst will ________ (decrease, increase, not change) the rate of reaction and ________ (decrease,

increase, not change) the spontaneity of the reaction.

26) For the vaporization of solid rhombic sulfur, S(s, rhombic) ⇌ S(g), ΔG° = 236.7 kJ/mol. At 25°C the

vapor pressure of rhombic sulfur is ________ atm.