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Chapter 19: Problem 69

For a particular reaction, \(\Delta H=-32 \mathrm{~kJ}\) and \(\Delta S=-98 \mathrm{~J} / \mathrm{K}\). Assume that \(\Delta H\) and \(\Delta S\) do not vary with temperature. (a) At what temperature will the reaction have \(\Delta G=0 ?(\mathbf{b})\) If \(T\) is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?

Short Answer

Expert verified
The temperature at which ΔG equals 0 for this reaction is approximately 326.53 K. If the temperature is increased from 326.53 K, the reaction will be non-spontaneous since it is exothermic and has a decrease in entropy.

Step by step solution

01

(Step 1: Calculate the temperature for ΔG = 0)

To find the temperature at which ΔG equals 0, we need to set the Gibbs free energy equation to zero and solve for T. 0 = -32 kJ - T(-98 J/K)
02

(Step 2: Convert units to match)

Since our ΔH is in kJ and ΔS is in J/K, we need to make sure that all of our units are consistent before moving forward. Our goal is to express ΔH in J: -32 kJ = -32,000 J 0 = -32,000 J - T(-98 J/K)
03

(Step 3: Solve for T)

Now, we can solve for the temperature T. 0 = -32,000 J + 98 J/K * T 32,000 J = 98 J/K * T T = 32,000 J / (98 J/K) = 326.53 K Thus, the temperature at which ΔG equals 0 is approximately 326.53 K.
04

(Step 4: Determine spontaneity of the reaction for increased T)

With temperature T = 326.53 K, we know ΔG = 0. When the temperature is increased, we can analyze the signs of ΔH and ΔS to predict whether the reaction will be spontaneous or non-spontaneous. ΔH = -32 kJ (exothermic reaction) ΔS = -98 J/K (decrease in entropy) For an exothermic reaction with a decrease in entropy, when the temperature increases, the reaction will become less spontaneous because the TΔS term in the Gibbs free energy equation will become more positive, causing ΔG to become more positive. Therefore, if the temperature is increased from 326.53 K, the reaction will be non-spontaneous.

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Most popular questions from this chapter

A particular constant-pressure reaction is spontaneous at \(390 \mathrm{~K}\). The enthalpy change for the reaction is \(+23.7 \mathrm{~kJ}\). What can you conclude about the sign and magnitude of \(\Delta S\) for the reaction?

The crystalline hydrate \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s)\) loses water when placed in a large, closed, dry vessel: $$ \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) $$ This process is spontaneous and \(\Delta H\) is positive. Is this process an exception to Bertholet's generalization that all spontaneous changes are exothermic? Explain.

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which two moles of gaseous reactants are converted to three moles of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(\mathrm{C}\) to predict how \(\Delta \mathrm{G}^{\circ}\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G^{\circ}\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at \(800 \mathrm{~K} ?\) (c) Calculate \(\Delta G^{\circ}\) at \(1000 \mathrm{~K}\). Is the reaction spontaneous under standard conditions at this temperature?

For the majority of the compounds listed in Appendix \(\mathrm{C},\) the value of \(\Delta G_{f}^{\circ}\) is more positive (or less negative) than the value of \(\Delta H_{f}^{\circ} .\) (a) Explain this observation, using \(\mathrm{NH}_{3}(g), \mathrm{CCl}_{4}(l)\), and \(\mathrm{KNO}_{3}(s)\) as examples. (b) An exception to this observation is \(\mathrm{CO}(g)\). Explain the trend in the \(\Delta H_{f}^{\circ}\) and \(\Delta G_{f}^{\circ}\) values for this molecule.
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