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Chapter 19: Problem 55

For a certain chemical reaction, \(\Delta H^{\circ}=-35.4 \mathrm{kJ}\) and \(\Delta S^{\circ}=-85.5 \mathrm{J} / \mathrm{K}\) . (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system?(c) Calculate \(\Delta G^{\circ}\) for the reaction at 298 \(\mathrm{K}\) . (d) Is the reaction spontaneous at 298 \(\mathrm{K}\) under standard conditions?

Short Answer

Expert verified
The reaction is exothermic, as \(\Delta H^{\circ} = -35.4 \mathrm{kJ}\) is negative. There is a decrease in randomness, as \(\Delta S^{\circ} = -85.5 \mathrm{J} / \mathrm{K}\) is negative. The \(\Delta G^{\circ}\) at 298 K is -9921 J, and the reaction is spontaneous under standard conditions at this temperature since \(\Delta G^{\circ}\) is negative.

Step by step solution

01

Determine if the reaction is exothermic or endothermic

We are given \(\Delta H^{\circ} = -35.4 \mathrm{kJ}\), which is a negative value. Therefore, the reaction is exothermic.
02

Determine if the reaction increases or decreases the randomness

We are given \(\Delta S^{\circ} = -85.5 \mathrm{J} / \mathrm{K}\), which is a negative value. Therefore, there is a decrease in randomness (or disorder) in the reaction.
03

Calculate \(\Delta G^{\circ}\) at 298 K

We are given the temperature as \(T=298\,\mathrm{K}\). To calculate \(\Delta G^{\circ}\), we will use the equation: $$ \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} $$ First, we convert \(\Delta H^{\circ}\) to J/mol: $$ \Delta H^{\circ} = -35.4\,\mathrm{kJ} * 1000\,\mathrm{J}/\mathrm{kJ} = -35400\,\mathrm{J} $$ Now, we plug in the values and get: $$ \Delta G^{\circ} = -35400\,\mathrm{J} - (298\,\mathrm{K} * -85.5\,\mathrm{J}/\mathrm{K}) = -35400\,\mathrm{J} + 25479\,\mathrm{J} = -9921\,\mathrm{J} $$
04

Determine if the reaction is spontaneous at 298 K

Since the value of \(\Delta G^{\circ} = -9921\,\mathrm{J}\) is negative, the reaction is spontaneous at 298 K under standard conditions. In summary, the reaction is exothermic, decreases randomness, has a \(\Delta G^{\circ}\) of -9921 J, and is spontaneous at 298 K under standard conditions.

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Most popular questions from this chapter

Sulfur dioxide reacts with strontium oxide as follows: $$ \mathrm{SO}_{2}(g)+\mathrm{SrO}(g) \longrightarrow \mathrm{SrSO}_{3}(s) $$ (a) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ} .\) (b) If you had only standard enthalpy data for this reaction, how would you estimate the value of \(\Delta G^{\circ}\) at \(298 \mathrm{K},\) using data from Appendix Con other substances.

(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of \(\Delta S ?\) (b) How does the entropy of the system change in the processes described in Exercise 19.12\(?\)

Use data in Appendix C to calculate \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for each of the following reactions. $$ \begin{array}{l}{\text { (a) } 4 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)} \\ {\text { (b) } \mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)} \\\ {\text { (c) } 2 \mathrm{P}(s)+10 \mathrm{HF}(g) \longrightarrow 2 \mathrm{PF}_{5}(g)+5 \mathrm{H}_{2}(g)} \\ {\text { (d) } \mathrm{K}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{KO}_{2}(s)}\end{array} $$

Ammonium nitrate dissolves spontaneously and endothermally in water at room temperature. What can you deduce about the sign of \(\Delta S\) for this solution process?

Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a solution?
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