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Chapter 19: Problem 67

For a particular reaction, \(\Delta H=30.0 \mathrm{~kJ}\) and $\Delta S=90.0 \mathrm{~J} / \mathrm{K}\(. Assume that \)\Delta H\( and \)\Delta S$ do not vary with temperature. (a) At what temperature will the reaction have \(\Delta G=0 ?\) (b) If \(\mathrm{T}\) is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?

Short Answer

Expert verified
The reaction has ΔG = 0 at a temperature of approximately 333.33 K. When the temperature is increased from 333.33 K, the reaction becomes spontaneous.

Step by step solution

01

Part (a): Finding the temperature when ΔG = 0

We are given the values of ΔH and ΔS and we need to find the temperature (T) at which ΔG becomes zero. ΔG = ΔH - TΔS Since we need to find T when ΔG = 0, we can rearrange the formula as follows: T = ΔH / ΔS Now, plug in the given values of ΔH and ΔS: T = (30.0 kJ) / (90.0 J/K) Keep in mind that 1 kJ = 1000 J. Therefore, convert ΔH to J: T = (30,000 J) / (90.0 J/K) Now, divide to find the temperature: T = 333.33 K So, the reaction has ΔG = 0 at a temperature of approximately 333.33 K.
02

Part (b): Spontaneous or non-spontaneous reaction

We have to determine if the reaction becomes spontaneous or non-spontaneous as the temperature increases from 333.33 K (found in part (a)). To do this, we have to consider the effect of increasing temperature on ΔG. ΔG = ΔH - TΔS In this equation, ΔH and ΔS are constants, while the temperature (T) is a variable. As we increase the temperature, the value of TΔS will increase. Since ΔH is positive (given as 30.0 kJ), this means that as T increases, ΔG will become more negative, hence driving the reaction towards spontaneity. So, when T is increased from 333.33 K, the reaction becomes spontaneous.

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Most popular questions from this chapter

The \(K_{b}\) for methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix \(D\). (a) Write the chemical equation for the equilibrium that corresponds to \(K_{b}\). (b) By using the value of \(K_{b}\), calculate \(\Delta G^{\circ}\) for the equilibrium in part (a). (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when $\left[\mathrm{H}^{+}\right]=6.7 \times 10^{-9} \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\right]=2.4 \times 10^{-3} \mathrm{M}$ and \(\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.098 \mathrm{M} ?\)

Which of the following processes are spontaneous: (a) the evaporation of water at \(\$ T P\) to form water vapor of 101.3 kPa pressure; (b) separation of a mixture of water and oil into two separate phases; (c) the souring of milk; (d) the neutralization of hydrochloric acid with sodium hydroxide at \(\mathrm{STP} ;(\mathbf{e})\) the formation of ice from water at \(20^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa} ?\)

For a certain chemical reaction, $\Delta H^{\circ}=-40.0 \mathrm{k} \mathrm{J}\( and \)\Delta S^{\circ}=-150.0 \mathrm{~J} / \mathrm{K}$. (a) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the surroundings? (c) Calculate \(\Delta G^{\circ}\) for the reaction at \(298 \mathrm{~K}\). (d) Is the reaction spontaneous at $298 \mathrm{~K}$ under standard conditions?

Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

The reaction $$ \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 3 \mathrm{~S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is the basis of a suggested method for removal of \(\mathrm{SO}_{2}\) from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at $298 \mathrm{~K} ?(\mathbf{b})$ In principle, is this reaction a feasible method of removing \(\mathrm{SO}_{2}\) ? (c) If \(P_{5 \mathrm{O}_{2}}=P_{\mathrm{H}_{2}}\) s and the vapor pressure of water is \(3.33 \mathrm{kPa}\), calculate the equilibrium \(\mathrm{SO}_{2}\) pressure in the system at \(298 \mathrm{~K}\). (d) Would you expect the process to be more or less effective at higher temperatures?
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