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Chapter 12: Problem 59

Are exothermic reactions spontaneous only at low temperature? Explain your answer.

Short Answer

Expert verified
Explain why or why not. Answer: No, exothermic reactions are not always spontaneous at low temperatures. The spontaneity of an exothermic reaction depends on the balance between enthalpy change (螖H) and entropy change (螖S), as well as temperature. A reaction is spontaneous when its Gibbs Free Energy (螖G) is negative. An exothermic reaction can be spontaneous at both low and high temperatures if the combined effects of enthalpy (螖H) and entropy (螖S) are favorable.

Step by step solution

01

Understanding exothermic reactions

An exothermic reaction is a type of chemical reaction that releases energy in the form of heat. In these reactions, the total energy of the products is lower than that of the reactants, resulting in a negative enthalpy change.
02

Understanding reaction spontaneity

A spontaneous reaction is one that occurs without any external influence, such as a catalyst or added energy. Spontaneous reactions typically occur when the products are at a lower energy state than the reactants. The Gibbs Free Energy (螖G) is used to determine the spontaneity of a reaction and is described by the following equation: 螖G = 螖H - T螖S, where 螖H is the change in enthalpy, T is the temperature in Kelvin, and 螖S is the change in entropy of the system. A reaction is spontaneous when 螖G is negative.
03

Examining the relation between Gibbs Free Energy and temperature

By analyzing the equation 螖G = 螖H - T螖S, we can understand the effect of temperature on the spontaneity of a reaction. In an exothermic reaction, 螖H is negative, so the term 螖H - T螖S will be negative if the second term, -T螖S, is smaller in magnitude than 螖H or positive if it's larger in magnitude. When T is low, the term -T螖S is smaller, making the Gibbs Free Energy more likely to be negative, suggesting the exothermic reaction is likely to be spontaneous at low temperatures.
04

Considering the effect of entropy on reaction spontaneity

However, the entropy change (螖S) also plays a significant role in determining spontaneity. In a reaction with a positive 螖S, the entropy of the system increases, favoring spontaneity. In contrast, a negative 螖S denotes a decrease in entropy and usually opposes spontaneity. Therefore, the spontaneity of an exothermic reaction at different temperatures depends on the interplay between 螖H and 螖S.
05

Final conclusion

It's not accurate to say that exothermic reactions are spontaneous only at low temperatures. The spontaneity of exothermic reactions depends on the balance between enthalpy change (螖H) and entropy change (螖S), as well as temperature. An exothermic reaction can be spontaneous at both low and high temperatures if the combined effects of enthalpy and entropy are favorable.

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Most popular questions from this chapter

For each of the reactions given, indicate whether \(\Delta S\) should have a positive sign or a negative sign. If it is not possible to judge the sign of \(\Delta S\) based on the information provided, indicate why that is the case. a. \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NaCl}(s)\) b. \(4 \mathrm{H}_{3} \mathrm{PO}_{3}(\ell) \rightarrow \mathrm{PH}_{3}(g)+3 \mathrm{H}_{3} \mathrm{PO}_{4}(\ell)\) c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) d. \(\mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\)

Which of the following processes is/are spontaneous? a. A tornado forms. b. A broken cell phone fixes itself. c. You get an \(A\) in this course. d. Hot soup gets cold before it is served.

Lime Enormous amounts of lime (CaO) are used in steel industry blast furnaces to remove impurities from iron. Lime is made by heating limestone and other solid forms of \(\mathrm{CaCO}_{3}(s) .\) Why is the standard molar entropy of \(\mathrm{CaCO}_{3}(s)\) higher than that of \(\mathrm{CaO}(s)\) ? At what temperature is the pressure of \(\mathrm{CO}_{2}(g)\) over \(\mathrm{CaCO}_{3}(s)\) equal to 1.0 atm?$$\begin{array}{lcc} & \Delta H_{f}^{\circ}(\mathrm{k} J / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\C a C O_{3}(s) & -1207 & 93 \\\\\hline \mathrm{CaO}(s) & -636 & 40 \\\\\hline \mathrm{CO}_{2}(g) & -394 & 214 \\\\\hline\end{array}$$

Acid Precipitation Aerosols (fine droplets) of sulfuric acid form in the atmosphere as a result of the following combination reaction:$$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\ell)$$.Use the appropriate \(\Delta G_{f}^{\circ}\) data in Appendix 4 to calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for this reaction.

Use the standard molar entropies in Appendix 4 to calculate the \(\Delta S^{\circ}\) value for each of the following reactions of sulfur compounds. a. \(\mathrm{H}_{2} \mathrm{S}(g)+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g)\) b. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) c. \(\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) d. \(S(g)+O_{2}(g) \rightarrow S O_{2}(g)\).
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