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Chapter 19: Problem 11

Which of the following processes are spontaneous and which are nonspontaneous: (a) mixing of water and ethanol, \((\mathbf{b})\) dissolution of sugar in a cup of hot coffee, (c) formation of oxygen atoms from \(\mathrm{O}_{2}\) molecules at \(\mathrm{STP}\), (d) rusting of iron, (e) formation of glucose from \(\mathrm{CO}_{2}\) and $\mathrm{H}_{2} \mathrm{O}\( at \)\mathrm{STP} ?$

Short Answer

Expert verified
(a) Mixing of water and ethanol is spontaneous because it has an increase in entropy and an exothermic reaction. (b) Dissolution of sugar in hot coffee is spontaneous due to an increase in entropy and an exothermic reaction. (c) Formation of oxygen atoms from O2 molecules at STP is nonspontaneous because it involves a positive enthalpy change and a decrease in entropy. (d) Rusting of iron is spontaneous because it is an exothermic reaction and has an increase in entropy. (e) Formation of glucose from CO2 and H2O at STP is nonspontaneous since it is endothermic with a positive enthalpy change and a decrease in entropy, and requires sunlight to occur.

Step by step solution

01

Process (a): Mixing of water and ethanol

In a mixing process, both entropy and enthalpy changes are important factors. When water and ethanol mix, the overall entropy increases due to the formation of a more homogeneous and disordered mixture. The enthalpy change in the system is slightly negative (exothermic) because new hydrogen bonds are formed between water and ethanol molecules. Both these factors (increased entropy and negative enthalpy change) make this process spontaneous.
02

Process (b): Dissolution of sugar in a cup of hot coffee

When sugar is dissolved in hot coffee, the solid sugar molecules separate into individual molecules, resulting in an increase in entropy (greater disorder). Moreover, the dissolution process is usually exothermic, which releases heat to the surroundings. The combination of increased entropy and an exothermic reaction indicates a spontaneous process at constant temperature and pressure.
03

Process (c): Formation of oxygen atoms from O2 molecules at STP

The formation of oxygen atoms from O2 molecules requires an input of energy to break the oxygen-oxygen double bond. This makes the process endothermic (positive enthalpy change). Additionally, the process involves a decrease in entropy as the molecules transform into individual atoms that occupy less volume. Given these factors (positive enthalpy change and decreased entropy), the process is nonspontaneous under standard temperature and pressure.
04

Process (d): Rusting of iron

The rusting of iron is an oxidation process involving iron atoms reacting with oxygen molecules to form Fe2O3 (iron oxide), which is commonly known as rust. This process is exothermic, releasing energy in the form of heat and light. Also, the process results in increased entropy, as the solid iron molecules are transformed into solid rust molecules and occupy a larger volume. Therefore, the rusting of iron is a spontaneous process.
05

Process (e): Formation of glucose from CO2 and H2O at STP

The formation of glucose from CO2 and H2O is a complex process occurring in plants via photosynthesis. This process requires an input of energy (sunlight), which makes it endothermic (positive enthalpy change). Also, the process leads to a decrease in entropy as individual CO2 and H2O molecules form a more ordered glucose molecule. Overall, the formation of glucose from CO2 and H2O at STP is found to be nonspontaneous since it requires an external source of energy (sunlight) to occur.

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Most popular questions from this chapter

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?

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 \(\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.098 \mathrm{M} ?\)

Using the data in Appendix \(C\) and given the pressures listed, calculate \(K_{\mathrm{p}}\) and \(\Delta G\) for each of the following reactions: $$ \begin{array}{l} \text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \\ \quad R_{\mathrm{N}_{2}}=263.4 \mathrm{kPa}, P_{\mathrm{H}_{2}}=597.8 \mathrm{kPa}, P_{\mathrm{NH}_{3}}=101.3 \mathrm{kPa} \\ \text { (b) } 2 \mathrm{~N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ \(P_{\mathrm{N}_{2} \mathrm{H}_{4}}=P_{\mathrm{NO}_{2}}=5.07 \mathrm{kPa}\) $$ \begin{array}{l} \quad R_{\mathrm{N}_{2}}=50.7 \mathrm{kPa}, P_{\mathrm{H}_{2} \mathrm{O}}=30.4 \mathrm{kPa} \\ \text { (c) } \mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \\ P_{\mathrm{N}_{2} \mathrm{H}_{4}}=101.3 \mathrm{kPa}, P_{\mathrm{N}_{2}}=152.0 \mathrm{kPa}, P_{\mathrm{H}_{2}}=253.3 \mathrm{kPa} \end{array} $$

Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: (a) $\mathrm{H}_{2}(g)+\mathrm{NiO}(s) \longrightarrow \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $\mathrm{H}_{2}(g)+\mathrm{S}(s) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)$ (c) $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$
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