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Chapter 19: Problem 12

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 \(101.3 \mathrm{kPa} ?\)

Short Answer

Expert verified
(a) Spontaneous, since evaporation increases entropy and the process is endothermic; (b) Spontaneous, since the separation increases entropy; (c) Spontaneous, due to an exothermic reaction and an increase in entropy; (d) Spontaneous at STP, because it is an exothermic reaction with an increase in entropy; (e) Not spontaneous, as it is an endothermic process with a decrease in entropy.

Step by step solution

01

1. Evaporation of water at T P to form water vapor of 101.3 kPa pressure

In this process, water changes from a liquid to a gaseous state (water vapor). This change leads to an increase in entropy because the molecules in the gaseous state are more disordered than in the liquid state. Also, the evaporation process is endothermic because it absorbs energy from the surroundings. However, as long as the temperature is not below the boiling point of water, the entropy increase will outweigh the energy absorbed, making the process spontaneous.
02

2. Separation of a mixture of water and oil into two separate phases

When a mixture of water and oil separates into two phases, it is due to the immiscible nature of water and oil. The separation process increases the overall entropy of the system because the molecules in each phase are more disordered than they were in the mixed state. The process does not require an external source of energy, so separating water and oil is a spontaneous process.
03

3. Souring of milk

The souring of milk is a complex process, involving the conversion of lactose (a sugar) into lactic acid by bacteria present in the milk. This conversion is accompanied by a release of energy, making it an exothermic process. The presence of a spontaneous chemical reaction, as well as an increase in the number of particles from lactose to lactic acid and gases, results in an increase in entropy. Thus, the souring of milk is a spontaneous process.
04

4. Neutralization of hydrochloric acid with sodium hydroxide at STP

The neutralization reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) involves the transfer of a proton from the acid to the base, forming water and sodium chloride. This reaction is exothermic, meaning it releases energy, and leads to an overall increase in entropy because it forms more stable products. Therefore, the neutralization process is spontaneous at standard temperature and pressure (STP).
05

5. Formation of ice from water at 20°C and 101.3 kPa

The formation of ice from water at 20°C involves cooling the water molecules and changing their state from liquid to solid. This process requires the removal of heat from the system, making it an endothermic process. Additionally, the entropy decreases as the water molecules become more ordered in the solid state (ice). To be spontaneous, the entropy change and the energy change should favor the process. In this case, since the process requires energy input and the entropy decreases, the formation of ice from water at 20°C and 101.3 kPa is not a spontaneous process.

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Most popular questions from this chapter

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} ?$

Indicate whether each statement is true or false. (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) "Translational motion" of molecules refers to their change in spatial location as a function of time. (c) "Rotational" and "vibrational" motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$, is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) $$ In practice, this reaction is carried out in the presence of oxygen: $$ 2 \mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ (a) Using the data in Appendix \(C\), calculate \(K\) for these reactions at \(25^{\circ} \mathrm{C}\) and \(500^{\circ} \mathrm{C}\). (b) Is the difference in \(\Delta G^{\circ}\) for the two reactions due primarily to the enthalpy term \((\Delta H)\) or the entropy term \((-T \Delta S)\) ? (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the "Chemistry and Life" box in Section 19.7. (d) The reaction of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{H}_{2} \mathrm{O}\) must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction?

The reaction $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$ is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for \(\Delta S^{\circ}\). Did your classmate make a mistake in the calculation? Explain.

Indicate whether each statement is true or false. (a) A reaction that is spontaneous in one direction will be nonspontaneous in the reverse direction under the same reaction conditions. (b) All spontaneous processes are fast. (c) Most spontaneous processes are reversible. (d) An isothermal process is one in which the system loses no heat. (e) The maximum amount of work can be accomplished by an irreversible process rather than a reversible one.
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