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Chapter 19: Problem 14

(a) Can endothermic chemical reactions be spontaneous? (b) Can a process be spontaneous at one temperature and nonspontaneous at a different temperature? (c) Water can be decomposed to form hydrogen and oxygen, and the hydrogen and oxygen can be recombined to form water. Does this mean that the processes are thermodynamically reversible? (d) Does the amount of work that a system can do on its surroundings depend on the path of the process?

Short Answer

Expert verified
(a) Yes, endothermic chemical reactions can be spontaneous if the entropy change (∆S) is positive and large enough, causing ∆G to be negative at certain temperatures. (b) A process can be spontaneous at one temperature and nonspontaneous at another temperature due to changes in the Gibbs free energy (∆G) as temperature changes. (c) The decomposition and recombination of water does not necessarily mean these processes are thermodynamically reversible; conditions for reversibility must be met. (d) The amount of work that a system can do on its surroundings depends on the path of the process, as work and heat transferred differ depending on the specific path taken between initial and final states.

Step by step solution

01

Answer (a)

Yes, endothermic chemical reactions can be spontaneous. The spontaneity of a reaction depends on the Gibbs free energy change (∆G), which is defined as ∆G = ∆H - T∆S, where ∆H is the enthalpy change, T is temperature, and ∆S is the entropy change. A reaction is spontaneous if ∆G is negative. Endothermic reactions have a positive ∆H; however, if the entropy change (∆S) is positive and large enough, the reaction will be spontaneous at certain temperatures.
02

Answer (b)

Yes, a process can be spontaneous at one temperature and nonspontaneous at another temperature. This is because the spontaneity of a process is determined by the Gibbs free energy change (∆G), which is dependent on both the enthalpy change (∆H) and the entropy change (∆S), as well as the temperature (T). As the temperature changes, the terms T∆S and ∆H in the equation ∆G = ∆H - T∆S can have different magnitudes and signs, causing the value of ∆G to change. If ∆G is negative, the process is spontaneous, and if ∆G is positive, the process is nonspontaneous.
03

Answer (c)

The decomposition of water into hydrogen and oxygen, and the recombination of hydrogen and oxygen into water, can be considered as two different processes. Just because these two processes can occur does not necessarily mean that they are thermodynamically reversible. In a thermodynamically reversible process, the system is in equilibrium with its surroundings throughout the process, and a small change in a variable can reverse the process. For the water decomposition and recombination processes to be thermodynamically reversible, the conditions for reversibility must be met, which is not always the case in reality.
04

Answer (d)

Yes, the amount of work that a system can do on its surroundings depends on the path of the process. Work, heat, and internal energy are state functions that depend on the initial and final states of the system. However, the amounts of work and heat transferred differ depending on the specific path taken between those states. A system might do more work along one path than another, even if the initial and final states are the same. For example, during an isothermal expansion, the work done by an ideal gas on its surroundings depends on whether the expansion occurs reversibly or irreversibly.

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Most popular questions from this chapter

A certain constant-pressure reaction is barely nonspontaneous at \(45^{\circ} \mathrm{C}\) . The entropy change for the reaction is 72 \(\mathrm{J} / \mathrm{K} .\) Estimate \(\Delta H .\)

(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\(?\)

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\) , the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at 350 \(\mathrm{K}\) is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

Consider what happens when a sample of the explosive TNT is detonated under atmospheric pressure. (a) Is the detonation a reversible process? (b) What is the sign of \(q\) for this process? (c) Is \(w\) positive, negative, or zero for the process?
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