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Chapter 19: Problem 19

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is \(\Delta H\) zero for the process?

Short Answer

Expert verified
For an ice cube to melt reversibly, the system needs to be isolated with no heat or mass transfer between the system and the surroundings, the processes must be carried out infinitesimally slowly to ensure equilibrium at all stages, and there should be no friction or dissipation of energy. In a reversible melting process, the enthalpy change (ΔH) for melting and freezing would be equal in magnitude but opposite in sign, resulting in an overall ΔH of zero for the entire reversible process.

Step by step solution

01

(Step 1: Understand the concept of reversible process)

(A process is said to be reversible if it can be reversed without leaving any net effect on either the system or the surroundings. For an ice cube melting to be reversible, it must melt and then refreeze, returning to its exact original state without any net change in the system or surroundings.)
02

(Step 2: Determine under what conditions an ice cube can melt reversibly)

(For an ice cube to melt and then refreeze in a perfect cycle, the system needs to be isolated, i.e., no heat or mass transfer between the system and the surroundings. In addition, the processes need to be carried out infinitesimally slowly to ensure equilibrium at all stages, and there should be no friction or dissipation of energy.)
03

(Step 3: Understand the concept of enthalpy change (ΔH))

(Enthalpy change, denoted as ΔH, is the change in heat energy of a system at constant pressure. It is usually a measure of the total energy of a thermodynamic system. It can be viewed as the energy the system has available to do work, plus the energy that has already been expended to create the system.)
04

(Step 4: Determine the value of ΔH for the reversible melting of an ice cube)

( For a phase transition like ice melting into water, there is an energy change corresponding to the energy needed to break the structures in the solid phase and form the liquid phase. This will be absorbed from the surroundings (as heat). And if the process is reversible, the same amount of energy would be re-transferred to the surroundings when the water refreezes into the exact same amount of ice. Accounting for the direction of the energy flow, the ΔH of the melting process should be the negative of the ΔH of the freezing process. Overall for the complete cycle, this means they will cancel out and ΔH for the whole reversible process would be zero.)

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Most popular questions from this chapter

(a) Is the standard free-energy change, \(\Delta G^{\circ}\), always larger than \(\Delta G ?\) (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0 ?\) (c) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process necessarily has a low activation barrier?

(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 doon its Id on the nath of the nrocese?

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

Indicate whether \(\Delta G\) increases, decreases, or stays the same for each of the following reactions as the partial pressure of \(\mathrm{O}_{2}\) is increased: (a) \(\mathrm{HgO}(s) \longrightarrow \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (b) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$ (c)

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on!). What do you observe? Are your observations consistent with your answer to part (b)?
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