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Chapter 17: Problem 3

Which of the following processes are spontaneous? (a) a ball rolling down a hill (b) a drop of ink dispersing in water (c) melting wax at \(10^{\circ} \mathrm{C}\)

Short Answer

Expert verified
a) A ball rolling down a hill b) A drop of ink dispersing in water c) Melting wax at \(10^{\circ} \mathrm{C}\) Answer: a) Spontaneous b) Spontaneous c) Non-spontaneous (unless external heat is supplied)

Step by step solution

01

Process (a)

A ball rolling down a hill As the ball rolls down the hill, its potential energy decreases and its kinetic energy increases. The total energy of the system remains constant. Since the system moves towards a state of minimum potential energy, this process is spontaneous.
02

Process (b)

A drop of ink dispersing in water When a drop of ink is placed in water, the ink molecules will begin to randomly spread out until they are uniformly distributed throughout the water. This results in an increase in entropy, as the system moves from an ordered to a disordered state. According to the second law of thermodynamics, processes that increase entropy are spontaneous, so this process is spontaneous.
03

Process (c)

Melting wax at \(10^{\circ} \mathrm{C}\) The melting point of wax is typically around \(45^{\circ} \mathrm{C}\). If the wax is at \(10^{\circ}\mathrm{C}\), this means that it is in a solid state and not yet at a temperature where it would typically melt. However, if we apply heat to it, the wax will eventually melt, its entropy will increase, and the potential energy will decrease. In this case, the wax melting is not spontaneous at \(10^{\circ} \mathrm{C}\) in an isolated system. But if external heat is supplied, then the process can be spontaneous, as it moves towards the state of increased entropy and lower potential energy.

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Most popular questions from this chapter

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{CCl}_{4}(l)+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{ClO}_{2}(g)\) (b) \(8 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{S}_{8}(s) \longrightarrow 8 \mathrm{H}_{2} \mathrm{~S}(g)+4 \mathrm{O}_{2}(g)\) (c) \(\mathrm{Br}_{2}(l) \longrightarrow \mathrm{Br}_{2}(s)\) (d) \(2 \mathrm{NH}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\)

Some bacteria use light energy to convert carbon dioxide and water to glucose and oxygen: \(6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{O}_{2}(g) \quad \Delta G^{\circ}=2870 \mathrm{~kJ}\) at \(25^{\circ} \mathrm{C}\) Other bacteria, those that do not have light available to them, couple the reaction $$ \mathrm{H}_{2} \mathrm{~S}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{S}(s) $$ to the glucose synthesis above. Coupling the two reactions, the overall reaction is \(24 \mathrm{H}_{2} \mathrm{~S}(g)+6 \mathrm{CO}_{2}(g)+6 \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+18 \mathrm{H}_{2} \mathrm{O}(l)+24 \mathrm{~S}(s)\) Show that the reaction is spontaneous at \(25^{\circ} \mathrm{C}\).

Predict the sign of \(\Delta S\) for the following. (a) ice cream melting (b) boiling water (c) dissolving instant coffee in hot water (d) sugar, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), decomposing to carbon and steam

In your own words, explain why (a) \(\Delta S^{\circ}\) is negative for a reaction in which the number of moles of gas decreases. (b) we take \(\Delta S^{\circ}\) to be independent of \(T\), even though entropy increases with \(T\). (c) a solid has lower entropy than its corresponding liquid.

Red phosphorus is formed by heating white phosphorus. Calculate the temperature at which the two forms are at equilibrium, given $$ \text { white } \text { P: } \Delta H_{\mathrm{f}}^{\circ}=0.00 \mathrm{~kJ} / \mathrm{mol} ; S^{\circ}=41.09 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} $$ red \(\mathrm{P}: \Delta H_{\mathrm{f}}^{\circ}=-17.6 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{S}^{\circ}=22.80 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\).
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