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Chapter 15: Problem 40

Use Le Châtelier's principle to explain why the equilibrium vapor pressure of a liquid increases with increasing temperature.

Short Answer

Expert verified
According to Le Châtelier's principle, a system at equilibrium will adjust to counteract any changes. When the temperature increases, the equilibrium of a liquid-vapor system shifts towards the vapor phase to counteract the added energy. This results in more molecules in the vapor phase, and thus an increase in the equilibrium vapor pressure.

Step by step solution

01

Understanding Le Châtelier's Principle

Le Châtelier's principle states that if a system in equilibrium is subjected to a change, the system will adjust itself in a way that counteracts the change. In the context of phase transitions, if the equilibrium between liquid and vapor phases is disturbed by a change in temperature, the system will counteract this by shifting either towards the liquid or vapor phase to re-establish equilibrium.
02

Equilibrium and Temperature

An increase in temperature adds energy to the system. In the context of a liquid-vapor equilibrium, this additional energy allows more liquid particles to overcome the intermolecular forces that keep them in the liquid phase, resulting in evaporation. Hence, more particles move to the gas phase.
03

Applying Le Châtelier's principle to Increasing Temperature

According to Le Châtelier's principle, the system will react to this increase in temperature by shifting the equilibrium to counteract the change. Since more energy results in more evaporation, the system counters this change by shifting the equilibrium towards the vapor phase. This shift implies an increase in the number of molecules in the vapor phase, which is reflected as an increase in the vapor pressure.

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Most popular questions from this chapter

The dissociation of molecular iodine into iodine atoms is represented as $$ \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g) $$ At \(1000 \mathrm{~K}\), the equilibrium constant \(K_{\mathrm{c}}\) for the reaction is \(3.80 \times 10^{-5}\). Suppose you start with 0.0456 mole of \(I_{2}\) in a 2.30 - \(L\) flask at \(1000 \mathrm{~K}\). What are the concentrations of the gases at equilibrium?

The equilibrium constant \(K_{P}\) for the reaction $$ \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) $$ is 1.05 at \(250^{\circ} \mathrm{C}\). The reaction starts with a mixture of \(\mathrm{PCl}_{5}, \mathrm{PCl}_{3},\) and \(\mathrm{Cl}_{2}\) at pressures of \(0.177 \mathrm{~atm}\) 0.223 atm, and 0.111 atm, respectively, at \(250^{\circ} \mathrm{C}\). When the mixture comes to equilibrium at that temperature, which pressures will have decreased and which will have increased? Explain why.

(a) Use the van't Hoff equation in Problem 15.97 to derive the following expression, which relates the equilibrium constants at two different temperatures $$ \ln \frac{K_{1}}{K_{2}}=\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right) $$ How does this equation support the prediction based on Le Châtelier's principle about the shift in equilibrium with temperature? (b) The vapor pressures of water are \(31.82 \mathrm{mmHg}\) at \(30^{\circ} \mathrm{C}\) and \(92.51 \mathrm{mmHg}\) at \(50^{\circ} \mathrm{C} .\) Calculate the molar heat of vaporization of water.

What do the symbols \(K_{c}\) and \(K_{P}\) represent?

Explain Le Châtelier's principle. How can this principle help us maximize the yields of reactions?
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