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Chapter 14: Problem 50

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

Short Answer

Expert verified
When the temperature increases, the system receives an excess of heat. According to Le Châtelier's principle, the equilibrium will shift in a direction to decrease this excess, which is in the direction of more evaporation in this case. More evaporation leads to an increased equilibrium vapor pressure.

Step by step solution

01

Understand the concept of equilibrium in a closed system

In a closed system, a liquid and its vapor are in equilibrium when the rate of evaporation equals the rate of condensation. The pressure exerted by the vapor in this state is the equilibrium vapor pressure.
02

Understand The concept of Le Châtelier's Principle

According to Le Châtelier's principle, if a state of equilibrium is disturbed, the system will adjust in such way as to counteract the change and restore a new equilibrium state. Applied to this case, if the temperature is increased, the system would shift in a direction that counteracts this change.
03

Apply Le Châtelier's Principle to the concept of vapor pressure

Evaporation is an endothermic process, meaning it absorbs heat. By increasing the temperature, you effectively add heat to the system. According to Le Châtelier's Principle, the system will respond by shifting the equilibrium position to reduce this heat - by increasing the evaporation, hence increasing the vapor pressure. Thus, the equilibrium vapor pressure of a liquid increases with increasing temperature.

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Most popular questions from this chapter

The equilibrium constant \(K_{P}\) for the reaction $$2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$$ is \(2 \times 10^{-42}\) at \(25^{\circ} \mathrm{C}\). (a) What is \(K_{\mathrm{c}}\) for the reaction at the same temperature? (b) The very small value of \(K_{P}\) (and \(K_{\mathrm{c}}\) ) indicates that the reaction overwhelmingly favors the formation of water molecules. Explain why, despite this fact, a mixture of hydrogen and oxygen gases can be kept at room temperature without any change.

Consider this equilibrium reaction in a closed container: $$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$ What will happen if the following occurs? (a) The volume is increased. (b) Some \(\mathrm{CaO}\) is added to the mixture. (c) Some \(\mathrm{CaCO}_{3}\) is removed. (d) Some \(\mathrm{CO}_{2}\) is added to the mixture. (e) A few drops of a \(\mathrm{NaOH}\) solution are added to the mixture. (f) A few drops of a \(\mathrm{HCl}\) solution are added to the mixture (ignore the reaction between \(\mathrm{CO}_{2}\) and water). (g) Temperature is increased.

The "boat" form and "chair" form of cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) interconverts as shown here: In this representation, the \(\mathrm{H}\) atoms are omitted and a \(\mathrm{C}\) atom is assumed to be at each intersection of two lines (bonds). The conversion is first order in each direction. The activation energy for the chair \(\longrightarrow\) boat conversion is \(41 \mathrm{~kJ} / \mathrm{mol} .\) If the frequency factor is \(1.0 \times 10^{12} \mathrm{~s}^{-1},\) what is \(k_{1}\) at \(298 \mathrm{~K} ?\) The equilibrium constant \(K_{\mathrm{c}}\) for the reaction is \(9.83 \times 10^{3}\) at \(298 \mathrm{~K}\).

The following equilibrium constants have been determined for hydrosulfuric acid at \(25^{\circ} \mathrm{C}\) $$\begin{array}{l}\mathrm{H}_{2} \mathrm{~S}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HS}^{-}(a q) \\\\\qquad \begin{aligned}K_{\mathrm{c}}^{\prime} &=9.5 \times 10^{-8} \\\\\mathrm{HS}^{-}(a q) \Longrightarrow \mathrm{H}^{+}(a q)+\mathrm{S}^{2-}(a q) \\\K_{\mathrm{c}}^{\prime \prime}=1.0 \times 10^{-19}\end{aligned}\end{array}$$ Calculate the equilibrium constant for the following reaction at the same temperature: $$\mathrm{H}_{2} \mathrm{~S}(a q) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+\mathrm{S}^{2-}(a q)$$

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