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Chapter 13: Problem 24

The reaction to prepare methanol from carbon monoxide and hydrogen $$\mathrm{CO}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(g)$$ is exothermic. If you wanted to use this reaction to produce methanol commercially, would high or low temperatures favor a maximum yield? Explain.

Short Answer

Expert verified
A low temperature would favor a maximum yield of methanol in this exothermic reaction, as it would shift the equilibrium towards the products according to Le Chatelier's principle. This is because lowering the temperature causes the reaction to produce more heat, favoring the formation of methanol.

Step by step solution

01

Identify the type of reaction and write the equilibrium expression

The given reaction is: \[ \mathrm{CO}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{3}\mathrm{OH}(g) \] This reaction is exothermic, which means it releases heat energy. The equilibrium constant expression for this reaction would be: \[ K_c = \frac{[\mathrm{CH}_3\mathrm{OH}]}{[\mathrm{CO}][\mathrm{H}_2]} \]
02

Apply Le Chatelier's principle

According to Le Chatelier's principle, if we increase the temperature of an exothermic reaction, the reaction will shift towards the reactants to oppose the change (i.e., consume the added heat by moving towards the endothermic direction). On the other hand, if we decrease the temperature, the reaction shifts towards the products to counteract the change (i.e., produce more heat by moving towards the exothermic direction).
03

Determine the effect of temperature on yield

Since we want to maximize the yield of methanol (\(\mathrm{CH}_{3}\mathrm{OH}\)), we need the reaction to favor the formation of products. Based on Le Chatelier's principle, lowering the temperature would favor the formation of methanol, as the reaction would shift towards the products to produce more heat in response to the decrease in temperature. Therefore, a low temperature would favor a maximum yield of methanol in this exothermic reaction.

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Most popular questions from this chapter

For the reaction $$2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$$ \(K=2.4 \times 10^{-3}\) at a given temperature. At equilibrium in a \(2.0-\) L container it is found that $\left[\mathrm{H}_{2} \mathrm{O}(g)\right]=1.1 \times 10^{-1} M\( and \)\left[\mathrm{H}_{2}(g)\right]=1.9 \times 10^{-2} \mathrm{M} .\( Calculate the moles of \)\mathrm{O}_{2}(g)$ present under these conditions.

The equilibrium constant is 0.0900 at \(25^{\circ} \mathrm{C}\) for the reaction $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)$$ For which of the following sets of conditions is the system at equilibrium? For those that are not at equilibrium, in which direction will the system shift? a. A 1.0 -L flask contains 1.0 mole of HOCl, 0.10 mole of $\mathrm{Cl}_{2} \mathrm{O}\( , and 0.10 mole of \)\mathrm{H}_{2} \mathrm{O}$ . b. A 2.0 -L flask contains 0.084 mole of HOCl, 0.080 mole of $\mathrm{Cl}_{2} \mathrm{O}\( , and 0.98 mole of \)\mathrm{H}_{2} \mathrm{O}$ . c. A 3.0 - flask contains 0.25 mole of HOCl, 0.0010 mole of $\mathrm{Cl}_{2} \mathrm{O},\( and 0.56 mole of \)\mathrm{H}_{2} \mathrm{O}$ .

Write expressions for \(K_{\mathrm{p}}\) for the following reactions. a. $2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)$ b. $\mathrm{CO}_{2}(g)+\mathrm{MgO}(s) \rightleftharpoons \mathrm{MgCO}_{3}(s)$ c. $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)$ d. $4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g)$

An 8.00 -g sample of \(\mathrm{SO}_{3}\) was placed in an evacuated container, where it decomposed at \(600^{\circ} \mathrm{C}\) according to the following reaction: $$\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)$$ At equilibrium the total pressure and the density of the gaseous mixture were 1.80 \(\mathrm{atm}\) and 1.60 \(\mathrm{g} / \mathrm{L}\) , respectively. Calculate \(K_{\mathrm{p}}\) for this reaction.

Explain the difference between \(K, K_{\mathrm{p}},\) and \(Q\)
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