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Chapter 15: Problem 66

Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) can be made by the reaction of \(\mathrm{CO}\) with \(\mathrm{H}_{2} :\) $$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) $$ (a) Use thermochemical data in Appendix C to calculate \(\Delta H^{\circ}\) for this reaction. (b) To maximize the equilibrium yield of methanol, would you use a high or low temperature? (c) To maximize the equilibrium yield of methanol, would you use a high or low pressure?

Short Answer

Expert verified
(a) The standard enthalpy change for the reaction, $\Delta H^{\circ}$, is calculated as: \[ \Delta H^{\circ} = \Sigma n \Delta H_{f}^{\circ}(\text{products}) - \Sigma m \Delta H_{f}^{\circ}(\text{reactants}) \] (b) Based on the calculated ∆H°, if the reaction is exothermic (∆H° < 0), low temperature would maximize the equilibrium yield of methanol; if the reaction is endothermic (∆H° > 0), high temperature would maximize the equilibrium yield of methanol. (c) High pressure conditions would maximize the equilibrium yield of methanol, since it shifts the equilibrium towards the side with fewer moles of gas, favoring the production of methanol.

Step by step solution

01

a) Calculate the standard enthalpy change (∆H°) for the reaction

To calculate the standard enthalpy change for the reaction, we need to look up the standard enthalpies of formation (∆Hf°) for CO, H2, and CH3OH in Appendix C. Next, use the following equation to calculate ∆H°: \[ \Delta H^{\circ} = \Sigma n \Delta H_{f}^{\circ}(\text{products}) - \Sigma m \Delta H_{f}^{\circ}(\text{reactants}) \]
02

b) Determine the temperature conditions for maximum methanol yield

According to Le Chatelier's principle, if the reaction is exothermic (∆H° < 0), high temperature would shift the equilibrium to the left, favoring reactants. Conversely, if the reaction is endothermic (∆H° > 0), high temperature would shift the equilibrium to the right, favoring products. Based on the calculated ∆H°, we can determine whether high or low temperature conditions would maximize the equilibrium yield of methanol.
03

c) Determine the pressure conditions for maximum methanol yield

According to Le Chatelier's principle, increasing the pressure will shift the equilibrium towards the side with fewer moles of gas. In our case, there are 3 moles of gas on the reactant side (1 mol CO + 2 mol H2) and 1 mole of gas on the product side (CH3OH). Increasing pressure will shift the equilibrium towards the side with fewer moles of gas, i.e., to the right, which will favor the production of methanol. So, high pressure conditions would maximize the equilibrium yield of methanol.

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Most popular questions from this chapter

An equilibrium mixture of \(\mathrm{H}_{2}, \mathrm{I}_{2},\) and \(\mathrm{HI}\) at \(458^{\circ} \mathrm{C}\) contains \(0.112 \mathrm{mol} \mathrm{H}_{2}, 0.112 \mathrm{mol} \mathrm{I}_{2},\) and 0.775 \(\mathrm{mol}\) HI in a 5.00 -L. vessel. What are the equilibrium partial pressures when equilibrium is reestablished following the addition of 0.200 \(\mathrm{mol}\) of \(\mathrm{HI}\) ?

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons\) \(\mathrm{PCl}_{5}(g) . \mathrm{A} 7.5-\mathrm{L}\) gas vessel is charged with a mixture of \(\mathrm{PCl}_{3}(g)\) and \(\mathrm{Cl}_{2}(g),\) which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are \(P_{\mathrm{PCl}_{3}}=0.124 \mathrm{atm}, P_{\mathrm{Cl}_{2}}=0.157 \mathrm{atm},\) and \(P_{\mathrm{PCl}_{\mathrm{s}}}=1.30 \mathrm{atm}\) (a) What is the value of \(K_{p}\) at this temperature? (b) Does the equilibrium favor reactants or products? (c) Calculate \(K_{c}\) for this reaction at 450 \(\mathrm{K}\)

At \(700 \mathrm{K},\) the equilibrium constant for the reaction $$\operatorname{CCI}_{4}(g) \Longrightarrow \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g)$$ is \(K_{p}=0.76 .\) A flask is charged with 2.00 atm of \(\mathrm{CCl}_{4}\) ,which then reaches equilibrium at 700 \(\mathrm{K}\) . (a) What fraction of the CCl\(_{4}\) is converted into \(\mathrm{C}\) and \(\mathrm{Cl}_{2} ?(\mathbf{b})\) what are the partial pressures of \(\mathrm{CCl}_{4}\) and \(\mathrm{Cl}_{2}\) at equilibrium?

A \(0.831-\) g sample of \(\mathrm{SO}_{3}\) is placed in a 1.00 -L container and heated to 1100 \(\mathrm{K}\) . The SO \(_{3}\) decomposes to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) : $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ At equilibrium, the total pressure in the container is 1.300 atm. Find the values of \(K_{p}\) and \(K_{c}\) for this reaction at 1100 \(\mathrm{K}\) .

When 2.00 \(\mathrm{mol}\) of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a 2.00 -L flask at 303 \(\mathrm{K}, 56 \%\) of the \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decomposes to \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2} :\) $$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$ (a) Calculate \(K_{c}\) for this reaction at this temperature. (b) Calculate \(K_{p}\) for this reaction at 303 \(\mathrm{K}\) . (c) According to Le Chatelier's principle, would the percent of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) that decomposes increase, decrease or stay the same if the mixture were transferred to a \(15.00-\mathrm{L}\) . vessel? (d) Use the equilibrium constant you calculated above to determine the percentage of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) that decomposes when 2.00 mol of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a \(15.00-\mathrm{L}\) vessel at 303 \(\mathrm{K}\) .
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