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Chapter 15: Problem 61

Consider the following exothermic equilibrium (Boudouard reaction) $$2 \mathrm{CO}(g) \rightleftharpoons \mathrm{C}(s)+\mathrm{CO}_{2}(g)$$ How will each of the following changes affect an equilibrium mixture of the three gases: (a) a catalyst is added to the mixture; $(\mathbf{b}) \mathrm{CO}_{2}(g)\( is added to the system; \)(\mathbf{c}) \mathrm{CO}(g)$ is added from the system; \((\mathbf{d})\) the reaction mixture is heated; (e) the volume of the reaction vessel is doubled; \((\mathbf{f})\) the total pressure of the system is increased by adding a noble gas?

Short Answer

Expert verified
(a) The equilibrium mixture remains unchanged. (b) The equilibrium shifts to the left, increasing the concentration of CO(g) and decreasing the concentration of C(s) and CO2(g). (c) The equilibrium shifts to the right, increasing the concentration of C(s) and CO2(g) and decreasing the concentration of CO(g). (d) The equilibrium shifts to the left, increasing the concentration of CO(g) and decreasing the concentration of C(s) and CO2(g). (e) The equilibrium shifts to the left, increasing the concentration of CO(g) and decreasing the concentration of C(s) and CO2(g). (f) Adding a noble gas has no effect on the equilibrium position or concentrations of the reactants or products.

Step by step solution

01

a) Addition of a catalyst

Adding a catalyst to the system speeds up both the forward and reverse reactions. However, it does not affect the position of the equilibrium. So in this case, the equilibrium mixture remains unchanged.
02

b) Adding CO2(g)

When CO2 is added to the system, according to Le Chatelier's principle, the equilibrium will shift in the direction that consumes the added substance. In this case, the equilibrium will shift to the left, increasing the concentration of CO(g) and decreasing the concentration of C(s) and CO2(g) until a new equilibrium is established.
03

c) Adding CO(g)

When CO(g) is added to the system, according to Le Chatelier's principle, the equilibrium will shift in the direction that consumes the added substance. In this case, the equilibrium will shift to the right, increasing the concentration of C(s) and CO2(g) and decreasing the concentration of CO(g) until a new equilibrium is established.
04

d) Heating the reaction mixture

As the given reaction is exothermic, heating the mixture will shift the equilibrium towards the endothermic direction (the reverse reaction) to counteract the change. In this case, the equilibrium will shift to the left, increasing the concentration of CO(g) and decreasing the concentration of C(s) and CO2(g) until a new equilibrium is established.
05

e) Doubling the volume of the reaction vessel

Doubling the volume of the reaction vessel reduces the pressure of the system. According to Le Chatelier's principle, the equilibrium will shift in the direction that increases the number of moles of gas. In this case, the equilibrium will shift to the left (as there are 2 moles of CO(g) on the left side and 1 mole of CO2(g) on the right side), increasing the concentration of CO(g) and decreasing the concentration of C(s) and CO2(g) until a new equilibrium is established.
06

f) Increasing the total pressure by adding a noble gas

Adding a noble gas to the system does not change the partial pressures of the original reactants or products, as noble gases do not interact with other chemicals in the reaction. Therefore, adding a noble gas will have no effect on the equilibrium position or the concentrations of the reactants or products.

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Most popular questions from this chapter

At \(1200 \mathrm{~K}\), the approximate temperature of automobile exhaust gases (Figure 15.15 ), \(K_{p}\) for the reaction $$2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)$$ is about \(1 \times 10^{-11}\). Assuming that the exhaust gas (total pressure \(101.3 \mathrm{kPa}\) ) contains \(0.2 \% \mathrm{CO}, 12 \% \mathrm{CO}_{2},\) and \(3 \% \mathrm{O}_{2}\) by volume, is the system at equilibrium with respect to the \(\mathrm{CO}_{2}\) reaction? Based on your conclusion, would the CO concentration in the exhaust be decreased or increased by a catalyst that speeds up the \(\mathrm{CO}_{2}\) reaction? Recall that at a fixed pressure and temperature, volume \(\%=\mathrm{mol} \%\).

The protein hemoglobin (Hb) transports \(\mathrm{O}_{2}\) in mammalian blood. Each Hb can bind \(4 \mathrm{O}_{2}\) molecules. The equilibrium constant for the \(\mathrm{O}_{2}\) binding reaction is higher in fetal hemoglobin than in adult hemoglobin. In discussing protein oxygen-binding capacity, biochemists use a measure called the \(P 50\) value, defined as the partial pressure of oxygen at which \(50 \%\) of the protein is saturated. Fetal hemoglobin has a \(\mathrm{P} 50\) value of \(2.53 \mathrm{kPa},\) and adult hemoglobin has a P50 value of \(3.57 \mathrm{kPa}\). Use these data to estimate how much larger \(K_{c}\) is for the aqueous reaction $4 \mathrm{O}_{2}(g)+\mathrm{Hb}(a q) \rightleftharpoons\left[\mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4}(a q)\right]\( in a fetus, compared to \)K_{c}$ for the same reaction in an adult.

At \(900^{\circ} \mathrm{C}, K_{p}=51.2\) for the equilibrium $$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ If the pressure of \(\mathrm{NO}(g)\) is half the pressure of \(\mathrm{NOBr}(g)\), what is the equilibrium pressure of \(\mathrm{Br}_{2}(g)\) ?

Consider the reaction $$\mathrm{CaSO}_{4}(s) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)$$ At \(25^{\circ} \mathrm{C}\), the equilibrium constant is $K_{c}=2.4 \times 10^{-5}\( for this reaction. (a) If excess \)\operatorname{CaSO}_{4}(s)$ is mixed with water at \(25^{\circ} \mathrm{C}\) to produce a saturated solution of \(\mathrm{CaSO}_{4},\) what are the equilibrium concentrations of \(\mathrm{Ca}^{2+}\) and \(\mathrm{SO}_{4}^{2-}\) ? (b) If the resulting solution has a volume of \(1.4 \mathrm{~L},\) what is the minimum mass of \(\operatorname{CaSO}_{4}(s)\) needed to achieve equilibrium?

(a) Is the dissociation of fluorine molecules into atomic fluorine, \(\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{~F}(g)\) an exothermic or endothermic process? (b) If the temperature is raised by \(100 \mathrm{~K}\), does the equilibrium constant for this reaction increase or decrease? (c) If the temperature is raised by \(100 \mathrm{~K},\) does the forward rate constant \(k_{f}\) increase by a larger or smaller amount than the reverse rate constant \(k_{r} ?\)
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