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Chapter 15: Problem 20

Which of the following statements are true and which are false? (a) For the reaction $2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2} \mathrm{~B}(g) K_{c}$ and \(K_{p}\) are numerically the same. (b) It is possible to distinguish \(K_{c}\) from \(K_{p}\) by comparing the units used to express the equilibrium constant. \((\mathbf{c})\) For the equilibrium in (a), the value of \(K_{c}\) increases with increasing pressure.

Short Answer

Expert verified
Statement (a) is false, as Kc and Kp are not numerically the same for the given reaction since \(\Delta n \neq 0\). Statement (b) is true, as Kc and Kp can be distinguished by their units. Statement (c) is false, as the value of Kc is not directly affected by changes in pressure but only by changes in temperature.

Step by step solution

01

a) Comparing Kc and Kp for the given reaction

For the given reaction, we have: \[2A(g) + B(g) \rightleftharpoons A_2B(g)\] Kc and Kp are related by the following equation: \[K_p = K_c(RT)^{\Delta n}\] where R is the gas constant, T is the temperature in Kelvin, and \(\Delta n\) is the change in the number of moles of gas in the balanced equation (products minus reactants). In this reaction, \(\Delta n = (1) - (2+1) = -2\). Since \(\Delta n\) is not equal to 0, Kc and Kp will not be numerically the same. Therefore, statement (a) is false.
02

b) Distinguishing Kc and Kp by their units

Kc and Kp are equilibrium constants that have different units. Kc is generally expressed in terms of concentrations (moles per liter, M) while Kp is expressed in terms of partial pressures (atmospheres, atm). It is indeed possible to distinguish between Kc and Kp by comparing the units used to express the equilibrium constant. Statement (b) is true.
03

c) Effect of increasing pressure on the value of Kc

For the given reaction, the value of Kc is not directly affected by changes in pressure. Kc can only be affected by changes in temperature. The position of equilibrium, however, can be affected by changes in pressure due to Le Chatelier's principle. In the given reaction, increasing pressure would shift the equilibrium towards the side with fewer moles of gas (the right side) in order to alleviate the increased pressure. This means that the amount of A2B would increase, while the amount of A and B would decrease. This change affects the ratio of concentrations at equilibrium, but the constant Kc itself would remain unchanged. So, statement (c) is false.

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Most popular questions from this chapter

For thereaction, at $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g), K_{c}=55.3\( at \)700 \mathrm{~K}$. In a 10.0-L flask containing an equilibrium mixture of the three gases, there are $1.30 \mathrm{~g} \mathrm{H}_{2}\( and \)21.0 \mathrm{~g} \mathrm{I}_{2}$. What is the mass of HI in the flask?

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?

At \(800 \mathrm{~K},\) the equilibrium constant for the reaction \(\mathrm{A}_{2}(g) \rightleftharpoons 2 \mathrm{~A}(g)\) is $K_{c}=3.1 \times 10^{-4}$. (a) Assuming both forward and reverse reactions are elementary reactions, which rate constant do you expect to be larger, \(k_{f}\) or \(k_{r} ?\) (b) If the value of $k_{f}=0.27 \mathrm{~s}^{-1}\(, what is the value of \)k_{r}\( at \)800 \mathrm{~K} ?$ (c) Based on the nature of the reaction, do you expect the forward reaction to be endothermic or exothermic? (d) If the temperature is raised to $1000 \mathrm{~K}\(, will the reverse rate constant \)k_{r}$ increase or decrease? Will the change in \(k_{r}\) be larger or smaller than the change in \(k_{f}\) ?

Bromine and hydrogen react in the gas phase to form hydrogen bromide: \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g) .\) The reaction enthalpy is \(\Delta H^{\circ}=-6 \mathrm{~kJ} .\) (a) To increase the equilibrium yield of hydrogen bromide would you use high or low temperature? (b) Could you increase the equilibrium yield of hydrogen bromide by controlling the pressure of this reaction? If so, would high or low pressure favor formation of \(\mathrm{HBr}(g) ?\)

Consider the reaction $\mathrm{IO}_{4}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\( \)\mathrm{H}_{4} \mathrm{IO}_{6}^{-}(a q) ; K_{c}=3.5 \times 10^{-2} .\( If you start with \)25.0 \mathrm{~mL}\( of a \)0.905 \mathrm{M}\( solution of \)\mathrm{NaIO}_{4}$, and then dilute it with water to \(500.0 \mathrm{~mL},\) what is the concentration of $\mathrm{H}_{4} \mathrm{IO}_{6}^{-}$ at equilibrium?
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