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Chapter 14: Problem 69

Consider the following reaction at equilibrium: $$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$$ From the data shown here, calculate the equilibrium constant (both \(K_{P}\) and \(K_{\mathrm{c}}\) ) at each temperature. Is the reaction endothermic or exothermic? $$ \begin{array}{clr} \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & {[\mathrm{A}](M)} & {[\mathrm{B}](M)} \\ 200 & 0.0125 & 0.843 \\ 300 & 0.171 & 0.764 \\ 400 & 0.250 & 0.724 \end{array} $$

Short Answer

Expert verified
After calculating the equilibrium constants, observe their temperature dependence to determine if the reaction is endothermic or exothermic. In an endothermic reaction, \( K_{\mathrm{c}} \) increases as the temperature increases, while in an exothermic reaction, \( K_{\mathrm{c}} \) decreases as the temperature increases.

Step by step solution

01

Understanding the Equilibrium Constants

For any chemical reaction, the equilibrium constant refers to the ratio of concentrations of the products to the reactants, each raised to the power equals to the stoichiometric coefficients at equilibrium. The equilibrium constant can be calculated using concentrations, denoted as \(K_{\mathrm{c}}\), or partial pressures, denoted as \(K_{P}\). In this exercise, the given reaction is: \(\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)\), with each compound's concentrations given at different temperatures.
02

Calculate the Equilibrium Constants

Starting with the equilibrium constant in terms of concentration, we have \[ K_{\mathrm{c}} = \frac{[\mathrm{B}]^2}{[\mathrm{A}]} \] We substitute the concentrations at each given temperature into the equation and calculate \( K_{\mathrm{c}} \) for each temperature. Equilibrium constant in terms of pressure, \( K_{\mathrm{P}} \), is not relevant in this case as we deal with concentrations and not pressures.
03

Determine if the Reaction is Endothermic or Exothermic

From the equilibrium constants calculated, if \( K_{\mathrm{c}} \) increases with the temperature, then the reaction is endothermic, since adding heat shifts the equilibrium to the right (to the products), resulting in a larger value of \( K_{\mathrm{c}} \). If the \( K_{\mathrm{c}} \) value decreases with temperature, then the reaction is exothermic, because adding heat shifts the equilibrium to the left (the reactants), leading to a smaller value of \( K_{\mathrm{c}} \).

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Most popular questions from this chapter

Based on rate constant considerations, explain why the equilibrium constant depends on temperature.

Heating solid sodium bicarbonate in a closed vessel establishes the following equilibrium: $$2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g)$$ What would happen to the equilibrium position if (a) some of the \(\mathrm{CO}_{2}\) were removed from the system; (b) some solid \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) were added to the system; (c) some of the solid \(\mathrm{NaHCO}_{3}\) were removed from the system? The temperature remains constant.

Write equilibrium constant expressions for \(K_{\mathrm{c}},\) and for \(K_{P}\), if applicable, for the following processes: (a) \(2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)\) (b) \(3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g)\) (c) \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)\) (d) \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) (e) \(\mathrm{HCOOH}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HCOO}^{-}(a q)\) (f) \(2 \mathrm{HgO}(s) \rightleftharpoons 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\)

Write the expressions for the equilibrium constants \(K_{P}\) of the following thermal decomposition reactions: (a) \(2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons\) $$\mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ (b) \(2 \mathrm{CaSO}_{4}(s) \rightleftharpoons\) $$2 \mathrm{CaO}(s)+2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$

Determine the initial and equilibrium concentrations of HI if the initial concentrations of \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) are both \(0.16 M\) and their equilibrium concentrations are both \(0.072 M\) at \(430^{\circ} \mathrm{C}\). The equilibrium constant \(\left(K_{\mathrm{c}}\right)\) for the reaction \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)\) is 54.2 at \(430^{\circ} \mathrm{C}\)
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