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Chapter 15: Problem 17

When the following reactions come to equilibrium, does the equilibrium mixture contain mostly reactants or mostly products? (a) \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) ; K_{c}=1.5 \times 10^{-10}\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) ; K_{p}=2.5 \times 10^{9}\)

Short Answer

Expert verified
For reaction (a), the equilibrium mixture will contain mostly reactants (N鈧� and O鈧�), as \(K_c = 1.5 \times 10^{-10} < 1\). For reaction (b), the equilibrium mixture will contain mostly products (SO鈧�), as \(K_p = 2.5 \times 10^{9} > 1\).

Step by step solution

01

Understand the equilibrium constant

The equilibrium constant (K) represents the ratio of the concentration of products to the concentration of reactants at equilibrium. If K > 1, the equilibrium mixture will contain mostly products; if K < 1, the equilibrium mixture will contain mostly reactants. (a) \(N_2(g) + O_2(g) \rightleftharpoons 2 NO(g) ; K_c = 1.5 \times 10^{-10}\)
02

Evaluate K for Reaction (a)

Since the equilibrium constant \(K_c = 1.5 \times 10^{-10} < 1\), the equilibrium mixture will contain mostly reactants. In this case, the mixture will primarily consist of N2 and O2. (b) \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) ; K_p = 2.5 \times 10^{9}\)
03

Evaluate K for Reaction (b)

For the second reaction, the equilibrium constant \(K_p = 2.5 \times 10^{9} > 1\). This means that the equilibrium mixture will contain mostly products. In this case, the equilibrium mixture will mostly consist of SO3.

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Most popular questions from this chapter

Consider the following equilibrium: $$ 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g) \quad K_{c}=1.08 \times 10^{7} \text { at } 700{ }^{\circ} \mathrm{C} $$ (a) Calculate \(K_{p-}\) (b) Does the equilibrium mixture contain mostly \(\mathrm{H}_{2}\) and \(\mathrm{S}_{2}\) or mostly \(\mathrm{H}_{2} \mathrm{~S}\) ? (c) Calculate the value of \(K_{c}\) if you rewrote the equation \(\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{~S}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{~S}(g)\).

Solid \(\mathrm{NH}_{4} \mathrm{SH}\) is introduced into an evacuated flask at \(24^{\circ} \mathrm{C}\). The following reaction takes place: $$ \mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g) $$ At equilibrium, the total pressure (for \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{~S}\) taken together) is \(0.614 \mathrm{~atm}\). What is \(K_{p}\) for this equilibrium at \(24^{\circ} \mathrm{C}\) ?

Consider the hypothetical reaction \(\mathrm{A}(\mathrm{g})+2 \mathrm{~B}(\mathrm{~g}) \rightleftharpoons\) \(2 \mathrm{C}(g)\), for which \(K_{c}=0.25\) at a certain temperature. A \(1.00-\mathrm{L}\) reaction vessel is loaded with \(1.00 \mathrm{~mol}\) of compound \(\mathrm{C}\), which is allowed to reach equilibrium. Let the variable \(x\) represent the number of \(\mathrm{mol} / \mathrm{L}\) of compound \(\mathrm{A}\) present at equilibrium. (a) In terms of \(x\), what are the equilibrium concentrations of compounds \(B\) and \(C\) ? (b) What limits must be placed on the value of \(x\) so that all concentrations are positive? (c) By putting the equilibrium concentrations (in terms of \(x\) ) into the equilibriumconstant expression, derive an equation that can be solved for \(x\). (d) The equation from part (c) is a cubic equation (one that has the form \(a x^{3}+b x^{2}+c x+d=0\) ). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of \(x\) that you specified in part (b). The point at which the cubic equation crosses the \(x\)-axis is the solution. (e) From the plot in part (d), estimate the equilibrium concentrations of \(A, B\), and \(C\). (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

(a) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (b) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of \(Q_{c}\) at this point in the reaction?

A sample of nitrosyl bromide (NOBr) decomposes according to the equation $$ 2 \operatorname{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) $$ An equilibrium mixture in a \(5.00-\mathrm{L}\) vessel at \(100^{\circ} \mathrm{C}\) contains \(3.22 \mathrm{~g}\) of \(\mathrm{NOBr}, 3.08 \mathrm{~g}\) of \(\mathrm{NO}\), and \(4.19 \mathrm{~g}^{2}\) of \(\mathrm{Br}_{2}\). (a) Calculate \(K_{c}\). (b) What is the total pressure exerted by the mixture of gases? (c) What was the mass of the original sample of NOBr?
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