Judging Whether a Mixture Is at Equilibrium The following pictures represent mixtures of A molecules (red spheres) and B molecules (blue spheres), which interconvert according to the equation A ⇔ B. If mixture (1) is at equilibrium, which of the other mixtures are also at equilibrium? Explain.

Question

Judging Whether a Mixture Is at Equilibrium

The following pictures represent mixtures of A molecules (red spheres) and B molecules (blue spheres), which interconvert according to the equation A [latex]\rightleftharpoons[/latex] B. If mixture (1) is at equilibrium, which of the other mixtures are also at equilibrium? Explain.

STRATEGY

The equilibrium constant for the reaction is given by [latex]K_c[/latex] = [B]/[A], where the concentrations are equilibrium concentrations in units of mol/L. Since the equilibrium-constant expression has the same number of concentration terms in the numerator and denominator, the volume cancels and [latex]K_c[/latex] = (moles of B)/(moles of A). Because the number of moles is directly proportional to the number of molecules, [latex]K_c[/latex] = (molecules of B)/(molecules of A) in the equilibrium mixture, mixture (1). To determine whether the other mixtures are at equilibrium, count the number of molecules and compare the B/A ratio in mixtures (2)–(4) with the B/A ratio in the equilibrium mixture.

Accepted Answer

For mixture (1), [latex]K_{\mathrm{c}}=[\mathrm{B}] /[\mathrm{A}]=2 / 6=1 / 3[/latex]

For mixture (2), [latex][\mathrm{B}] /[\mathrm{A}]=4 / 4=1 eq K_c .[/latex]

For mixture (3), [latex][\mathrm{B}] /[\mathrm{A}]=3 / 9=1 / 3=K_{\mathrm{c}}[/latex]

For mixture (4), [latex][\mathrm{B}] /[\mathrm{A}]=9 / 3=3 eq K_{\mathrm{c}}[/latex]

Mixture (3) is at equilibrium, but mixtures (2) and (4) are not at equilibrium because their equilibrium-constant expressions [B]/[A] do not equal [latex]K_c[/latex].

Chapter 13

Q. 13.4

Q. 13.4

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