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Chapter 15: Problem 70

If \(K_{c}=1\) for the equilibrium \(2 \mathrm{~A}(g) \rightleftharpoons \mathrm{B}(g)\), what is the relationship between \([\mathrm{A}]\) and \([\mathrm{B}]\) at equilibrium?

Short Answer

Expert verified
The relationship between the concentrations of A and B at equilibrium is \[[A]^2 = [B]\], given that the equilibrium constant \(K_c = 1\) for the reaction \(2A(g) \rightleftharpoons B(g)\).

Step by step solution

01

Write the equilibrium expression.

The equilibrium expression for the reaction 2A(g) ⇌ B(g) is given by: \[K_c = \frac{[B]}{[A]^2}\] This expression gives us the relation between the concentrations of A, B, and the equilibrium constant Kc at equilibrium.
02

Substitute the given values.

We are given that the equilibrium constant Kc is equal to 1. Now, we can substitute this value into the equilibrium expression along with the unknown equilibrium concentrations of A (represented by [A]) and B (represented by [B]): \[1 = \frac{[B]}{[A]^2}\]
03

Solve the equation for the relationship between the concentrations of A and B at equilibrium.

The goal of this step is to find the relationship between [A] and [B] at equilibrium. To do this, we can rearrange the equation from step 2: \[1 = \frac{[B]}{[A]^2}\] Multiplying both sides by \([A]^2\): \[[A]^2 = [B]\] This is the relationship between the concentrations of A and B at equilibrium.

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Most popular questions from this chapter

For a certain gas-phase reaction, the fraction of products in an equilibrium mixture is increased by either increasing the temperature or by increasing the volume of the reaction vessel. (a) Is the reaction exothermic or endothermic? (b) Does the balanced chemical equation have more molecules on the reactant side or product side?

The following equilibria were attained at \(823 \mathrm{~K}\) : $$\begin{aligned} \mathrm{CoO}(s)+\mathrm{H}_{2}(g) & \rightleftharpoons \mathrm{Co}(s)+\mathrm{H}_{2} \mathrm{O}(g) & K_{c} &=67 \\ \mathrm{CoO}(s)+\mathrm{CO}(g) & \rightleftharpoons \mathrm{Co}(s)+\mathrm{CO}_{2}(g) & K_{c} &=490 \end{aligned}$$ Based on these equilibria, calculate the equilibrium constant $$\text { for } \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \text { at } 823 \mathrm{~K} \text { . }$$

The following graph represents the yield of the compound \(\mathrm{AB}\) at equilibrium in the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow \mathrm{AB}(g)\) at two different pressures, \(x\) and \(y\), as a function of temperature. (a) Is this reaction exothermic or endothermic? (b) Is \(P=x\) greater or smaller than $P=y ?

Methane, \(\mathrm{CH}_{4}\), reacts with \(\mathrm{I}_{2}\) according to the reaction \(\mathrm{CH}_{4}(g)+\mathrm{l}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{l}(g)+\mathrm{HI}(g) .\) At \(630 \mathrm{~K}, K_{p}\) for this reaction is \(2.26 \times 10^{-4}\). A reaction was set up at \(630 \mathrm{~K}\) with initial partial pressures of methane of 105.1 torr and of 7.96 torr for \(\mathrm{I}_{2}\). Calculate the pressures, in torr, of all reactants and products at equilibrium.

Consider the following equilibrium: \(2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g) \quad K_{c}=1.08 \times 10^{7}\) 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 values of \(\mathrm{K}_{c}\) and \(K_{p}\) if you rewrote the balanced chemical equation with \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2}(g)\) instead of \(2 \mathrm{~mol}\).
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