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Chapter 15: Problem 72

If \(K_{c}=1\) for the equilibrium $3 \mathrm{~A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$, what is the relationship between [A] and [B] at equilibrium?

Short Answer

Expert verified
The relationship between the concentrations of A and B at equilibrium is: \[[B] = \sqrt{[A]^3}\]

Step by step solution

01

Write down the equilibrium constant expression

For the given equilibrium, we can write the Kc expression as follows: \[K_c = \frac{[B]^2}{[A]^3}\] Since we're given that Kc = 1 for this reaction, the equation becomes: \[1 = \frac{[B]^2}{[A]^3}\]
02

Solve for the relationship between [A] and [B]

To find the relationship between the concentrations of A and B, we simply solve the equation for one of the variables in terms of the other. In this case, let's solve for [B]^2: \[[B]^2 = [A]^3\] Now, we can find the relationship between [A] and [B] by taking the square root of both sides of the equation: \[[B] = \sqrt{[A]^3}\] This equation shows the relationship between the concentrations of A and B at equilibrium. That is, the concentration of B is equal to the square root of the cube of the concentration of A.

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Most popular questions from this chapter

For the reaction $\mathrm{I}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \operatorname{IBr}(g), K_{c}=310\( at \)140^{\circ} \mathrm{C}$. Suppose that \(1.00 \mathrm{~mol}\) IBr in a \(5.00-\mathrm{L}\) flask is allowed to reach equilibrium at \(140^{\circ} \mathrm{C}\). What are the equilibrium concentrations of \(\mathrm{IBr}, \mathrm{I}_{2},\) and \(\mathrm{Br}_{2}\) ?

How do the following changes affect the value of the \(K_{P}\) for a gas-phase endothermic reaction: (a) increase in the total pressure by adding a noble gas, \((\mathbf{b})\) addition of a reactant, \((\mathbf{c})\) increase in the temperature (d) increase in the volume, \((\mathbf{e})\) decrease in the temperature?

The equilibrium constant for the reaction $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ is \(K_{c}=1.3 \times 10^{-2}\) at \(1000 \mathrm{~K}\). (a) At this temperature does the equilibrium favor \(\mathrm{NO}\) and \(\mathrm{Br}_{2}\), or does it favor NOBr? (b) Calculate \(K_{c}\) for $2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) .$ (c) Calculate \(K_{c}\) for $\mathrm{NOBr}(g) \rightleftharpoons \mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)$.

Consider the equilibrium $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) $$ Calculate the equilibrium constant \(K_{p}\) for this reaction, given the following information (at \(298 \mathrm{~K}\) ): $$ \begin{array}{l} 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) \quad K_{c}=2.0 \\ 2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \quad K_{c}=2.1 \times 10^{30} \end{array} $$

Calculate \(K_{c}\) at \(900 \mathrm{~K}\) for $2 \mathrm{CO}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{C}(s)\( if \)K_{p}=0.0572$ at this temperature.
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