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Chapter 13: Problem 101

For the reaction: $$3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g)$$ \(K=1.8 \times 10^{-7}\) at a certain temperature. If at equilibrium \(\left[\mathrm{O}_{2}\right]=0.062 M,\) calculate the equilibrium \(\mathrm{O}_{3}\) concentration.

Short Answer

Expert verified
The equilibrium concentration of O₃ is \(2.06 \times 10^{-6}\,M\).

Step by step solution

01

Write down the equilibrium constant expression

Based on the chemical reaction, we can write the equilibrium constant as: \[K = \frac{[\mathrm{O}_3]^2}{[\mathrm{O}_2]^3}\] where \([\mathrm{O}_3]\) and \([\mathrm{O}_2]\) are the equilibrium concentrations of O₃ and O₂, respectively.
02

Plug in the given values

We are given that at equilibrium, \([\mathrm{O}_2] = 0.062\, M\) and the equilibrium constant \(K = 1.8 \times 10^{-7}\). Substitute these values into the equilibrium constant expression: \(1.8 \times 10^{-7} = \frac{[\mathrm{O}_3]^2}{(0.062)^3}\)
03

Calculate the equilibrium concentration of O₃

Solve for \([\mathrm{O}_3]\): \[\begin{aligned} [\mathrm{O}_3]^2 &= 1.8 \times 10^{-7} \times (0.062)^3 \\ [\mathrm{O}_3]^2 &= 4.23 \times 10^{-11} \\ [\mathrm{O}_3] &= \sqrt{4.23 \times 10^{-11}} \end{aligned}\] Calculate the square root: \[[\mathrm{O}_3] = 2.06 \times 10^{-6}\,M\]
04

State the equilibrium concentration of O₃

The equilibrium concentration of O₃ is \(2.06 \times 10^{-6}\,M\).

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Most popular questions from this chapter

The equilibrium constant is 0.0900 at \(25^{\circ} \mathrm{C}\) for the reaction $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)$$ For which of the following sets of conditions is the system at equilibrium? For those that are not at equilibrium, in which direction will the system shift? a. A 1.0 -L flask contains 1.0 mole of HOCl, 0.10 mole of $\mathrm{Cl}_{2} \mathrm{O}\( , and 0.10 mole of \)\mathrm{H}_{2} \mathrm{O}$ . b. A 2.0 -L flask contains 0.084 mole of HOCl, 0.080 mole of $\mathrm{Cl}_{2} \mathrm{O}\( , and 0.98 mole of \)\mathrm{H}_{2} \mathrm{O}$ . c. A 3.0 - flask contains 0.25 mole of HOCl, 0.0010 mole of $\mathrm{Cl}_{2} \mathrm{O},\( and 0.56 mole of \)\mathrm{H}_{2} \mathrm{O}$ .

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Suppose a reaction has the equilibrium constant \(K=1.3 \times 10^{8} .\) What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached? Is this reaction likely to be a good source of the products?

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