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Chapter 13: Problem 25

For the reaction $$ 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ it is determined that, at equilibrium at a particular temperature, the concentrations are as follows: \([\mathrm{NO}(g)]=8.1 \times 10^{-3}\) \(M,\left[\mathrm{H}_{2}(g)\right]=4.1 \times 10^{-5} M,\left[\mathrm{~N}_{2}(g)\right]=5.3 \times 10^{-2} M\), and \(\left[\mathrm{H}_{2} \mathrm{O}(g)\right]=2.9 \times 10^{-3} M .\) Calculate the value of \(K\) for the reaction at this temperature.

Short Answer

Expert verified
The value of the equilibrium constant (K) for the reaction at this temperature is approximately \(4.04 \times 10^{6}\).

Step by step solution

01

Identify the given concentrations

We are given the equilibrium concentrations for each substance as follows: $$[\text{NO}] = 8.1 \times 10^{-3}\,M$$ $$[\text{H}_2] = 4.1 \times 10^{-5}\,M$$ $$[\text{N}_2] = 5.3 \times 10^{-2}\,M$$ $$[\text{H}_2\text{O}] = 2.9 \times 10^{-3}\,M$$
02

Apply the equilibrium constant formula

Now we will use the formula for the equilibrium constant (K) and plug in the given concentrations: $$K = \frac{[\text{N}_2][\text{H}_2\text{O}]^2}{[\text{NO}]^2[\text{H}_2]^2}$$
03

Substitute the given concentrations

Replace the substance concentrations with their given values: $$K = \frac{(5.3 \times 10^{-2})(2.9 \times 10^{-3})^2}{(8.1 \times 10^{-3})^2(4.1 \times 10^{-5})^2}$$
04

Calculate the equilibrium constant (K)

Perform the calculations to find the value of K: $$K = \frac{(5.3 \times 10^{-2})(8.41 \times 10^{-6})}{(6.561 \times 10^{-5})(1.681 \times 10^{-9})}$$ $$K = \frac{4.4553 \times 10^{-7}}{1.10261 \times 10^{-13}}$$ $$K \approx 4.04 \times 10^{6}$$ The value of the equilibrium constant (K) for the reaction at this temperature is approximately \(4.04 \times 10^{6}\).

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Most popular questions from this chapter

Write expressions for \(K_{\mathrm{p}}\) for the following reactions. a. \(2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) b. \(\mathrm{CO}_{2}(g)+\mathrm{MgO}(s) \rightleftharpoons \mathrm{MgCO}_{3}(s)\) c. \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) d. \(4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g)\)

Write the equilibrium expression ( \(K\) ) for each of the following gas-phase reactions. a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) b. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) c. \(\mathrm{SiH}_{4}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)+2 \mathrm{H}_{2}(g)\) d. \(2 \mathrm{PBr}_{3}(g)+3 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{PCl}_{3}(g)+3 \mathrm{Br}_{2}(g)\)

At a particular temperature, \(12.0\) moles of \(\mathrm{SO}_{3}\) is placed into a 3.0-L rigid container, and the \(\mathrm{SO}_{3}\) dissociates by the reaction $$ 2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) $$ At equilibrium, \(3.0\) moles of \(\mathrm{SO}_{2}\) is present. Calculate \(K\) for this reaction.

At a particular temperature a \(2.00-\mathrm{L}\) flask at equilibrium contains \(2.80 \times 10^{-4}\) mole of \(\mathrm{N}_{2}, 2.50 \times 10^{-5}\) mole of \(\mathrm{O}_{2}\), and \(2.00 \times 10^{-2}\) mole of \(\mathrm{N}_{2} \mathrm{O}\). Calculate \(K\) at this temperature for the reaction $$ 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{~N}_{2} \mathrm{O}(g) $$ If \(\left[\mathrm{N}_{2}\right]=2.00 \times 10^{-4} M,\left[\mathrm{~N}_{2} \mathrm{O}\right]=0.200 M\), and \(\left[\underline{ \left.\mathrm{O}_{2}\right]}=\right.\) \(0.00245 M\), does this represent a system at equilibrium?

Consider the following reaction: $$ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) $$ Amounts of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2}\), and \(\mathrm{CO}_{2}\) are put into \(\underline{\mathrm{a}}\) flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive \({ }^{14} \mathrm{C}\), will \({ }^{14} \mathrm{C}\) be found only in CO molecules for an indefinite period of time? Explain.
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