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Chapter 15: Problem 30

For the synthesis of ammonia $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ the equilibrium constant \(K_{\mathrm{c}}\) at \(375^{\circ} \mathrm{C}\) is \(1.2 .\) Starting with \(\left[\mathrm{H}_{2}\right]_{0}=0.76 \mathrm{M},\left[\mathrm{N}_{2}\right]_{0}=0.60 \mathrm{M},\) and \(\left[\mathrm{NH}_{3}\right]_{0}=0.48 M,\) when this mixture comes to equilibrium, which gases will have increased in concentration and which will have decreased in concentration?

Short Answer

Expert verified
When the mixture comes to equilibrium, the concentrations of \(N_{2}(g)\) and \(H_{2}(g)\) will decrease while the concentration of \(NH_{3}(g)\) will increase.

Step by step solution

01

Calculating the Reaction Quotient Qc

The reaction quotient (Qc) is a measure of the relative amounts of products and reactants present during a reaction at a particular instant. It is given by: \(Q_c = \frac{[NH_{3}]^2}{[N_{2}][H_{2}]^3}\). Substitute the initial concentrations into the equation: \(Q_c = \frac{(0.48)^2}{(0.60)*(0.76)^3} = 0.43. \)
02

Comparing Qc with Kc

The given equilibrium constant (Kc) at \(375^{\circ}C\) is 1.2. Compare the reaction quotient Qc with the equilibrium constant Kc. Since \(Q_c (0.43) < K_c (1.2)\), the reaction is not at equilibrium and will shift to the right (towards greater product concentrations) to adjust and reach equilibrium.
03

Determine the changes in concentration

The reaction shifts towards the product, meaning more reactants are converted into products. As a result, the concentrations of reactants \(N_{2}(g)\) and \(H_{2}(g)\) will decrease, while the concentration of the product \(NH_{3}(g)\) will increase.

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Most popular questions from this chapter

Use Le Châtelier's principle to explain why the equilibrium vapor pressure of a liquid increases with increasing temperature.

Pure phosgene gas \(\left(\mathrm{COCl}_{2}\right), 3.00 \times 10^{-2} \mathrm{~mol}\), was placed in a 1.50 - \(\mathrm{L}\) container. It was heated to \(800 \mathrm{~K}\), and at equilibrium the pressure of \(\mathrm{CO}\) was found to be 0.497 atm. Calculate the equilibrium constant \(K_{P}\) for the reaction $$ \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) $$

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