Nitric oxide (NO) reacts readily with chlorine gas as follows: $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) $$ At \(700 \mathrm{~K}\) the equilibrium constant \(K_{p}\) for this reaction is \(0.26 .\) Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) \(P_{\mathrm{NO}}=0.15 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.31 \mathrm{~atm},\) and \(P_{\mathrm{NOCl}}=0.11 \mathrm{~atm} ;\) (b) \(P_{\mathrm{NO}}=0.12 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.10 \mathrm{~atm},\) and \(P_{\mathrm{NOCl}}=0.050 \mathrm{~atm} ;\) (c) \(P_{\mathrm{NO}}=0.15 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.20 \mathrm{~atm},\) and \(P_{\mathrm{NOCl}}=5.10 \times\) \(10^{-3}\) atm.

Step by step solution

01

Write down the given information

We have the following balanced chemical equation, equilibrium constant, and three mixtures: Equation: \(2 \mathrm{NO}(g) + \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) Equilibrium constant at 700 K: \(K_p = 0.26\) Mixture (a): \(P_{\mathrm{NO}} = 0.15 \mathrm{~atm}\), \(P_{\mathrm{Cl}_{2}} = 0.31 \mathrm{~atm}\), and \(P_{\mathrm{NOCl}} = 0.11 \mathrm{~atm}\) Mixture (b): \(P_{\mathrm{NO}} = 0.12 \mathrm{~atm}\), \(P_{\mathrm{Cl}_{2}} = 0.10 \mathrm{~atm}\), and \(P_{\mathrm{NOCl}} = 0.050 \mathrm{~atm}\) Mixture (c): \(P_{\mathrm{NO}} = 0.15 \mathrm{~atm}\), \(P_{\mathrm{Cl}_{2}} = 0.20 \mathrm{~atm}\), and \(P_{\mathrm{NOCl}} = 5.10 \times 10^{-3} \mathrm{~atm}\)

02

Calculate the reaction quotient, Qp, for each mixture

For the given reaction, the reaction quotient Qp can be calculated as follows: \(Q_p = \frac{P_{\mathrm{NOCl}}^2}{P_{\mathrm{NO}}^2 \times P_{\mathrm{Cl}_{2}}}\) Mixture (a): \(Q_p = \frac{(0.11)^2}{(0.15)^2 \times 0.31} \approx 0.182\) Mixture (b): \(Q_p = \frac{(0.050)^2}{(0.12)^2 \times 0.10} \approx 0.173\) Mixture (c): \(Q_p = \frac{(5.10 \times 10^{-3})^2}{(0.15)^2 \times 0.20} \approx 0.00114\)

03

Compare Qp and Kp for each mixture to determine equilibrium status

If Qp = Kp, the mixture is at equilibrium. If Qp > Kp, the mixture will shift toward reactants. If Qp < Kp, the mixture will shift toward products. Mixture (a): Qp (0.182) < Kp (0.26), so the reaction will shift towards products. Mixture (b): Qp (0.173) < Kp (0.26), so the reaction will shift towards products. Mixture (c): Qp (0.00114) < Kp (0.26), so the reaction will shift towards products.

04

Summarize the findings for each mixture

For each mixture, the reaction is not at equilibrium and will need to produce more products to reach equilibrium. (a) More products needed (b) More products needed (c) More products needed

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!