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Chapter 12: Problem 101

At \(35^{\circ} \mathrm{C}, K=1.6 \times 10^{-5}\) for the reaction $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$.If 2.0 moles of \(\mathrm{NO}\) and 1.0 mole of \(\mathrm{Cl}_{2}\) are placed into a \(1.0-\mathrm{L}\) flask, calculate the equilibrium concentrations of all species.

Short Answer

Expert verified
The equilibrium concentrations of NOCl, NO, and Cl₂ are 0.074 mol/L, 1.926 mol/L, and 0.963 mol/L, respectively.

Step by step solution

01

Write the balanced reaction equation

The balanced reaction equation is given as: \[2\mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\]
02

Set up an ICE table

Using the given information, we can set up an ICE table to keep track of the concentrations: | | NOCl | NO | Cl₂ | |---------|-------|------|-------| | Initial | 0 | 2.0 | 1.0 | | Change | +2x | -2x | -x | | Equil. | 2x | 2-2x | 1-x | In which x stands for the change in concentration.
03

Write the equilibrium expression

The equilibrium constant K expression is: \[K = \frac{[\mathrm{NO}]^2[\mathrm{Cl}_{2}]}{[\mathrm{NOCl}]^2}\]
04

Substitute equilibrium concentrations into the expression

Substitute equilibrium concentrations from the ICE table into the equilibrium constant expression and the given K value: \[1.6 \times 10^{-5} = \frac{(2- 2x)^2(1-x)}{(2x)^2}\]
05

Solve for x

Solve for x: \[x = 0.037\]
06

Calculate the equilibrium concentrations

Substitute the value of x back into the equilibrium row of the ICE table and calculate the equilibrium concentrations of all species: - Equilibrium concentration of NOCl = 2x = 2(0.037) = 0.074 mol/L - Equilibrium concentration of NO = 2 - 2x = 2 - 2(0.037) = 1.926 mol/L - Equilibrium concentration of Cl₂ = 1 - x = 1 - 0.037 = 0.963 mol/L So, the equilibrium concentrations of NOCl, NO, and Cl₂ are 0.074 mol/L, 1.926 mol/L, and 0.963 mol/L, respectively.

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Most popular questions from this chapter

For a typical equilibrium problem, the value of \(K\) and the initial reaction conditions are given for a specific reaction, and you are asked to calculate the equilibrium concentrations. Many of these calculations involve solving a quadratic or cubic equation. What can you do to avoid solving a quadratic or cubic equation and still come up with reasonable equilibrium concentrations?

Consider the reaction \(\mathrm{A}(g)+2 \mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g)\) in a 1.0-L rigid flask. Answer the following questions for each situation (a-d): i. Estimate a range (as small as possible) for the requested substance. For example, [A] could be between \(95 M\) and \(100 M\),ii. Explain how you decided on the limits for the estimated range. iii. Indicate what other information would enable you to narrow your estimated range. iv. Compare the estimated concentrations for a through d, and explain any differences. a. If at equilibrium \([\mathrm{A}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for [A] once equilibrium is reestablished. b. If at equilibrium \([\mathrm{B}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for \([\mathbf{B}]\) once equilibrium is reestablished. c. If at equilibrium \([\mathrm{C}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for \([\mathrm{C}]\) once equilibrium is reestablished. d. If at equilibrium \([\mathrm{D}]=1 M,\) and then 1 mole of \(\mathrm{C}\) is added, estimate the value for [D] once equilibrium is reestablished.

Lexan is a plastic used to make compact discs, eyeglass lenses, and bulletproof glass. One of the compounds used to make Lexan is phosgene \(\left(\mathrm{COCl}_{2}\right),\) an extremely poisonous gas. Phosgene decomposes by the reaction,$$\operatorname{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)$$,for which \(K_{\mathrm{p}}=6.8 \times 10^{-9}\) at \(100^{\circ} \mathrm{C}\). If pure phosgene at an initial pressure of 1.0 atm decomposes, calculate the equilibrium pressures of all species.

Le Châtelier's principle is stated (Section \(12-7\) ) as follows: "If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change." The system \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) is used as an example in which the addition of nitrogen gas at equilibrium results in a decrease in \(\mathrm{H}_{2}\) concentration and an increase in \(\mathrm{NH}_{3}\) concentration. In the experiment the volume is assumed to be constant. On the other hand, if \(\mathrm{N}_{2}\) is added to the reaction system in a container with a piston so that the pressure can be held constant, the amount of \(\mathrm{NH}_{3}\) actually could decrease, and the concentration of \(\mathrm{H}_{2}\) would increase as equilibrium is reestablished. Explain how this can happen. Also, if you consider this same system at equilibrium, the addition of an inert gas, holding the pressure constant, does affect the equilibrium position. Explain why the addition of an inert gas to this system in a rigid container does not affect the equilibrium position.

At \(125^{\circ} \mathrm{C}, K_{\mathrm{p}}=0.25\) for the reaction $$2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$.A 1.00 -L flask containing \(10.0 \mathrm{g}\) NaHCO \(_{3}\) is evacuated and heated to \(125^{\circ} \mathrm{C}\) a. Calculate the partial pressures of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) after equilibrium is established. b. Calculate the masses of \(\mathrm{NaHCO}_{3}\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) present at equilibrium. c. Calculate the minimum container volume necessary for all of the \(\mathrm{NaHCO}_{3}\) to decompose.
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