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Chapter 15: Problem 36

\(1.00 \mathrm{g}\) each of \(\mathrm{CO}, \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{H}_{2}\) are sealed in a \(1.41 \mathrm{L}\) vessel and brought to equilibrium at 600 K. How many grams of \(\mathrm{CO}_{2}\) will be present in the equilibrium mixture? $$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=23.2$$

Short Answer

Expert verified
The mass of \(\mathrm{CO}_2\) in the equilibrium mixture cannot be determined without further calculations and it will depend on the computed positive value of x in step 4.

Step by step solution

01

Calculating Initial Moles

Calculate the initial moles of the reactants and products. Use the molar mass of the substances to convert the grams to moles. For \(\mathrm{CO}\): \(\frac{1.00 \, \mathrm{g}}{28.01 \, \mathrm{g/mol}} \approx 0.036 \, \mathrm{mol}\)For \(\mathrm{H_2O}\): \(\frac{1.00 \, \mathrm{g}}{18.02 \, \mathrm{g/mol}} \approx 0.055 \, \mathrm{mol}\)For \(\mathrm{H_2}\) and \(\mathrm{CO}_2\): Initially, these are 0 as the reaction hasn't started yet.
02

Write the ICE Table

Set up an ICE (Initial, Change, Equilibrium) table to determine the changes in the moles at equilibrium. The reaction is \(\mathrm{CO}\) + \(\mathrm{H_2O}\) ⇌ \(\mathrm{CO}_2\) + \(\mathrm{H_2}\). The change in moles during the reaction is represented as x. At equilibrium, there is -x change for reactants and +x change for the products.
03

Use the Equilibrium Constant

Use the equilibrium constant expression to write the equation. \(K_c\) equals the ratio of the product concentrations to the reactant concentrations, each raised to the power equal to their coefficients in the balanced equation. Given \(K_c = 23.2\), we can write: \[23.2 = \frac{[(0+x)(0+x)]}{[(0.036-x)(0.055-x)]}\]
04

Solve for x

This is a quadratic equation, rewrite it as one and solve for x. You will get two values. Choose the value that makes physical sense (moles cannot be negative).
05

Find the mass of \(\mathrm{CO}_2\)

Substitute x into the equilibrium moles of \(\mathrm{CO}_2\) to get the moles of \(\mathrm{CO}_2\) at equilibrium. Convert this amount into grams by using the molar mass of \(\mathrm{CO}_2\) (about 44.01 g/mol). The result will give you the mass of \(\mathrm{CO}_2\) at equilibrium.

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Most popular questions from this chapter

For the following reaction, \(K_{\mathrm{c}}=2.00\) at \(1000^{\circ} \mathrm{C}\) $$2 \operatorname{COF}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{CF}_{4}(\mathrm{g})$$ If a \(5.00 \mathrm{L}\) mixture contains \(0.145 \mathrm{mol} \mathrm{COF}_{2}, 0.262 \mathrm{mol}\) \(\mathrm{CO}_{2},\) and \(0.074 \mathrm{mol} \mathrm{CF}_{4}\) at a temperature of \(1000^{\circ} \mathrm{C}\) (a) Will the mixture be at equilibrium? (b) If the gases are not at equilibrium, in what direction will a net change occur? (c) How many moles of each gas will be present at equilibrium?

An equilibrium mixture of \(\mathrm{SO}_{2}, \mathrm{SO}_{3},\) and \(\mathrm{O}_{2}\) gases is maintained in a \(2.05 \mathrm{L}\) flask at a temperature at which \(K_{\mathrm{c}}=35.5\) for the reaction $$2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})$$ (a) If the numbers of moles of \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\) in the flask are equal, how many moles of \(\mathrm{O}_{2}\) are present? (b) If the number of moles of \(\mathrm{SO}_{3}\) in the flask is twice the number of moles of \(\mathrm{SO}_{2}\), how many moles of \(\mathrm{O}_{2}\) are present?

The following data are given at \(1000 \mathrm{K}: \mathrm{CO}(\mathrm{g})+\) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) ; \quad \Delta H^{\circ}=-42 \mathrm{k} \mathrm{J}\) \(K_{\mathrm{c}}=0.66 .\) After an initial equilibrium is established in a \(1.00 \mathrm{L}\) container, the equilibrium amount of \(\mathrm{H}_{2}\) can be increased by (a) adding a catalyst; (b) increasing the temperature; (c) transferring the mixture to a 10.0 L container; (d) in some way other than (a), (b), Or (c).

A mixture of \(1.00 \mathrm{g} \mathrm{H}_{2}\) and \(1.06 \mathrm{g} \mathrm{H}_{2} \mathrm{S}\) in a 0.500 Lflask comes to equilibrium at \(1670 \mathrm{K}: 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{S}_{2}(\mathrm{g}) \rightleftharpoons\) \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) .\) The equilibrium amount of \(\mathrm{S}_{2}(\mathrm{g})\) found is \(8.00 \times 10^{-6}\) mol. Determine the value of \(K_{p}\) at 1670 K.

In the Ostwald process for oxidizing ammonia, a variety of products is possible- \(\mathrm{N}_{2}, \mathrm{N}_{2} \mathrm{O}, \mathrm{NO},\) and \(\mathrm{NO}_{2}-\) depending on the conditions. One possibility is $$\begin{aligned} \mathrm{NH}_{3}(\mathrm{g})+\frac{5}{4} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g}) &+\frac{3}{2} \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ K_{\mathrm{p}} &=2.11 \times 10^{19} \mathrm{at} 700 \mathrm{K} \end{aligned}$$ For the decomposition of \(\mathrm{NO}_{2}\) at \(700 \mathrm{K}\) $$\mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad K_{\mathrm{p}}=0.524$$ (a) Write a chemical equation for the oxidation of \(\mathrm{NH}_{3}(\mathrm{g})\) to \(\mathrm{NO}_{2}(\mathrm{g})\) (b) Determine \(K_{\mathrm{p}}\) for the chemical equation you have written.
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