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Chapter 13: Problem 55

An initial mixture of nitrogen gas and hydrogen gas is reacted in a rigid container at a certain temperature by the reaction $$3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ At equilibrium, the concentrations are $\left[\mathrm{H}_{2}\right]=5.0 M,\left[\mathrm{N}_{2}\right]=$ \(8.0 M,\) and \(\left[\mathrm{NH}_{3}\right]=4.0 \mathrm{M} .\) What were the concentrations of nitrogen gas and hydrogen gas that were reacted initially?

Short Answer

Expert verified
The initial concentration of hydrogen gas (H2) was 11 mol/L, and the initial concentration of nitrogen gas (N2) was 10 mol/L.

Step by step solution

01

Set up the equilibrium constant and balance the equation

First, balance the given chemical equation: \[ 3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \] Then, write down the equilibrium constant expression for this reaction: \[ K_{c} = \frac{\left[\mathrm{NH}_{3}\right]^{2}}{\left[\mathrm{H}_{2}\right]^{3} \left[\mathrm{N}_{2}\right]} \]
02

Let the initial concentrations be x and y

Let the initial concentrations of hydrogen gas and nitrogen gas be x mol/L and y mol/L, respectively.
03

Set up the reaction table for the stoichiometry

Set up an ICE (Initial, Change, Equilibrium) table to represent the changes from the initial concentrations to the equilibrium concentrations: | Substance | Initial (mol/L) | Change (mol/L) | Equilibrium (mol/L) | |---|---|---|---| | H2 | x | -3z | 5 | | N2 | y | -z | 8 | | NH3 | 0 | 2z | 4 | Where z represents the change that occurred in the concentrations during the reaction.
04

Calculate z from the given equilibrium concentrations

We can now use the equilibrium concentrations to solve for z: \[5 = x - 3z\] \[8 = y - z\] \[4 = 2z\] From the last equation, we can find the value of z: \[ z = \frac{4}{2} = 2 \]
05

Find the initial concentrations of H2 and N2

Using the value of z, we can now find the initial concentrations of hydrogen gas (x) and nitrogen gas (y): For H2: \[ x = 5 + 3z = 5 + 3(2) = 5 + 6 = 11 \ \text{mol/L} \] For N2: \[ y = 8 + z = 8 + 2 = 10 \ \text{mol/L} \] So, the initial concentration of hydrogen gas was 11 mol/L, and the initial concentration of nitrogen gas was 10 mol/L.

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Most popular questions from this chapter

The reaction $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ has \(K_{\mathrm{p}}=109\) at \(25^{\circ} \mathrm{C}\) . If the equilibrium partial pressure of \(\mathrm{Br}_{2}\) is 0.0159 atm and the equilibrium partial pressure of NOBr is 0.0768 atm, calculate the partial pressure of \(\mathrm{NO}\) at equilibrium.

The reaction $$\mathrm{NH}_{4} \mathrm{SH}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g)$$ has \(K_{\mathrm{p}}=0.10\) at \(27^{\circ} \mathrm{C} .\) What is the minimum amount of \(\mathrm{NH}_{4} \mathrm{SH}\) that must be present for this reaction to be at equilibrium in a 10.0 \(\mathrm{-L}\) container?

Le Chatelier's principle is stated (Section 13.7\()\) 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 a particular temperature, \(K=3.75\) for the reaction $$\mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g)$$ If all four gases had initial concentrations of \(0.800 M,\) calculate the equilibrium concentrations of the gases.

At \(25^{\circ} \mathrm{C}, K=0.090\) for the reaction $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)$$ Calculate the concentrations of all species at equilibrium for each of the following cases. a. 1.0 \(\mathrm{g} \mathrm{H}_{2} \mathrm{O}\) and 2.0 $\mathrm{g} \mathrm{Cl}_{2} \mathrm{O}$ are mixed in a 1.0 -L flask. b. 1.0 mole of pure HOCl is placed in a 2.0 \(\mathrm{L}\) flask.
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