Question

Nitrogen gas reacts with hydrogen gas to form ammonia gas $\mathbf{\left(}{\mathbf{\text{NH}}}_{\mathbf{\text{3}}}\mathbf{\right)}$. Consider the following illustration representing the original reaction mixture (the numbers of each molecule shown are relative numbers):

Assume this reaction mixture goes to completion. The piston apparatus allows the container volume to change in order to keep the pressure constant at $\mathbf{\text{1.00atm}}$. Assume ideal behaviour and constant temperature.

(a) What is the partial pressure of ammonia in the container when the reaction is complete?

(b) What is the mole fraction of ammonia in the container when the reaction is complete?

(c) What is the volume of the container when the reaction is complete?

Short answer

(a) The partial pressure of ammonia in the reaction container is $\text{0.5atm}$.

(b) The mole fraction of ammonia in the container is$\text{0.5}$.

(c) The volume of the container when the reaction is complete is $\text{10L}$.

Step-by-step solution

Concept Introduction:

Partial pressure is the amount of pressure that each gas exerts in a container that contains multiple gases. Any gas contained in a container has a partial pressure, which is its pressure.

(a) Partial Pressure of Ammonia:

The total pressure will be $\text{1atm}$because the reaction pressure remains constant. In the exercise, it was specified that the reaction mixture would complete with the same molar ratio of hydrogen to nitrogen molecules. As a result, the reaction container's total pressure will be equal to the partial ammonia pressure and remaining nitrogen $\left(\text{1atm}\right)$. Hydrogen is the limiting reactant. Use the figure as an example and use all six hydrogen molecules $\left(6\right)$and two nitrogen molecules ($4$left). Four ammonia molecules will develop in the interim. As a result, given the same amount of molecules, the partial pressure will be the same $(\text{0.5atm}+\text{0.5atm}=1\text{atm})$.

Therefore, the value for partial pressure is obtained as $\text{0.5atm}$.

(b) Mole fraction of Ammonia:

Due to the lack of hydrogen, the mole fraction will also be the same because the partial pressures of the remaining, unreacted nitrogen and the produced ammonia are the same (both containing the same number of molecules). As a result, each mole fraction of ammonia and nitrogen will be $0.5$.

Therefore, the value of mole fraction is obtained as $0.5$.

(c) Volume of the container:

At the beginning of the reaction, there was no ammonia and there was the same amount of nitrogen and hydrogen (each $6$, total $12$). At the end of the reaction, $6$molecules of hydrogen were spent,$4$ ammonia molecules were formed and the number of nitrogen molecules was reduced from $6$to $4$. So, at the end of the reaction, $8$molecules were left in total. Since temperature and pressure are constant, the volume/ mole ratio can be calculated.

$$\begin{gathered} PV=nRT \\ \frac{V}{n}=\frac{RT}{P} \\ \frac{V}{n}=\text{constant} \\ \frac{V_1}{n_1}=\frac{V_2}{n_2} \end{gathered}$$

$\begin{array}{rcl}{V}_2& =& \frac{V_1{n}_2}{n_1}\\ & =& \frac{15\text{L}\times 8}{12}\\ & =& 10\text{L}\end{array}$

Hence, the value for the volume is obtained as $\text{10L}$.