Question

Some nitrogen for use in synthesizing ammonia is heated slowly, maintaining the external pressure close to the internal pressure of 50.0 atm, until its volume has increased from 542 to 974 L. Calculate the work done on the nitrogenas it is heated, and express it in joules.

Short answer

The work done on nitrogen is ${\text{- 2.188×10}}^{\text{6}}\text{J}$.

Step-by-step solution

Pressure-Volume Work

The compression or expansion of a particular fluid performs a certain work termed as pressure-volume work. This work happens when the pressure is constant and there is a change in the volume. The formula is:

$\mathbf{\text{W = P∆V}}$

Calculating the work done in joules

The pressure is 50.0 atm.

The change in volume can be found as:

$$\begin{gathered} \text{∆V = 974 L - 542 L} \\ \text{= 432 L} \end{gathered}$$

The work done on the gas against constant external pressure is given as:

$\text{W = P∆V}$

Where,

P is the constant external pressure.

$∆V$is change in volume.

Substituting the values in the equation,

$$\begin{gathered} \text{W = P∆V} \\ \text{= - 50.0 atm×}\left(\text{432 L}\right) \\ \text{= - 21600 Latm} \end{gathered}$$

The value of 1 atm is equal to 101.325 J.

The work done on gas in J is:

$$\begin{gathered} \text{Work done in joules = - 21600 Latm×}\frac{\text{101.325 J}}{\text{1 Latm}} \\ {\text{= - 2.188×10}}^{\text{6}}\text{J} \end{gathered}$$

Hence the work done on nitrogen is${\text{- 2.188×10}}^{\text{6}}\text{J}$ .