ART coursework $2023-24$

In all cases, show your working and clearly state all assumptions used within calculations. Remember to cite data sources thoroughly. Each question contributes $25\%$ to the total mark.

Question $1$: The reaction between nitrogen and hydrogen to form ammonia is outlined in the following chemical equation;

$N_2+3H_{2}2N{H}_3$

plot the equilibrium conversion for this reaction between a temperature range of $300$ to $900K$ for a range of pressures. Explain the steps in your method, and the assumptions that you make.

Question $2$: Plot a set of isotherms on a PV diagram for carbon dioxide, using any suitable equation of state. Identifying any key points and regions on the plot; explain your calculation method in detail, together with the reasons for your choice of method and equation of state.

Question $3$: In terms of the compressibility factor, $Z($given by $Z=\frac{P{V}_m}{RT}),$ rewrite the Redlich Kwong equation;

$P=\frac{RT}{V_m-B}-\frac{A}{T^{\frac{1}{2}}{V}_m(V_m+B)}$

Then derive expressions for the limiting gradients of a $Z$ vs $P$ plot, i$.$e;

$\underset{P0}{lim}(\frac{\text{d}\text{e}\text{l}\text{Z}}{\text{d}\text{e}\text{l}\text{P}}{)}_T$;$\underset{P}{lim}(\frac{\text{d}\text{e}\text{l}\text{Z}}{\text{d}\text{e}\text{l}\text{P}}{)}_T$