Question

Derive the relationship between $\Delta H$ and $\Delta U.$

Answer 1

$\text{It is known that the equation for an ideal gas is}$$PV=nRT$

$So,$

$\text{for gas A, the equation will be}$$P{V}_A=n_{A}RT$ ...........(1)

$\text{For gas B, equation will be}$$P{V}_B=n_{B}RT$ ............(2)

$\text{Now, on subtracting equation (1) from equation (2) we get :}$

$P{V}_B-P{V}_A=n_{B}RT-n_{A}RT$

$P(V_B-V_A)=(n_B-n_A)RT$

$P\Delta V=\Delta n_{g}RT$

$\text{Also, it is known that the relation between}\Delta H\text{and}\Delta U\text{is as follows :}$

$\Delta H=\Delta U+P\Delta V$ or, $\Delta H=\Delta U+\Delta n_{g}RT$

Therefore, we can conclude that a relationship between $\Delta H$ and $\Delta U$ is $\Delta H=\Delta U+\Delta n_{g}RT$