Question

Derive the relation between rU and rH for a chemical reaction. How is this
relation given for the condensed phases and ideal gases?

Answer 1

consider a chemical reaction occuring at constant temperature, T and constant pressure, P.

let's volume of reactants is $V_A$ and number of moles in reactants is $n_A$.

similarly, the volume of products is $V_B$ and number of moles in products is $n_B$.

according to ideal gas equation,

PV = nRT,

for reactants , $PV_A=n_ART$

for products , $PV_B=n_BRT$

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

so, $P\Delta V=\Delta n_gRT$....(1)

according to first law of thermodynamics,

∆H = ∆U + P∆V

from equation (1),

$\boxed{\bf{\Delta H=\Delta U+\Delta n_gRT}}$