Q.Derive the relationship between delta-U and delta-H. OR Two moles of H2 and three moles of I2 are taken in 2 dm^3 vessel and heated. If the equilibrium mixture contains 0.8 moles of HI, calculate Kp and Kc for the reaction, H2(g) + I2(g) <=> 2HI(g).

Starting from H = U + PV, the relation dH = dU + dn(g)RT is derived for reactions involving ideal gases at constant temperature and pressure.

This question offers an OR alternative (a numerical Kp/Kc equilibrium problem); the derivation (the primary question) is answered here.

Enthalpy (H) is defined as:

H = U + PV

where U is the internal energy, P is pressure, and V is volume.

For a process occurring at constant pressure, taking the change in each quantity between the final and initial states:

dH = dU + d(PV)

Since pressure P is constant, d(PV) = PdV, so:

dH = dU + PdV ... (at constant P)

Now consider a chemical reaction involving ideal gases as reactants and/or products, carried out at constant temperature T and pressure P. Applying the ideal gas equation PV = nRT to both the reactant and product gaseous states:

For products: P.Vproducts = n(products, gas).RT

For reactants: P.Vreactants = n(reactants, gas).RT

Subtracting: P(Vproducts - Vreactants) = (n(products,gas) - n(reactants,gas)).RT

i.e., PdV = dng.RT …