Enthalpy, heat capacity and extensive properties

Enthalpy is defined as H = U + pV; at constant pressure its change equals the heat absorbed, ΔH = q_p.

ΔH = ΔU + pΔV; for reactions involving gases this becomes ΔH = ΔU + Δn_gRT, where Δn_g = moles of gaseous products − moles of gaseous reactants.

Liquids and solids are left out of Δn_g; their volume change is negligible.

If Δn_g = 0 (e.g. H₂(g) + I₂(g) → 2HI(g)), ΔH = ΔU; if Δn_g < 0, ΔH is smaller (more negative) than ΔU, and if Δn_g > 0, ΔH is larger than ΔU.

ΔH negative means an exothermic reaction (heat released); ΔH positive means endothermic (heat absorbed).

Extensive properties depend on the amount of matter (mass, volume, U, H, heat capacity); intensive properties do not (temperature, pressure, density, molar heat capacity).

The ratio of two extensive properties is intensive; for example molar volume V/n and density m/V.

Heat capacity: q = CΔT; molar heat capacity C_m = C/n; specific heat capacity c relates to mass by q = m c ΔT.

For an ideal gas, C_p − C_v = R, where these are molar heat capacities at constant pressure and constant volume.