CHAPTER 4. THERMODYNAMICS: THE FIRST LAW

4-8
Therefore,
dH = dU + P dV. ext
at constant pressure.
For liquids and solids, (PV) is usually very small (typically - 0.1% of U), and hence H
. U. For ideal gases,
H = U + PV = U + nRT,
so
H = U + nRT
at constant temperature. It should be noted that n is the change in the number of moles of gas.
Exercise:
A total of 885.7 kJ of heat is evolved in the reaction
CH + 2O ! CO + 2H O
4(g) 2(g) 2(g) 2 (l)
o
Carried out at fixed volume and 25 C. Calculate U and H for this reaction.
U = q = !885.7 kJ
H = U + (PV) = U + nRT; n = 1 ! 3 = !2
!3
H = !885.7 ! 2(8.314)(298)x10 = !890.6 kJ
Exercise:
A 10.0 g sample of benzene at its boiling temperature (353.2 K) is placed in contact
with a resistance heater. It evaporates when 3942 J of heat have been produced by
the heater. Calculate the molar enthalpy change and the the molar internal energy
change. (Neglect the volume of the liquid).
This is a constant pressure process in which H = U + (PV) = q.
n = 10.0 g C H x 1 mol C H /78 g C H = 0.128 mol
6 6 6 6 6 6
H = 3942 J/0.128 mol = 30797 J/mol = 30.8 kJ/mol
m
U = H ! (PV ! PV )/n = H ! RT
m m gas liq m