PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 146

Solution

It follows from the specification thatQ=− 6870 J. Substituting into (6.36) gives

∆solHi=

− 6870

0. 2

=− 34530 J mol−^1.

The relative amount of solvent according to (6.37) is

nrel=

54. 045 / 18. 015

0. 2

= 15.

Calculation of the enthalpy of a binary mixture using the heat of solution. If we

denote the solvent with the subscript 1 and the solute with the subscript 2, we get

H=nrelHm•, 1 +Hm⊗, 2 + ∆solH 2 , (6.38)

whereHis the enthalpy of the mixture andH⊗m, 2 is the molar enthalpy of a pure substance 2.
S Symbols:The superscript⊗indicates a pure substance which may be in a different phase than
that of the mixture before solution at a given temperature and pressure.

6.2.3.1 Relations between the heat of solution and the enthalpy of mixing for a

binary mixture

Given that a pure substance 2 is in the same phase as the mixture, i.e.Hm⊗, 2 =Hm•, 2 , it holds

∆HM= ∆HE =

∆solH 2

nrel+ 1

, (6.39)

∆solH 2 =

∆HM

x 2

. (6.40)

Example

If we mix 4.607 g (≡0.1 mol) of ethanol with 88.273 g (≡4.9 mol) of water at temperature

25 ◦C and pressure 101.325 kPa, a heat of 980 J will pass to the surroundings. Calculate the

heat of solution of ethanol and the enthalpy of mixing.