Page 187 - Physical chemistry understanding our chemical world

154 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

Worked Example 4.9 The pressure inside a water pump is the same
Equation (4.39) in- as the vapour pressure of water (28 mmHg). The pressure of gas inside
volves a ratio of pres- a flask is the same as atmospheric pressure (760 mmHg). What is
sures, so, although
the change in Gibbs function per mole of gas that moves? Take T =
mmHg (millimetres of 298 K.
mercury) is not an SI
unit of pressure, we
are permitted to use Inserting values into Equation (4.39) yields
it here. 28 mmHg
G = 8.414 J K −1 mol −1 × 298 K × ln
760 mmHg
The pressure of vapour −1 −2
above a boiling liquid G = 2477 J mol × ln(3.68 × 10 )
is the same as the −1
G = 2477 J mol × (−3.301)
atmospheric pressure.
G =−8.2kJ mol −1

SAQ 4.7 A flask of methyl-ethyl ether (V) is being evaporated. Its boiling
temperature is 298 K (the same as room temperature) so the vapour
pressure of ether above the liquid is the same as atmospheric pressure,
i.e. at 100 kPa. The source of the vacuum is a water pump, so the pressure
is the vapour pressure of water, 28 mmHg.

CH 2 CH 3
CH 3 O
(V)

(1) Convert the vacuum pressure p (vacuum) into an SI pressure,
remembering that 1 atm = 101 325 kPa = 760 mmHg.

(2) What is the molar change in Gibbs function that occurs when
ether vapour is removed, i.e. when ether vapour goes from the
flask at p O into the water pump at p (vacuum) ?

Justification Box 4.4
We have already obtained the first Maxwell relation (Equation (4.37)) by comparing the
Gibbs–Duhem equation with the total differential:
∂G
= V
∂p

The ideal-gas equation says pV = nRT ,or, usinga
We obtain the molar molar volume for the gas (Equation (1.13)):
volume V m as V ÷ n.
pV m = RT