SME
Physical Chemistry I: Thermodynamics & Kinetics · Problem type
Activity and activity coefficient
Use this for “Over a mixture with xA = 0.250 the vapor holds 41.5 torr of A; pure A gives 120 torr. Find the activity and activity coefficient of A.”
Chart
This is an example. Type your own values to start a new problem.
aA
=
pA (torr)
pA° (torr)
γA
=
aA
xA
Formulas
aA
=
pA
pA
°
0.48
=
72
150
γA
=
aA
xA
1.2
=
0.48
0.4
Assumptions
•
The vapor is an ideal gas, so the activity of A is its partial pressure over the pressure of pure A at the same temperature.
•
The pure liquid is the standard state: γA = 1 when A follows Raoult’s law, pA = xApA°.
•
The graph shows Raoult’s line xApA° and the measured point above or below it.
Step-by-step
WE KNOW
xA = 0.4, pA = 72 torr, pA° = 150 torr
FIND
activity of A (aA), activity coefficient of A (γA)
Step 1 · Find activity of A (aA)
Use aA = pA ÷ pA°
Divide the partial pressure of A by the vapor pressure of pure A.
aA
=
72
150
aA = 0.48
Step 2 · Find activity coefficient of A (γA)
Use γA = aA ÷ xA
Divide the activity by the mole fraction.
γA
=
0.48
0.4
γA = 1.2 → γA > 1: positive deviation; A escapes more than Raoult’s law says, held less by B than by itself.
Check
Put the numbers back in. Both sides should match.
0.48
=
72
150
✓
1.2
=
0.48
0.4
✓
Topic check
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