Question

Express partial molar temperature and partial molar pressure in terms of temperature and pressure of the mixture. Explain your result

Answer 1

The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone."

P_total = P₁ + P₂ + . . . P_n

• P_t is the total pressure of a sample which contains a mixture of gases
• P₁, P₂, P₃, etc. are the partial pressures (in the same units) of the gases in the mixture

However, there is an unavoidable problem. The gas saturates with water vapor and now the total pressure inside the bottle is the sum of two pressures - the gas itself and the added water vapor.

WE DO NOT WANT THE WATER VAPOR PRESSURE.

So we get rid of it by subtraction.

P_{dry gas} = P_total - P_{water vapor}

This means we must get the water vapor pressure from somewhere.

We get it from a table because the water vapor pressure depends only on the temperature, NOT how big the container is or the pressure of the other gas.

Temp (oC)	Vapor Pressure (mmHg)	Temp (oC)	Vapor Pressure (mmHg)
-10	2.15	40	55.3
0	4.58	60	149.4
5	6.54	80	355.1
10	9.21	95	634
11	9.84	96	658
12	10.52	97	682
13	11.23	98	707
14	11.99	99	733
15	12.79	100	760
20	17.54	101	788
25	23.76	110	1074.6
30	31.8	120	1489
37	47.07	200	11659

The most useful partial molar quantity is the partial molar free energy Gi,pm. It is so useful that it is given the name of chemical potential and a separate sumbol