Contradiction BR Gen Chem VII #33 pg. 103; Partial Pressures

[AlexB]

This question concerns gas partial pressures and seems to be a contradiction of an earlier topic. Previously, on pg. 20 of Gen Chem II, it says:

Ptot=Sum (Pa + Pb + Pc) (the total pressure is the sum of the individual pressures).

But in the explanation for #33 on pg. 103, it says the total pressure is found by averaging the vapor pressure of the two present compounds, pure methanol and pure ethanol, both at 27 deg. celcius.

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[Pulsar]

This question concerns gas partial pressures and seems to be a contradiction of an earlier topic. Previously, on pg. 20 of Gen Chem II, it says:

Ptot=Sum (Pa + Pb + Pc) (the total pressure is the sum of the individual pressures).

But in the explanation for #33 on pg. 103, it says the total pressure is found by averaging the vapor pressure of the two present compounds, pure methanol and pure ethanol, both at 27 deg. celcius.

This problem is an application of Raoult's law (http://en.wikipedia.org/wiki/Raoult%27s_law). If you have a 50% mixture of compound A with vapor pressure A* and 50% compound B with vapor pressure B* then the pressure over the mixture is Ptot = 0.5*A* + 0.5*B*. If it was 30% A and 70% B then it would be 0.3*A* + 0.7*B*.

There is no contradiction -- Ptot = Pa + Pb. It's just that Pa =/= vapor pressure of A and Pb =/= vapor pressure of B. Pa = mol frac of A * vapor pressure of A and Pb = mol fraction B * vapor pressure of B.

The key is understanding that the partial pressure of each species is not simply the vapor pressure listed for that species -- it is the mole fraction times the vapor pressure.

 

[AlexB]

Ahhh I get it now!!! Thanks. A very subtle yet very important difference.