Guys please help. Partial pressure of gasses

Question

200 g of Helium and 200 g of Hydrogen are introduced into a 100 L tank at a temperature of 0° C. If the cylinder is then heated to 25° C, how much will the partial pressures of the two gases vary?

 

Thanks in advanced!

Answer 1

The partial pressure of a gas in a mixture of gases is the pressure it would exert if present alone. Thus, first find moles of each gas, and using PV = nRT find pressure of each at the original temperature (0ºC = 273 K).  Then find the pressure at the 2nd temperature (25ºC = 298 K).

moles Helium = 200 g x 1 mole/4 g = 50 moles He

moles Hydrogen = 200 g x 1 mole/2 g = 100 moles H2

Pressure of He @ 273K = P = nRT/V = (50 mol)(0.0821 Latm/Kmol)(273K)/100 L = 11.2 atm

Pressure of H2 @ 273 = P = 2x11.2 atm = 22.4 atm (2x since there are 2x as many moles of H2 as there are He)

 

Pressure of He at 298K: P1/T1 = P2/T2;  11.2 atm/273K = P2/298K and P2 = 12.2 atm

Pressure of He at 298 = 24.5 atm (2x the pressure of He, rounding using 3 sig. figs.)

 

So, the partial pressure of He varies from11.2 atm to 12.2 atm

The partial pressure of H2 varies from 22.4 atm to 24.5 atm.

 

NOTE: You could have also done this several other ways, for example:

Total moles = 50 + 100 = 150

Total pressure @ 273K: PV = nRT

P = nRT/V = (150)(0.0821)(273)/100 = 33.62 atm

moles ratio of He/H2 = 50/150 = 1/3 so partial pressure of He = 1/3 x 33.62 = 11.2 atm, etc., etc.