Partial and Total Pressure Problem

Question

Mixtures of helium and oxygen are used in scuba diving tanks to help prevent "the bends". For a particular dive, 35.7 L of oxygen gas at 25.0^oC and 1.08 atm, and 6.33 L of helium gas at 25.0^oC and 2.74 atm were pumped into a tank with a volume of 6.00 L at 25.0^oC.

Calculate (in atm):

1. the partial pressure of oxygen

2. the partial pressure of helium

3. the total pressure in the tank at 25.0^oC.

I found the total pressure to around 1.0922, but not sure if this is correct and how to then find partial pressure.

Answer 1

Daltons law of partial pressure tells us that the total pressure of a container will be equal to the sum of the partial pressure of the individual gasses inside the container (P_tot=P₁+P₂+P₃....). For this question we can see that the temperature never changes and remains at 25 ^oC throughout.

This is great as it means we can simplify our ideal gas law equation PV=nRT to only be P1V1=P2V2

For oxygen

p1v1=p2v2

(35.7)(1.08)=(p2)(6)

p2 = 6.43

for helium

p1v1=p2v2

(2.74)(6.33)=(p2)(6)

p2 = 2.89

Ptotal = 6.43 + 2.89 = 9.32 atm

Now lets look at the answer you had and the ideal gas law (PV=nRT) again. You had over 40 litres of gas pumped into a container no bigger than 6 liters. moles of gas didn't change, temperature didn't change, and R is a constant. Therefore if volume decreased pressure must go up! This is a way you can quickly check your answers to see if they feel right. Your calculated total pressure was only slightly higher than the pressure of oxygen before it was pumped into the tank. This can immediately signal to you that you need to rethink how you approached the question.