Question

Part 1: A cylinder containing 20.0 L of compressed nitrogen is connected to an empty (evacuated) vessel with an unknown volume. The gas pressure in the cylinder starts at 25 atm and drops to 2 atm without a change in temperature. Determine the volume of the vessel.Part 2: A mixture of H2 and He are in a 10.0 L vessel at 273 K. The total pressure is 756 torr. What is the partial pressure of H2 in the vessel if XHe = 0.75?

Answer 1

Answer:

The volume of the vessel is 250 L

Partial pressure of hydrogen = 189 torr

Explanation:

Using Boyle's law  

${P_1}\times {V_1}={P_2}\times {V_2}$

Given ,  

V₁ = 20.0 L

V₂ = ?

P₁ = 25 atm

P₂ = 2 atm

Using above equation as:

${P_1}\times {V_1}={P_2}\times {V_2}$

${25}\times {20.0}={2}\times {V_2}$

${V_2}=\frac {{25}\times {20.0}}{2}\ L$

${V_2}=250\ L$

The volume of the vessel is 250 L.

According to Dalton's law of partial pressure:-

$P_{H_2}=Mole\ fraction\times Total\ Pressure$

So, according to definition of mole fraction:

$Mole\ fraction\ of\ H_2=\frac {n_{H_2}}{n_{H_2}+n_{He}}$

Also,

Mole fraction of H₂ = 1 - Mole fraction of He = 1 - 0.75 = 0.25

So,

Total pressure = 756 torr

Thus,

$P_{H_2}=0.25\times 756\ torr$

Partial pressure of hydrogen = 189 torr.