What Is the Boiling Temperature of the Liquid Using Van der Waals Equation?

[VoteSaxon]

Homework Statement

The bulb of a constant volume gas thermometer is immersed in an ice/water/water vapour mixture at equilibrium and the recorded pressure is 0.400 atm. It is then immersed in a boiling liquid and the pressure is 0.844 atm. Sufficient gas is then removed from the bulb such that, when the experiment is repeated, the gas pressures are 0.200 atm and 0.401 atm respectively. Calculate the boiling temperature of the liquid.

Homework Equations

van der Waals equations of state are probably relevant here:
[p + a(n/V)²][V - nb] = nRT
∴ [p + (a/V_m²)][V_m - b] = RT

The Attempt at a Solution

I tried to arrange things better. If at first it was immersed in an "ice/water/water vapour mixture" then T = the triple point of water. So as I see it:

V = constant
T₁ = 273.16 K, p₁= 0.400 atm
T₂ = boiling point, p₂ = 0.844 atm
Some gas removed
T₁ = 273.16 K, p₁= 0.200 atm
T₂ = boiling point, p₂ = 0.401 atm

Observations:

• From T₁ to T₂, the pressure of the gas doubles
• After the gas is removed, the pressure is halved, despite there being the same conditions is before

I feel like the solution is in my head somewhere, but I've been rattling with it for eons without success. Any and all help very much appreciated.

 

[MexChemE]

Have you tried solving the van der Waals equation for P and then find an expression for P₂ - P₁?

 

[rude man]

Homework Statement

[p + (a/V_m²)][V_m - b] = RT

You have four unknowns to solve for. You have 4 equations (2 for each experiment). Solve accordingly.
P.S. the pressure does not double in experiment 1.