Question

What is the composition of a methanol (CH₃OH) -propanol(CH₃CH₂CH₂OH)solution that has a vapor pressure of 174 torr at`40⁰C? At40⁰Cthe vapor pressures of pure methanol and pure propanol are 303 and 44.6 torr, respectively. Assume that the solution exhibits ideal behavior.

Short answer

At 40⁰C, the composition of methanol and propanol solution is 1.99.

Step-by-step solution

Individual Composition of Methanol and Propanol

According to the question, it is given that:

The vapor pressure of pure methanol = 303 torr

The vapor pressure of pure propanol = 44.6 torr

The vapor pressure of the solution = 174 torr

The composition of methanol and propanol can be determined by the relation:$\text{X=}\frac{{\text{P}}^{°}}{{\text{P}}_{\text{Solution}}}$

Here, x is the mole fraction or composition of the solute/solvent, ${\text{P}}^{°}$ is the partial pressure of the pure solute/solvent and ${\text{P}}_{\text{Solution}}$ is the pressure of solution.

Therefore,

${\text{X}}_{\text{Methanol}}\text{=}\frac{{{\text{P}}^{°}}_{\text{Methanol}}}{{\text{P}}_{\text{Solution}}}\text{=}\frac{303}{174}\text{=1.74}$

${\text{X}}_{\text{Propanol}}\text{=}\frac{{{\text{P}}^{°}}_{\text{Propanol}}}{{\text{P}}_{\text{Solution}}}\text{=}\frac{44.6}{174}\text{=0.25}$

Composition of the solution

The composition of the solution of methanol and propanol will 74 + 0.25 = 1.991.