Question

Calculate the vapor pressure (in torr) at 298 K in a solution prepared by dissolving 46.8 g of the non-volatile non-electrolye glucose in 117 g of methanol. The vapor pressure of methanol at 298 K is 122.7 torr. Enter your answer to 2 decimal places.

Answer 1

Answer: The total partial pressure of the solution is 131.37 torr.

Explanation:

The number of moles is defined as the ratio of the mass of a substance to its molar mass. The equation used is:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$ ......(1)

• For glucose:

Given mass of glucose = 46.8 g

Molar mass of glucose = 180 g/mol

Plugging values in equation 1:

$\text{Moles of glucose}=\frac{46.8g}{180g/mol}=0.26 mol$

• For methanol:

Given mass of methanol = 117 g

Molar mass of methanol = 32 g/mol

Plugging values in equation 1:

$\text{Moles of methanol}=\frac{117g}{32g/mol}=3.66 mol$

Mole fraction is defined as the moles of a component present in the total moles of a solution. It is given by the equation:

$\chi_A=\frac{n_A}{n_A+n_B}$ .....(2)

where n is the number of moles

Putting values in equation 2:

$\chi_{methanol}=\frac{3.66}{0.26+3.66}=0.934$

Raoult's law is the law used to calculate the partial pressure of the individual gases present in the mixture. The equation for Raoult's law follows:

$p_A=\chi_A\times p_T$ .....(3)

where $p_A$ is the partial pressure of component A in the mixture and $p_T$ is the total partial pressure of the mixture

We are given:

$p_{methanol}=122.7torr\\\chi_{methanol}=0.934$

Putting values in equation 3, we get:

$122.7torr=0.066\times p_T\\\\p_T=\frac{122.7torr}{0.934}=131.37torr$

Hence, the total partial pressure of the solution is 131.37 torr.