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.

Step-by-step 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}=(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}=(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=(n_A)/(n_A+n_B)` .....(2)

where n is the number of moles

Putting values in equation 2:

`\chi_(methanol)=(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* 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* p_T\\\\p_T=(122.7torr)/(0.934)=131.37torr`

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