# A solution contains 3.95g of CS2 and 2.43g CH3COCH3.vapor pressures at 35°C of pure CS2 and pure CH3COCH3 are 616 torr and 332 torr respectively.Assume ideal ,calculate vapor pressure of each component n the total vapor pressure?

##### 1 Answer
Sep 11, 2015

The total vapor pressure is $\text{489 torr}$.

#### Explanation:

This problem requires you to have some idea about Raoult's Law, which allows you to calculate the partial vapor pressure of a liquid that's part of a mixture by using the vapor pressure of the pure substance and its mole fraction in the mixture.

color(blue)(P_"A" = chi_"A" * P_"A"^@)" ", where

${P}_{\text{A}}$ - the partial vapor pressure of the component;
${\chi}_{\text{A}}$ - the mole fraction of the component;
${P}_{\text{A}}^{\circ}$ - the vapor pressure of the pure component.

You need to use the molar masses of the two substances to find how many moles of each you have. For carbon disulfide you have

3.95color(red)(cancel(color(black)("g"))) * "1 mole"/(76.13color(red)(cancel(color(black)("g")))) = "0.0519 moles CS"""_2

For acetone, you have

2.43color(red)(cancel(color(black)("g"))) * "1 mole"/(58.08color(red)(cancel(color(black)("g")))) = "0.0418 moles" ("CH"""_3)_2"CO"

The total number of moles in the mixture is

${n}_{\text{total}} = {n}_{C {S}_{2}} + {n}_{{\left(C {H}_{3}\right)}_{2} C O}$

${n}_{\text{total" = 0.0519 + 0.0418 = "0.0937 moles}}$

The mole fraction of carbon sulfide is

${\chi}_{C {S}_{2}} = {n}_{C {S}_{2}} / {n}_{\text{total}}$

chi_(CS_2) = (0.0519color(red)(cancel(color(black)("moles"))))/(0.0937color(red)(cancel(color(black)("moles")))) = "0.554"

The mole fraction of acetone is

${\chi}_{\text{acetone" = n_"acetone"/n_"total}}$

${\chi}_{\text{acetone" = (0.0418color(red)(cancel(color(black)("moles"))))/(0.0937color(red)(cancel(color(black)("moles")))) = "0.446}}$

This means that the partial vapor pressure of carbon disulfide is

${P}_{C {S}_{2}} = {\chi}_{C {S}_{2}} \cdot {P}_{C {S}_{2}}^{\circ}$

P_(CS_2) = 0.554 * "616 torr" = color(green)("341 torr")

The partial vapor pressure of acetone will be

P_"acetone" = 0.446 * "332 torr" = color(green)("148 torr")

The total vapor pressure will be

${P}_{\text{total" = P_(CS_2) + P_"acetone}}$

P_"total" = "341 torr" + "148 torr" = color(green)("489 torr")