Question

If the partial molar volumes of the two components of a binary solution are VA 30 m2/mol and Vg 20 m3/mol and the mole fraction of component A is 0.4, find the molar volume of the solution.

Answer 1

Answer : The molar volume of the solution is,
`24m^3/mole`

Explanation : Given,

Partial molar volumes of component A =
`30m^3/mole`

Partial molar volumes of component B =
`20m^3/mole`

Mole fraction of component A = 0.4

First we have to calculate the mole fraction of component B.

As we know that,

`\text{Mole fraction of component A}+\text{Mole fraction of component B}=1`

`\text{Mole fraction of component B}=1-0.4=0.6`

Now we have to calculate the molar volume of the solution.

Expression used :

`V_s=X_A* \bar V_A+X_B* \bar V_B`

where,

`\bar V_A` = partial molar volumes of component A

`\bar V_B` = partial molar volumes of component B

`V_s` = molar volume of the solution

`X_A` = mole fraction of of component A

`X_B` = mole fraction of of component B

Now put all the give values in the above expression, we get:

`V_s=0.4* 30m^3/mole+0.6* 20m^3/mole`

`V_s=24m^3/mole`

Therefore, the molar volume of the solution is,
`24m^3/mole`