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 :

$V_s=X_A\times \bar V_A+X_B\times \bar V_B$

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:

$V_s=0.4\times 30m^3/mole+0.6\times 20m^3/mole$

$V_s=24m^3/mole$

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