Question

If $X_m,X_p$ and $X_v$ are mole fraction, pressure fraction and volume fraction respectively for a gaseous component in mixture. Select the correct relationship between them.

• A. $X_m=X_p=X_v$
• B. $X_p=\frac{1}{X_v}$
• C. $X_m=\frac{1}{X_P}=\frac{1}{X_V}$
• D. $X_V=\frac{1}{X_p}=\frac{1}{X_m}$

Answer 1

Answer: (A)

As we know,
$P_A^{\prime }=P_T\cdot X_A$
$\therefore X_A=\frac{P_A^{\prime }}{P_T}$
i.e., Pressure fraction $=$ mole fraction
Also, from Amagat's law of partial volume total volume of a mixture of gas is equal to the sum of partial volume of the constituents gases, i.e.,
$V_A^{\prime }=V_T\cdot X_A$
$\frac{V_A^{\prime }}{V_T}=X_A$
i.e., volume fraction is equal to mole fraction.
So, pressure fraction $=$ mole fraction $=$ volume fraction