Question

ii) A binary solution of two volatile liquids A and B in which mole fraction of A is xA , is reported to have total vapour pressure equal to P mbar (m atm). P is defined by the relation, P = 255 - 120 xA . What are the values of p0 A and p0 B ?

Answer 1

Answer:$p_A^0=375mbar$ and $p_B^0=255mbar$  

Explanation: According to Raoult's law, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component multiplied by the vapor pressure of that component in the pure state.

$p_A=x_Ap_A^0$ and $p_B=x_BP_B^0$

where, x = mole fraction

$p^0$ = pressure in the pure state

According to Dalton's law, the total pressure is the sum of individual pressures.

$p_{total}=p_A+p_B$

$p_{total}=x_Ap_A^0+x_BP_B^0$

Also $x_B=1-x_A$  (as the sum of mole fractions is always one)

Thus $p_{total}=x_Ap_A^0+(1-x_A)P_B^0$

$p_{total}=x_A(p_A^0-P_B^0)+P_B^0$   (1)

Given : $p_{total}=255 - 120 x_A$    (2)

Comparing (1) and (2)

$(p_A^0-p_B^0)=120$  

$p_B^0=255mbar$  

Thus $p_A^0-255=120$

$p_A^0=120+255=375mbar$

Answer 2

Answer : p°a= 135

Explanation: p°a-p°b=-120

P°b=255

P°a=-120+255

P°a=135