Calculating Mole Fraction of C6H6(l) in Solution

[mikep]

does anyone know how to do this problem?
The total vapor pressure above a solution of $$C_6H_6(l)$$ and $$C_7H_8(l)$$ is 0.485 atm. What is the mole fraction of $$C_6H_6(l)$$ in the liquid solution?
$$P^o C6H6(l) = 0.526 atm$$
$$P^o C7H8(l) = 0.188 atm$$

the answer is 0.879 but I'm not sure how to get that using the formula $$P_A = (X_A)(P^o _A)$$

 

[Gokul43201]

does anyone know how to do this problem?
The total vapor pressure above a solution of $$C_6H_6(l)$$ and $$C_7H_8(l)$$ is 0.485 atm. What is the mole fraction of $$C_6H_6(l)$$ in the liquid solution?
$$P^o C6H6(l) = 0.526 atm$$
$$P^o C7H8(l) = 0.188 atm$$

the answer is 0.879 but I'm not sure how to get that using the formula $$P_A = (X_A)(P^o _A)$$

It's a direct substitution problem.

$$P_{tot} = P_A + P_B = (X_A)(P^o _A) + (X_B)(P^o _B) = (X_A)(P^o _A) + (1-X_A)(P^o _B)$$

Now just plug in the given numbers and solve for $X_A$