At a given temperature , total vapour pressure (in Torr) of a mixture of volatile components A and B is given by
`"P"_("total")=120-785"X"_("B")`
hence, vapour pressure of pure A and B respectively (in Torr) are

Options

A. 120,75
B. 120195
C. 120,45
D. 75,45

Explanation

To solve the problem, we need to determine the vapor pressures of pure components A and B from the given total vapor pressure equation of the mixture.

### Step-by-Step Solution:

1. **Understand the Given Equation:**
The total vapor pressure \( P_{\text{total}} \) of the mixture is given by the equation:
\[ P_{\text{total}} = 120 - 75X_B \]
where \( X_B \) is the mole fraction of component B in the mixture.

2. **Apply Raoult's Law:**
According to Raoult's Law, the total vapor pressure of a mixture of volatile components can be expressed as:
\[ P_{\text{total}} = X_A P_A^0 + X_B P_B^0 \]
where \( P_A^0 \) and \( P_B^0 \) are the vapor pressures of pure components A and B, respectively, and \( X_A \) and \( X_B \) are their mole fractions in the mixture.

3. **Relate Mole Fractions:**
Since \( X_A + X_B = 1 \), we can express \( X_A \) as:
\[ X_A = 1 - X_B \]

4. **Substitute into Raoult's Law:**
Substituting \( X_A \) into the Raoult's Law equation gives:
\[ P_{\text{total}} = (1 - X_B) P_A^0 + X_B P_B^0 \]

5. **Set the Two Expressions for \( P_{\text{total}} \) Equal:**
Now we have two expressions for \( P_{\text{total}} \):
\[ 120 - 75X_B = (1 - X_B) P_A^0 + X_B P_B^0 \]

6. **Compare Coefficients:**
To find \( P_A^0 \) and \( P_B^0 \), we can compare the coefficients from both equations. Rearranging gives:
\[ P_A^0 - P_B^0 = 75 \]
and from the constant term, we can see that:
\[ P_A^0 = 120 \]

7. **Substitute \( P_A^0 \) to Find \( P_B^0 \):**
Now substituting \( P_A^0 \) into the equation:
\[ 120 - P_B^0 = 75 \]
Rearranging gives:
\[ P_B^0 = 120 - 75 = 45 \]

8. **Final Results:**
Thus, the vapor pressures of pure A and B are:
\[ P_A^0 = 120 \text{ Torr} \]
\[ P_B^0 = 45 \text{ Torr} \]

### Summary:
- Vapor pressure of pure A, \( P_A^0 = 120 \) Torr
- Vapor pressure of pure B, \( P_B^0 = 45 \) Torr