3 moles of P and 2 moles of Q are mixed , what will be their total vapour pressure in the solution if their partial vapour pressures are 80 and 60 torr respectively ?

Options

A. 80 torr
B. 140 torr
C. 72 torr
D. 70 torr

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given data
- Moles of P (nP) = 3 moles
- Moles of Q (nQ) = 2 moles
- Partial vapor pressure of P (P₀P) = 80 torr
- Partial vapor pressure of Q (P₀Q) = 60 torr

### Step 2: Calculate the total moles in the solution
Total moles (n_total) = nP + nQ
n_total = 3 + 2 = 5 moles

### Step 3: Calculate the mole fraction of P (xP)
Mole fraction of P (xP) = nP / n_total
xP = 3 / 5 = 0.6

### Step 4: Calculate the mole fraction of Q (xQ)
Mole fraction of Q (xQ) = nQ / n_total
xQ = 2 / 5 = 0.4

### Step 5: Use Raoult's Law to calculate the total vapor pressure (P_total)
According to Raoult's Law, the total vapor pressure (P_total) is given by:
\[ P_{total} = x_P \cdot P_{0P} + x_Q \cdot P_{0Q} \]

Substituting the values:
\[ P_{total} = (0.6 \cdot 80) + (0.4 \cdot 60) \]

### Step 6: Calculate the contributions to the total vapor pressure
Calculating each term:
- Contribution from P: \( 0.6 \cdot 80 = 48 \) torr
- Contribution from Q: \( 0.4 \cdot 60 = 24 \) torr

### Step 7: Add the contributions to find the total vapor pressure
\[ P_{total} = 48 + 24 = 72 \text{ torr} \]

### Final Answer
The total vapor pressure of the solution is **72 torr**.

---