An ideal solution is obtained by mixing `CH_(3)CHBr_(2)` and `CH_(2)Br - CH_(2)Br` in the ratio 2 : 1 `P_(CH_(3)CHBr_(2))^(@)=173, P_(CH_(2)BrCH_(2)Br)^(@)=127`. Thus total vapour pressure is

Options

A. 158
B. 257
C. 137
D. 197

Answer

To solve the problem of finding the total vapor pressure of an ideal solution formed by mixing `CH3CHBr2` and `CH2BrCH2Br` in the ratio of 2:1, we can use Raoult's Law. Here is a step-by-step solution:

### Step 1: Identify the Components
We have two components:
- Component A: `CH3CHBr2`
- Component B: `CH2BrCH2Br`

### Step 2: Given Data
- Vapor pressure of pure `CH3CHBr2` (P0A) = 173 mmHg
- Vapor pressure of pure `CH2BrCH2Br` (P0B) = 127 mmHg
- Ratio of components A to B = 2:1

### Step 3: Calculate Moles of Each Component
Let the number of moles of `CH3CHBr2` be 2x and the number of moles of `CH2BrCH2Br` be x.

### Step 4: Calculate Total Moles
Total moles (n_total) = moles of A + moles of B = 2x + x = 3x.

### Step 5: Calculate Mole Fractions
- Mole fraction of A (xA) = moles of A / total moles = (2x) / (3x) = 2/3
- Mole fraction of B (xB) = moles of B / total moles = x / (3x) = 1/3

### Step 6: Apply Raoult's Law
According to Raoult's Law, the total vapor pressure (P_total) of the solution is given by:
\[ P_{\text{total}} = P_{0A} \cdot x_A + P_{0B} \cdot x_B \]

### Step 7: Substitute Values
Substituting the values we have:
\[ P_{\text{total}} = (173 \, \text{mmHg}) \cdot \left(\frac{2}{3}\right) + (127 \, \text{mmHg}) \cdot \left(\frac{1}{3}\right) \]

### Step 8: Calculate Each Term
Calculating each term:
- For component A:
\[ 173 \cdot \frac{2}{3} = \frac{346}{3} \approx 115.33 \, \text{mmHg} \]
- For component B:
\[ 127 \cdot \frac{1}{3} = \frac{127}{3} \approx 42.33 \, \text{mmHg} \]

### Step 9: Add the Contributions
Now, add the contributions from both components:
\[ P_{\text{total}} = 115.33 + 42.33 = 157.66 \, \text{mmHg} \]

### Step 10: Round Off
Rounding off gives us:
\[ P_{\text{total}} \approx 158 \, \text{mmHg} \]

### Final Answer
Thus, the total vapor pressure of the solution is **158 mmHg**.

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