Two vessels of capacities 3 litres and 4 litres are separately filled with a gas. The pressure are respectively 202 KPa and 101 KPa. The two vessels are connected. The gas pressure now, at constant temperature, will be

Options

A. 151.5 KPa
B. 144 KPa
C. 303 KPa
D. 175 KPa

Answer

To solve the problem of finding the gas pressure after connecting two vessels of different capacities and pressures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Vessel 1 (V1): Capacity = 3 liters, Pressure (P1) = 202 kPa
- Vessel 2 (V2): Capacity = 4 liters, Pressure (P2) = 101 kPa

2. **Use the Ideal Gas Law:**
The ideal gas equation is given by:
\[ PV = nRT \]
Since the temperature (T) and the number of moles (n) remain constant, we can say:
\[ PV = \text{constant} \]
Therefore, for two vessels connected together, we can express the total pressure (P_total) in terms of the pressures and volumes of the individual vessels.

3. **Calculate the Total Pressure:**
The total pressure can be calculated using the formula:
\[ P_{\text{total}} = \frac{P_1V_1 + P_2V_2}{V_1 + V_2} \]
Substituting the values:
- \(P_1 = 202 \, \text{kPa}\)
- \(V_1 = 3 \, \text{liters}\)
- \(P_2 = 101 \, \text{kPa}\)
- \(V_2 = 4 \, \text{liters}\)

Plugging in the values:
\[ P_{\text{total}} = \frac{(202 \, \text{kPa} \times 3 \, \text{liters}) + (101 \, \text{kPa} \times 4 \, \text{liters})}{3 \, \text{liters} + 4 \, \text{liters}} \]

4. **Perform the Calculations:**
- Calculate \(P_1V_1\):
\[ P_1V_1 = 202 \times 3 = 606 \, \text{kPa liters} \]
- Calculate \(P_2V_2\):
\[ P_2V_2 = 101 \times 4 = 404 \, \text{kPa liters} \]
- Add these two results:
\[ P_1V_1 + P_2V_2 = 606 + 404 = 1010 \, \text{kPa liters} \]
- Calculate the total volume:
\[ V_1 + V_2 = 3 + 4 = 7 \, \text{liters} \]
- Now calculate \(P_{\text{total}}\):
\[ P_{\text{total}} = \frac{1010}{7} \approx 144.2857 \, \text{kPa} \]

5. **Round to Appropriate Significant Figures:**
Rounding this value gives us:
\[ P_{\text{total}} \approx 144 \, \text{kPa} \]

### Final Answer:
The gas pressure now, at constant temperature, will be approximately **144 kPa**.