The weight of one litre of a gas at latm pressure and 300K is 4g. At what temperature the weight of the gas is 4g when the pressure is made 0.5 atm and volume is 1 litre?

Options

A. 200K
B. 150K
C. 600K
D. 1200K

Answer

To solve the problem, we will use Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature when the volume is held constant. The formula we will use is:

\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

### Step-by-step Solution:

1. **Identify the Given Values:**
- Initial pressure, \( P_1 = 1 \, \text{atm} \)
- Initial temperature, \( T_1 = 300 \, \text{K} \)
- Final pressure, \( P_2 = 0.5 \, \text{atm} \)
- Final temperature, \( T_2 = ? \)

2. **Set Up the Equation Using Gay-Lussac's Law:**
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

3. **Substitute the Known Values into the Equation:**
\[ \frac{1 \, \text{atm}}{300 \, \text{K}} = \frac{0.5 \, \text{atm}}{T_2} \]

4. **Cross-Multiply to Solve for \( T_2 \):**
\[ 1 \times T_2 = 0.5 \times 300 \]
\[ T_2 = 0.5 \times 300 \]

5. **Calculate \( T_2 \):**
\[ T_2 = 150 \, \text{K} \]

### Final Answer:
The temperature at which the weight of the gas is 4g when the pressure is 0.5 atm and the volume is 1 liter is **150 K**.

---