If the pressure and absolute temperature of 2 litres of `CO_(2)` are doubled the volume of `CO_(2)` would become

Options

A. 2 litres
B. 4 litres
C. 5 litres
D. 7 liters

Explanation

To solve the problem, we can use the combined gas law, which relates pressure, volume, and temperature of a gas. The combined gas law is given by:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

### Step-by-step Solution:

1. **Identify Initial Conditions:**
- Let the initial pressure be \( P_1 \).
- Let the initial temperature be \( T_1 \).
- The initial volume \( V_1 \) is given as 2 liters.

2. **Identify Final Conditions:**
- The final pressure \( P_2 \) is double the initial pressure, so \( P_2 = 2P_1 \).
- The final temperature \( T_2 \) is double the initial temperature, so \( T_2 = 2T_1 \).

3. **Substitute Values into the Combined Gas Law:**
- Substitute the known values into the combined gas law:
\[ \frac{P_1 \cdot 2 \, \text{liters}}{T_1} = \frac{2P_1 \cdot V_2}{2T_1} \]

4. **Simplify the Equation:**
- On the right side, the \( 2 \) in the numerator and denominator cancels out:
\[ \frac{P_1 \cdot 2 \, \text{liters}}{T_1} = \frac{P_1 \cdot V_2}{T_1} \]

5. **Cancel Common Terms:**
- Since \( P_1 \) and \( T_1 \) are common on both sides, we can cancel them out:
\[ 2 \, \text{liters} = V_2 \]

6. **Conclusion:**
- Therefore, the final volume \( V_2 \) is 2 liters.

### Final Answer:
The volume of \( CO_2 \) would remain **2 liters**.

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