The pressure of temperature of `4 dm^(3)` of carbon dioxide gas are doubled. Then the volume of carbon dioxide gas would be

Options

A. `2 dm^(3)`
B. `3 dm^(3)`
C. `4 dm^(3)`
D. `8 dm^(3)`

Explanation

To solve the problem, we will use the Ideal Gas Law, which states that:

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

Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( T \) = Temperature

Given:
- Initial volume \( V_1 = 4 \, \text{dm}^3 \)
- The pressure and temperature are both doubled, so:
- \( P_2 = 2P_1 \)
- \( T_2 = 2T_1 \)

We need to find the new volume \( V_2 \).

### Step-by-Step Solution:

1. **Write down the initial conditions**:
- Initial volume \( V_1 = 4 \, \text{dm}^3 \)
- Initial pressure \( P_1 \)
- Initial temperature \( T_1 \)

2. **Set up the equation using the Ideal Gas Law**:
\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

3. **Substitute the new conditions into the equation**:
- Substitute \( P_2 = 2P_1 \) and \( T_2 = 2T_1 \):
\[ \frac{P_1 V_1}{T_1} = \frac{(2P_1) V_2}{(2T_1)} \]

4. **Simplify the equation**:
- Cancel \( P_1 \) and \( T_1 \) from both sides:
\[ \frac{V_1}{1} = \frac{2V_2}{2} \]
- This simplifies to:
\[ V_1 = V_2 \]

5. **Substitute the known volume**:
- We know \( V_1 = 4 \, \text{dm}^3 \):
\[ V_2 = 4 \, \text{dm}^3 \]

### Conclusion:
The volume of carbon dioxide gas after the pressure and temperature are doubled is \( V_2 = 4 \, \text{dm}^3 \).

### Final Answer:
**The volume of carbon dioxide gas would be \( 4 \, \text{dm}^3 \)**.