Step 1: Apply the combined gas law.
The combined gas law, derived from the ideal gas law, establishes a relationship between pressure, volume, and temperature:
\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]
where:
- \( P_1 \), \( V_1 \), and \( T_1 \) represent the initial pressure, volume, and temperature, respectively.
- \( P_2 \), \( V_2 \), and \( T_2 \) represent the final pressure, volume, and temperature, respectively.
Step 2: Input the known values.
Provided data:
- \( P_1 = 2.0 \, \text{atm} \)
- \( V_1 = 10.0 \, \text{L} \)
- \( T_1 = 300 \, \text{K} \)
- \( P_2 = 4.0 \, \text{atm} \)
- \( T_2 = 600 \, \text{K} \)
The objective is to determine \( V_2 \).
\[
\frac{(2.0)(10.0)}{300} = \frac{(4.0)(V_2)}{600}
\]
Step 3: Calculate \( V_2 \).
\[
\frac{20.0}{300} = \frac{4.0 V_2}{600}
\]
\[
\frac{1}{15} = \frac{2 V_2}{300}
\]
\[
V_2 = \frac{1}{15} \times 150 = 5.0 \, \text{L}
\]
Answer: The final volume of the gas following the changes is \( 5.0 \, \text{L} \).