To find the new volume of the gas when the pressure is increased, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is held constant. This can be expressed with the formula:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure
- \( V_1 \) is the initial volume
- \( P_2 \) is the final pressure
- \( V_2 \) is the final volume
Given:
- \( P_1 = 1 \) atm
- \( V_1 = 2.0 \) L
- \( P_2 = 2.0 \) atm
We need to find \( V_2 \). Plugging the values into Boyle's Law:
\[ 1 , \text{atm} \times 2.0 , \text{L} = 2.0 , \text{atm} \times V_2 \]
\[ 2.0 , \text{L} = 2.0 , \text{atm} \times V_2 \]
Now, divide both sides by 2.0 atm:
\[ V_2 = \frac{2.0 , \text{L}}{2.0 , \text{atm}} \]
\[ V_2 = 1.0 , \text{L} \]
So, the volume will occupy 1.0 L when the pressure is increased to 2.0 atm.
The answer is: a) 1.0 L