To determine the final volume of the gas at a pressure of 1.5 atm, we can use Boyle's Law. Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure and volume is always constant. Mathematically, this is expressed as:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
Where:
- [tex]\( P_1 \)[/tex] is the initial pressure
- [tex]\( V_1 \)[/tex] is the initial volume
- [tex]\( P_2 \)[/tex] is the final pressure
- [tex]\( V_2 \)[/tex] is the final volume
Given:
- Initial pressure, [tex]\( P_1 = 1.2 \)[/tex] atm
- Initial volume, [tex]\( V_1 = 2.5 \)[/tex] L
- Final pressure, [tex]\( P_2 = 1.5 \)[/tex] atm
First, we calculate the product of the initial pressure and initial volume:
[tex]\[ P_1 \times V_1 = 1.2 \, \text{atm} \times 2.5 \, \text{L} \][/tex]
[tex]\[ P_1 \times V_1 = 3.0 \, \text{atm} \cdot \text{L} \][/tex]
Next, we need to find the final volume, [tex]\( V_2 \)[/tex]. We rearrange Boyle's Law to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{P_1 \times V_1}{P_2} \][/tex]
Substitute the known values into the equation:
[tex]\[ V_2 = \frac{3.0 \, \text{atm} \cdot \text{L}}{1.5 \, \text{atm}} \][/tex]
[tex]\[ V_2 = 2.0 \, \text{L} \][/tex]
Therefore, the volume of the gas at a pressure of 1.5 atm will be 2.0 liters.
Among the given choices:
A. 1L
B. 2L
C. 3L
D. 4L
The correct answer is:
B. 2L
