To find the new pressure when the gas is transferred to a container with a different volume, we will use Boyle's Law. Boyle’s Law states that for a given mass of gas, its pressure (P) multiplied by its volume (V) is a constant as long as the temperature and the number of moles of gas remain unchanged. Mathematically, it is represented 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 values:
- [tex]\( P_1 = 2.15 \)[/tex] atm
- [tex]\( V_1 = 0.0900 \)[/tex] L
- [tex]\( V_2 = 4.75 \)[/tex] L
We need to find [tex]\( P_2 \)[/tex].
Using Boyle’s Law, we can rearrange the equation to solve for the final pressure [tex]\( P_2 \)[/tex]:
[tex]\[ P_2 = \frac{P_1 \times V_1}{V_2} \][/tex]
Substitute the given values into the equation:
[tex]\[ P_2 = \frac{2.15 \text{ atm} \times 0.0900 \text{ L}}{4.75 \text{ L}} \][/tex]
Now, we compute the value:
[tex]\[ P_2 = \frac{0.1935 \text{ atm} \cdot \text{L}}{4.75 \text{ L}} \][/tex]
[tex]\[ P_2 \approx 0.040736842105263155 \text{ atm} \][/tex]
Therefore, the new pressure when the gas is transferred to a container with a volume of 4.75 L is approximately [tex]\( 0.041 \)[/tex] atm (rounded to three decimal places).
