To calculate the volume of the gas when it is released to the atmospheric pressure, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely related when the temperature is held constant. The formula is:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \(P_1\) is the initial pressure of the gas,
- \(V_1\) is the initial volume of the gas,
- \(P_2\) is the final pressure of the gas (atmospheric pressure),
- \(V_2\) is the final volume of the gas.
Given:
- \(P_1 = 3.8 \times 10^3 \text{ mmHg}\)
- \(V_1 = 8.0 \text{ L}\)
- \(P_2 = 200 \text{ mmHg}\)
We are asked to find \(V_2\).
Rearranging the formula for \(V_2\):
\[ V_2 = \frac{P_1 V_1}{P_2} \]
Substituting the known values:
\[ V_2 = \frac{(3.8 \times 10^3 \text{ mmHg})(8.0 \text{ L})}{200 \text{ mmHg}} \]
Now we calculate \(V_2\):
\[ V_2 = \frac{(3.8 \times 10^3)(8.0)}{200} = \frac{30400}{200} = 152 \text{ L} \]
Thus, the volume of the gas when released at an atmospheric pressure of 200 mmHg is 152 liters.
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