The volume of 400 mL of chlorine gas at 400 mm Hg is decreased to 200 mL at constant temperature. What is the new gas pressure?

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Answer 1 · 2016-01-24T02:48:09

The new gas pressure is 800 mmHg.

This is an example of Boyle's law, which states that at constant mass and temperature, the volume of a gas is inversely proportional to the pressure.

The equation for Boyle's law is $P_{1} V_{1} = P_{2} V_{2}$ $P_1V_1=P_2V_2"$ .

Given
$V_{1} = 400 mL$ $V_1="400 mL"$
$P_{1} = 400 mmHg$ $P_1="400 mmHg"$
$V_{2} = 200 mL$ $V_2="200 mL"$

Unknown
$P_{2}$ $P_2$

Solution
Rearrange the equation to isolate $P_{2}$ $P_2$ . Substitute the given values into the equation and solve.

$P_{1} V_{1} = P_{2} V_{2}$ $P_1V_1=P_2V_2"$

$P_{2} = \frac{P_{1} V_{1}}{V_{2}}$ $P_2=(P_1V_1)/V_2$

$P_{2} = \frac{(400 mmHg) \cdot (400 mL)}{200 mL} = 800 mmHg$ $P_2=((400"mmHg") * (400"mL"))/(200"mL")="800 mmHg"$