A sample of a gas has a volume of of 2.0 liters at a pressure of 1.0 atmosphere. When the volume increases to 40 liters, at constant temperature, what will the pressure be?

Question

8139 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-16T04:56:39

The final pressure will be 0.05 atm.

This is an example of Boyle's law which states that the volume of a gas varies inversely with pressure, when mass and temperature are kept constant.

Equation
$V_{1} P_{1} = V_{2} P_{2}$ $V_1P_1=V_2P_2$ , where $V$ $V$ is volume and $P$ $P$ is pressure.

Known
$V_{1} = 2.0 L$ $V_1="2.0 L"$
$P_{1} = 1.0 atm$ $P_1="1.0 atm"$
$V_{2} = 40 L$ $V_2="40 L"$

Unknown
$P_{2}$ $P_2$

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

$P_{2} = \frac{V_{1} P_{1}}{V_{2}}$ $P_2=(V_1P_1)/V_2$

$P_2=((2.0cancel"L")xx(1.0"atm"))/(40cancel"L")="0.05 atm"$