If #16 L# of a gas at room temperature exerts a pressure of #5 kPa# on its container, what pressure will the gas exert if the container's volume changes to #2 L#?

1 Answer
Jun 6, 2017

Answer:

#40# #"kPa"#

Explanation:

To solve this problem, we can use the pressure-volume relationship of gases, illustrated by Boyle's law:

#P_1V_1 = P_2V_2#

We're asked to find the final pressure, #P_2#. Let's plug in the known variables, and rearrange the equation to solve for #P_2#:

#P_2 = (P_1V_1)/(V_2) = ((5"kPa")(16cancel("L")))/((2cancel("L"))) = color(red)(40# #color(red)("kPa"#

We know that from Boyle's law that a gas's pressure and volume it occupies are inversely proportional. Our result makes intuitive sense, because since the volume decreased (by a factor of #8#), our pressure must have increased (by a factor of #8#).