If #13/4 L# of a gas at room temperature exerts a pressure of #16 kPa# on its container, what pressure will the gas exert if the container's volume changes to #5/12 L#?

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Answer 1 · 2016-08-20T02:06:43

The gas will exert a pressure of #624/5 kPa#

Let's begin by identifying our known and unknown variables.

The first volume we have is #13/4#L, the first pressure is #16kPa# and the second volume is #5/12L#. Our only unknown is the second pressure.

We can obtain the answer using Boyle's Law:
www.physbot.co.uk

The letters i and f represent the initial and final conditions, respectively.

All we have to do is rearrange the equation to solve for the final pressure.

We do this by dividing both sides by #V_f# in order to get #P_f# by itself like so:
#P_f=(P_ixxV_i)/V_f#

Now all we do is plug in the values and we're done!

#P_f=(16\kPa xx 13/4\ cancel"L")/(5/12\cancel"L")# = #624/5kPa#