You purchase a butane tank that can hold gas safely up to a pressure of 38.1 atm.
When the tank contains 100 grams of butane (C4H10) at 19.9°C,
the gas exerts a pressure of 13.8 atm.
What is the highest temperature to which the butane can be heated safely?
(Report your answer in °C) Assume that butane is an ideal gas that does not liquify.
We're dealing with a gas here, so keeping the Ideal Gas Law
pV = nRT
in mind, is a good idea
Since we're not interested in the type of gas, i.e. moles (so we don't need R either)
and the volume remains constant,
pV = nRT
we'll end up with
p = T, also called Gay-Lussac's Law
Now, we can set up a ratio
13.8 atm/38.1atm
=
19.9 °C/x°C
to make this a bit easier and cleaner, let's flip the equation
38.1 atm/13.8 atm
=
x °C/19.9 °C
x =
[(38.1 atm)(19.9 °C)]/13.8 atm
x = 54.94 °C
This butane gas can be safely heated up to 54.9 °C