# The volume of a gas is reduced from 4 L to 0.5 L while the temperature is held constant. How does the gas pressure change?

##### 1 Answer
Jun 3, 2017

It increases by a factor of $8$.

#### Explanation:

We can use the pressure-volume relationship of gases, illustrated by Boyle's law:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

We're not given any pressure values, but we can solve this in terms of ${P}_{1}$, the original pressure (to calculate for the final pressure, ${P}_{2}$). Plugging in the known values, and solving for ${P}_{2}$, we have

P_2 = (P_1V_1)/(V_2) = (P_1(4cancel("L")))/(0.5cancel("L"))

So,

${P}_{2} = 8 \left({P}_{1}\right)$

Therefore, the value of the final pressure is $8$ times that of the original pressure; i.e. the pressure increases by a factor of $8$.