# A given mass of oxygen at room temperature occupies a volume of 500.0 mL at 1.50 atm pressure. What pressure must be applied to compress the gas to a volume of only 150.0 mL?

Jul 22, 2016

$\text{5.00 atm}$

#### Explanation:

The idea here is that pressure and volume have an inverse relationship when temperature and number of moles are kept constant, as described by Boyle's Law.

This implies that decreasing the pressure by a given factor, let's say $k$, will cause the volume to increase by the same factor $k$.

Similarly, increasing the pressure by a factor $k$ will cause the volume to decrease by the same factor $k$.

In your case, the volume decreases by a factor of

$\left(500.0 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL"))))/(150.0color(red)(cancel(color(black)("mL}}}}\right) = \textcolor{b l u e}{\frac{10}{3}}$

This means that the pressure of the gas increased by a factor of $\textcolor{b l u e}{\frac{10}{3}}$, which would make its final value equal to

P_"final" = color(blue)(10/3) * "1.50 atm" = color(green)(|bar(ul(color(white)(a/a)color(black)("5.00 atm")color(white)(a/a)|)))

The answer is rounded to three sig figs, the number of sig figs you have for the initial pressure of the gas.