# Question #17639

Apr 12, 2017

I'll show you!

#### Explanation:

For convenience, I will use kPa rather than mmHg. But that is a mere preference (and I will walk you through the same calculations using mmHg in the second part):

You should already know the relationship between volume and pressure:

$V \alpha \frac{1}{p}$

You may also know that:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$ <- This essentially means, that the initial conditions the final conditions

So, what do we know from the question?
${P}_{1} = 100 k P a$
${V}_{1} = 2.5 {\mathrm{dm}}^{3}$ (i.e. L)
${P}_{2} = 66.66 k P a$

Hence:
$100 \cdot 2.5 = 66.66 \cdot {V}_{2}$
${V}_{2} = 3.75 {\mathrm{dm}}^{3}$ (i.e. L)

The same thing is also true if you use mmHg:

${P}_{1} = 750 m m H g$
${V}_{1} = 2.5 {\mathrm{dm}}^{3}$ (i.e. L)
${P}_{2} = 500 m m H g$

Hence:
$750 \cdot 2.5 = 500 \cdot {V}_{2}$
${V}_{2} = 3.75 {\mathrm{dm}}^{3}$ (i.e. L)

Hope it helped :)