# 400 ml of a gas is contained at 300 mm Hg and 0°C. What will its volume be in mL at 140 mm Hg and 10°C?

Mar 13, 2017

The $\text{combined gas law}$ holds that for a given quantity of gas.......

..........${V}_{2} = 889 \cdot m L$

#### Explanation:

The $\text{combined gas law}$ holds that for a given quantity of gas.......

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$, so we convert to absolute temperature, and solve for ${V}_{2}$.

${V}_{2} = \frac{{P}_{1} {V}_{1} {T}_{2}}{{T}_{1} {P}_{2}}$.

We immediately see (do we?) that the right hand side of the equation has units of volume as required.

And so,

${V}_{2} = \frac{300 \cdot m m \cdot H g \times 400 \cdot m L \times 283 \cdot K}{273 \cdot K \times 140 \cdot m m \cdot H g} = 889 \cdot m L .$

Normally, we would have to convert the pressure measurement to a more conventional atmospheres (i.e. 760*mm*Hg-=1*atm), but we can forgo this step here since the pressure measurements cancel.