# 2.30 L of air at 4.53 atm is expanded to 2219 mmHg. What is the final volume in mL?

Feb 13, 2017

$2219$ $m m \cdot H g$ is an absurd unit.

#### Explanation:

$1 \cdot a t m$ will support a column of mercury $760 \cdot m m$ high. Often, we quote the pressure as $760 \cdot m m$ $H g$ (or thereabouts) in order to report daily fluctuations in pressure. In fact due to safety concerns, mercury has almost disappeared from modern laboratories.

It is tempting to say that $2219$ $m m \cdot H g$

$\equiv$ $\frac{2219 \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1} \cong 3 \cdot a t m$

But I would resist this temptation.

Feb 13, 2017

The final volume will be $\text{3570 mL}$, rounded to three significant figures.

#### Explanation:

First the units of pressure and volume need to be the same.

Pressure

$\text{1 atm=760.0 mmHg}$

Convert mmHg to atm.

2219color(red)(cancelcolor(black)("mmHg"))xx(1"atm")/(760.0color(red)(cancelcolor(black)("mmHg")))="2.920 atm"

Volume

$\text{1 L=1000 mL}$

Convert $\text{L}$ to $\text{mL}$.

2.30color(red)(cancel(color(black)("L")))xx(1000"mL")/(1color(red)(cancel(color(black)("L"))))="2300 mL"=2.30xx10^3"mL"

The number of mL above is given to three significant figures using scientific notation. I will use $\text{2300 mL}$ for convenience only.

This question is concerns Boyle's Law , which states that the volume $\left(V\right)$ of a gas held at constant amount and temperature, is inversely proportional to the pressure $\left(P\right)$. This means that if the pressure goes up, the volume goes down, and vice-versa. The equation to use is:

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

Write what you know:

${P}_{1} = \text{4.53 atm}$
${V}_{1} = 2.30 \times {10}^{3} \text{mL}$
${P}_{2} = \text{2.920 atm}$

Write what you don't know: ${V}_{2}$.

Solution
Rearrange the equation to isolate ${V}_{2}$. Substitute the known quantities into the equation and solve.

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

V_2=(4.53color(red)(cancel(color(black)("atm")))xx2300"mL")/(2.920color(red)(cancel(color(black)("atm"))))="3570 mL" rounded to three significant figures