# A sample of gas occupies 17 mL at -112°C. What volume does the sample occupy at 70°C?

Feb 7, 2016

Use Charles' Law, which states that at a constant pressure, temperature and volume are proportional.

It is also written as

$\left({\text{V"_1)/("T"_1)=("V"_2)/("T}}_{2}\right)$

Before we define our values, note that temperature in gas law equations always use Kelvin, not Celsius.

To go from degrees Celsius to Kelvin, add $273$.

Thus, we have

$\text{V"_1="17 mL}$
$\text{T"_1=-112^@"C"="161 K}$

"V"_2=???
$\text{T"_2=70^@"C"="343 K}$

Thus, we have

$\left(\text{17 mL")/("161 K")="V"_2/("343 K}\right)$

Cross-multiply to solve for ${\text{V}}_{2}$:

$17 \cdot {\text{343 mL" * "K"="161 K" * "V}}_{2}$

${\text{5831 mL"="161 V}}_{2}$

color(red)("V"_2="36.2173913043 mL"

The question technically has $1$ significant figure, since there's only one significant figure in ${70}^{\circ} \text{C}$.

This means the final answer is

color(blue)("V"_2=4xx10^1 color(blue)("mL"