# The volume of a gas is 27.5 mL at 22°C and 740 mmHg. What will be its volume at 15.0°C and 755 mmHg?

Oct 13, 2016

The new volume will be $\approx 26 \text{mL}$ rounded to two significant figures.

#### Explanation:

This question involves the combined gas law. The equation to use is:

When working with gas laws, the temperature is always in Kelvins. To get Kelvins from a Celsius temperature, add 273.15 to the Celsius temperature.

Determine what is known and what is unknown.

Known
${P}_{1} = \text{740 mmHg}$
${V}_{1} = \text{27.5 mL}$
${T}_{1} = \text{22"^@"C"+"273.15"="295 K}$
${P}_{2} = \text{755 mmHg}$
${T}_{2} = \text{15.0"^@"C"+"273.15"="288 K}$

Unknown
${V}_{2}$

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

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

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

${V}_{2} = \left(740 \text{mmHg"xx27.5"mL"xx288"K")/(295"K"xx755"mmHg}\right)$$=$$\approx 26 \text{mL}$ rounded to two significant figures