A volume of 50.0 milliliters of an ideal gas at STP increases to 100 milliliters. If the pressure remains constant, what must the new temperature be?

Dec 18, 2016

The final temperature will be 500 K rounded to one significant figure.

Explanation:

This question involves Charles' law , which states that the volume of a given amount of gas varies directly with its temperature, as long as pressure and amount are kept constant. This means that if the volume increases, so does the temperature, and vice versa.

Equation

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$, where $V$ represents volume, and $T$ represents the Kelvin temperature.

$\text{STP}$ can have more than one unit for pressure, but the temperature is ${0}^{\circ} \text{C}$ or $\text{273.15 K}$. The temperature in gas law problems is always in Kelvins.

Known
${V}_{1} = \text{50.0 mL}$
${T}_{1} = \text{273.15 K}$
${V}_{2} = \text{100 mL}$

Unknown
${T}_{2}$

Solution
Rearrange the equation to isolate ${T}_{2}$. Plug in your known values and solve.

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

T_2=(100cancel"mL"xx273.15"K")/(50.0cancel"mL")="546 K"="500 K" rounded to one significant figure