5.00 L of a gas is collected at 100 K and then allowed to expand to 50.0 L. What is the new temperature in order to maintain the same pressure?

Dec 16, 2014

The answer is $1000 K$.

According to Charles' law, the volume of a gas is proportional to its temeprature (in $K$).

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

Before doing any calculations, one should try and predict what the answer could look like. Now, since the volume increases by a factor of 10, we should expect the temperature to increase significantly in order to compensate for the larger volume - in the scope of keeping the pressure constant. Indeed,

${T}_{2} = {V}_{2} / {V}_{1} \cdot {T}_{1} = \frac{50.0 L}{5.00 L} \cdot 100 K = 1000 K$

Since volume and temperature are proportional to each other, the increase in temperature must match the increase in volume.