# A sample of helium has a volume of 521 dm3 at a pressure of 75 cm Hg and a temperature of 18° C. When the temperature is increased to 23° C, what is the volume of the helium?

May 10, 2014

The volume of the helium is 530. dm³.

When you examine the question, you see that the pressure does not change. The only things that change are the volume and the temperature.

This is an example of Charles' Law.

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

${V}_{1}$ = 521 dm³; ${T}_{1}$ = (18 + 273.15) K = 291 K
${V}_{2}$ = ?; ${T}_{2}$ = (23 + 273.15) K = 296 K

V_2 = V_1× T_2/T_1 = 521 dm³ ×$\left(296 \text{ K")/(291" K}\right)$ = 530. dm³

This makes sense. The absolute temperature increased by a factor of about 2 %, so the volume increased by about 2 % (10 dm³).