# A sample of oxygen occupies a volume of 160 dm3 at 91° C. What will be volume of oxygen when the temperature drops to 0.00° C?

May 30, 2014

The volume of the oxygen will be 120 dm³.

This is an example of Charles' Law.

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

${V}_{1}$ = 160 dm³; ${T}_{1}$ = (91 + 273.15) K = 364 K
${V}_{2}$ = ?; ${T}_{2}$ = (0.00 + 273.15) K = 273.15 K

V_2 = V_1× T_2/T_1 = 160 dm³ ×$\left(273.15 \text{K")/(364"K}\right)$ = 120 dm³

This makes sense. The final Kelvin temperature was about 25 % lower than the initial temperature. The final volume should be about 25 % (40 dm³) less than the initial volume.