# A sample of hydrogen has an initial temperature of 50.° C. When the temperature is lowered to -5.0° C, the volume of hydrogen becomes 212 cm3. What was the initial volume of the hydrogen in dm3?

May 30, 2014

The initial volume of the gas was 0.255 dm³.

#### Explanation:

This is an example of Charles' Law.

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

${V}_{1}$ = ?; ${T}_{1}$ = (50. + 273.15) K = 323 K

${V}_{2}$ = 212 cm³; ${T}_{2}$ = (-5.0 + 273.15) K = 268.2 K

V_1 = V_2× T_1/T_2 = 212 cm³ ×$\left(323 \text{K")/(268.2"K}\right)$ = 255 cm³

${V}_{1}$ = 255 cm³ × ${\left(\left(1 \text{dm")/(10"cm}\right)\right)}^{3}$ = 0.255 dm³

This makes sense. The initial Kelvin temperature was about 20 % higher than the final temperature. The original volume must also have been about 20 % (40 cm³) larger than the final volume.