Question

Equal volumes of hydrogen and helium gas are at the same pressure. The atomic mass of helium is four times that of hydrogen. If the total mass of both gases is the same, the ratio of the temperature of helium (He) to that of hydrogen (H2) is:

Answer 1

Answer:

The ratio of the temperature of helium to that of hydrogen gas is 2:1.

Explanation:

Atomic mass of hydrogen = M

Temperature of hydrogen gas =T

Pressure of the hydrogen gas = P

Mass of the hydrogen gas = m

Moles of the hydrogen gas = $n=\frac{m}{2M}$

Volume of the hydrogen gas = V

Using an ideal gas equation:

$PV=nRT=PV=\frac{mRT}{M}$...(1)

Temperature of helium gas =T'

Pressure of the helium gas = P'= P

Mass of the helium gas = m' =m

Moles of the helium  gas = $n'=\frac{m}{M'}=\frac{m}{4M}$

Volume of the helium gas = V' = V

Using an ideal gas equation:

$P'V'=n'RT'=\frac{mRT'}{4M}$...(2)

Divide (2) by (1)

$\frac{P'V'}{PV}=\frac{\frac{mRT'}{4M}}{\frac{mRT}{2M}}$

$\frac{T'}{T}=\frac{2}{1}$

The ratio of the temperature of helium to that of hydrogen gas is 2:1.