Question

Two flasks A and B have equal volumes. Flask A containing $H_2$ gas is maintained at $27{}^{o}C$ while B containing an equal mass of $C{H}_{2}S$ gas is maintained at $177{}^{o}C$. Using average velocity calculate by how many times the molecules of $H_2$ gas are moving faster than $C{H}_{2}S$ gas.

• A. 4.0
• B. 4.00
• C. 4

Answer 1

Answer: (A), (B), (C)

Average velocity of a gas is given as,
${\mu }_{avg}=\sqrt{\frac{8RT}{\pi M}}$
for $H_2$ gas, ${\mu }_{H_2}=\sqrt{\frac{8R{T}_1}{\pi M_1}}$
for $C{H}_{3}SH$ gas, ${\mu }_{C{H}_{3}SH}=\sqrt{\frac{8R{T}_2}{\pi M_2}}$
taking their ratio we get,
$\frac{{\mu }_{H_2}}{{\mu }_{C{H}_{3}SH}}=\sqrt{\frac{T_1\times M_2}{T_2\times M_1}}$
where $M_1=2g/mol$ and $M_2=48g/mol$

$\frac{{\mu }_{H_2}}{{\mu }_{C{H}_{3}SH}}=\sqrt{\frac{300\times 48}{450\times 2}}=\sqrt{16}=4$

Thus, $H_2$ molecules are moving 4 times faster than that of $C{H}_{3}SH$.