Question

At a constant temperature, which gas travels the fastest, hydrogen (H${}_2$) or carbon dioxide (CO${}_2$)? How many times faster is the fastest gas?

• A. Hydrogen, $4.7$ times faster
• B. Carbon dioxide, $4.7$ times faster
• C. Hydrogen, $22$ times faster
• D. Carbon dioxide, $22$ times faster
• E. As long as the temperature remains constant, they both travel at the same speed

Answer 1

The correct option is A Hydrogen, $4.7$ times faster

At same temperature and pressure, the speed of the gas particles depends upon the molar mass of the gas.
Hence, which has the least mass, will travel fastest.

So, here as the $H_2$ has lesser molar mass, hence, $H_2$ will travel faster than $C{O}_2$.

$\frac{r_{H_2}}{r_{C{O}_2}}=\sqrt{\frac{M_{C{O}_2}}{M_{H_2}}}=\sqrt{\frac{44}{2}}=\sqrt{2}2=4.7$

Hence, Hydrogen will travel $4.7$ times faster.