Question

At what temperature is the rms speed of $H_2$ molecules the same as that of oxygen molecules at ${1327}^{\circ }C$?

• A. $173K$
• B. $100K$
• C. $400K$
• D. $523K$

Answer 1

Answer: (B)

$100K$

Temperature of Oxygen $\left(T\right)=1327°C=(273+1327)K=1600K$

Molecular weight of Oxygen $\left(M_O\right)=32$

Molecular weight of Hydrogen $\left(M_H\right)=2$

The rms velocity of $O_2=C_0=\sqrt{\frac{3R{T}_O}{M_O}}=\sqrt{\frac{3R\times 1600}{32}}$

The rms velocity of $H_2=C_0=\sqrt{\frac{3R{T}_H}{M_H}}=\sqrt{\frac{3R{T}_H}{2}}$

as the rms velocities of equal $C_O=C_H$

$\sqrt{\frac{3R\times 1600}{32}}=\sqrt{\frac{3R{T}_H}{2}}\frac{3R\times 1600}{32}=\frac{3R{T}_H}{2}{T}_H=100K$

Therefore, the option is B.