Question

If the kinetic energy of $O_2$ gas is $4.0 \,kJ \; mol^{-1}$ . its RMS speed in $cm \; s^{-1}$ is

• A. $5.0 \times 10^2$
• B. $5.0 \times 10^3$
• C. $5.0 \times 10^4$
• D. $5.0 \times 10^{-4}$

Answer 1

Answer: (C)

Kinetic energy of $O _{2}=4.0\, kJ / mol$

$ KE =\frac{3 R T}{2}$ and $ v_{ rms }=\sqrt{\frac{3 R T}{M}}$

$ v_{ rms } =\sqrt{\frac{2 KE }{M}}$

$=\sqrt{\frac{2 \times 4 \times 10^{3} \,kg \,m ^{2} s ^{-2} \,mol ^{-1}}{32 \times 10^{-3} \,kg \,mol ^{-1}}} $

$\left[\because 1 \,J =1 \,kg \,m ^{2} s ^{-2}\right] $

$=\frac{10^{3}}{2}=5 \times 10^{2} \,m / s$

$V_{\text {rms }}$ in $cm / s =50 \times 10^{4} \,cm / s$