Question

If the kinetic energy of $O_2$ gas is $4.0kJmo{l}^{-1}$ . 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 $O_2=4.0kJ/mol$

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

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

$=\sqrt{\frac{2\times 4\times 10^{3}kg{m}^2{s}^{-2}mo{l}^{-1}}{32\times 10^{-3}kgmo{l}^{-1}}}$

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

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

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