Question

Find the rms , most probable and average speeds $S{O}_2$ at ${27}^{o}C$ .

Answer 1

Molar mass of $S{O}_2=32+32=64$ $g$;

Given,

$T=27+273=300$ $K$

$R=8.314$

$M=64\times {10}^{-3}$ $Kg$

RMS speed $=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times \left(8.314\right)\left(300\right)}{64\times {10}^{-3}}}=\sqrt{\frac{74.7\times 100\times {10}^3}{64}}=\sqrt{\frac{747\times {10}^4}{64}}=3.416\times {10}^2=341.6$ $m{s}^{-1}$

MP (Most probable) speed $=\sqrt{\frac{2RT}{M}}=\sqrt{\frac{2\times 8.314\times 300}{64\times {10}^{-3}}}=\sqrt{\frac{49.8\times 100}{64\times {10}^{-3}}}=\sqrt{\frac{49800\times {10}^2}{64}}={10}^2\times \sqrt{\frac{498}{64}}=278.9$ $m{s}^{-1}$

Average speed $=\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{2.54\times 8.314\times 300}{64\times {10}^{-3}}}=314.62$ $m{s}^{-1}$