Question

Calculate the root mean square, average and most probable speed of oxygen at ${27}^{\circ }C$.

Answer 1

${27}^{\circ }C=300K$
Root mean square speed $=\sqrt{\frac{3RT}{M}}$
$R=8.314\times {10}^{7}erg{K}^{-1}mo{l}^{-1};M=32gmo{l}^{-1};T=300K$
Substituting the values,
$=\sqrt{\frac{3\times 8.314\times {10}^7\times 300}{32}}$
$=483.56cm/sec$
$=483.56m/sec$
Average speed $=\sqrt{\frac{8RT}{\pi M}}$
$=\sqrt{\frac{8\times 8.314\times {10}^7\times 300\times 7}{22\times 32}}$
$=445.42cm/sec$
$=445.42m/sec$
Most probable speed $=\sqrt{\frac{2\times R\times T}{M}}$
$=\sqrt{\frac{2\times 8.314\times {10}^7\times 300}{32}}$
$=39482cm/sec$
$=394.83m/sec$.