Question

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

Answer 1

m = molar mass of $S{O}_2$ is. 64 gm. (6.4 x ${10}^{2-}$) kg/mol

T = 273+27 = 300K

R = gas constant = 8.314 joules/ mol k

To calculate RMs avg. speed.

$\mu$ = $\sqrt{\frac{3RT}{M}}$

= $\sqrt{\frac{3\times 8.314}{6.4\times {10}^{-}2}}$

= 19.74$\frac{m}{s}$

to calculate RMs most probable speed,

$V_{mp}$ = $\sqrt{\frac{2KT}{m}}$

here, K is the Boltzmann cinstant whichis equal to $1.38\times {10}^{-23}$ J/k

$V_{mp}$ = $\sqrt{\frac{2\times 1.38\times {10}^{-23}\times 300}{6.4\times {10}^{-2}}}$

$V_{mp}$ = $\sqrt{129.37\times {10}^{-21}}$

=$3.59\times {10}^{-10}$