Question

At a certain temperature and pressure, chlorine (cl2) molecules have an average velocity of 0. 0380 m/s. What is the average velocity of sulfur dioxide (so2) molecules under the same conditions?

Answer 1

Solution:-

$\longrightarrow$From the kinetic molecular theory of gases, the average speed of gas molecules at a specific temperature and pressure is given by :-

$\green{ \underline { \boxed{ \sf{v_{avg} = \frac{8RT}{\pi M}}}}}$

where

• R = 8.314 J/mol, the universal gas constant
• T is the absolute temperature of the gas
• M is the molar mass of the gas.

$\longrightarrow$For two different gases A and B at the same temperature, it can be shown that the average speeds are inversely proportional to the square root of their molecular masses-

$\green{ \underline { \boxed{ \sf{ \frac{v_{avg} ^A}{v_{avg}^B} = \sqrt{\frac{M_A}{M_B}}}}}}$

Given:-

$\sf average \:velocity \:of \:Cl_2,v_{avg} ^B= 0.0380 \:m/s$

Now,

$\sf Molar \:mass \:of \:Cl_2 = 2\times atomic \:mass \:of \:Cl$

$\implies$$\sf Molar \:mass \: of \:Cl_2 = 2\times 35.5$

$\implies$$\sf Molar \:mass \:of \: Cl_2 = 71 \:g$

similarly,

$\begin{gathered}\\\implies\quad \sf Molar \: mass \:of \: SO_2 = atomic \:mass \:of \:S +2\times \: atomic \: mass \: of \: O \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 32 +2\times 16 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 32 +32 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 64 \\\end{gathered}$

Putting Values in formula to get average velocity -

$\begin{gathered}\\\implies\quad \sf { \frac{v_{avg} ^{SO_2}}{v_{avg}^{Cl_2}} = \sqrt{\frac{M_{SO_2}}{M_{Cl_2}}}}\\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf { \frac{v_{avg} ^{SO_2}}{0.0380} = \sqrt{\frac{71}{64}}}\\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf \frac{v_{avg} ^{SO_2}}{0.0380} = 1.05 \: \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf v_{avg} ^{SO_2}= 1.05 \times 0.038 \: \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf v_{avg} ^{SO_2} = 0.4 \: m/s\: \\\end{gathered}$

$\longrightarrow$Thus the average velocity of sulphur dioxide molecules under the same conditions is 0.4 m/s