Answer:
Ratio of average kinetic energy will be 1:1.
Ratio of root mean square speeds of gases: [tex]\sqrt{\frac{1}{2}}[/tex]
Explanation:
Given the mixture of two gases ,at same temperature T.
Gas A = Sulfur oxide =[tex]SO_2[/tex]
Molar mass of sulfur oxide ,M= 0.064 kg/mol
Gas B = Oxygen gas = [tex]O_2[/tex]
Molar mass of oxygen gas ,M'= 0.032 kg/mo
Average kinetic energy of a molecule of a gas is given as:
[tex]K=\frac{3}{2}kT[/tex]
K = Boltzmann constant
T = temperature of the gas
[tex]K_A=\frac{3}{2}kT[/tex]..(1)
[tex]K_B=\frac{3}{2}kT[/tex]..(2)
Ratio of average kinetic energy will be:
[tex]\frac{K_A}{K_B}=\frac{\frac{3}{2}kT}{\frac{3}{2}kT}=\frac{1}{1}[/tex]
Root mean square speeds of the gas particles:
[tex]u_{rms}=\sqrt{\frac{3RT}{M}}[/tex]
M = molar mass of the gas
[tex]u_{rms,SO_2}=\sqrt{\frac{3RT}{0.064 kg/mol}}[/tex]..(3)
[tex]u_{rms,O_2}=\sqrt{\frac{3RT}{0.032 kg/mol}}[/tex]..(4)
Ratio of root mean square speeds of gases:
[tex]\frac{u_{rms,SO_2}}{u_{rms,O_2}}=\sqrt{\frac{\frac{3RT}{0.064 kg/mol}}{\frac{3RT}{0.032 kg/mol}}}=\sqrt{\frac{1}{2}}[/tex]
Ratio of average kinetic energy will be 1:1.
Ratio of root mean square speeds of gases: [tex]\sqrt{\frac{1}{2}}[/tex]
