Answer: The decreasing order of rate of effusion will be : [tex]He>C_3H_3>Ar[/tex]
Explanation: Rate of effusion is defined as the volume of gas which is effused in a given time. This is very well explained by Graham's Law.
This law states that the rate of effusion of gas is inversely proportional to the square root of the molar mass of the gas. More is the molar mass of the gas, its rate of effusion will be slow.
Mathematically,
[tex]\text{Rate of effusion}=\frac{1}{\sqrt{M}}[/tex]
Molar masses of the given gases are:
1) [tex]C_3H_3=(3\times 12)+(3\times 1)=39g/mol[/tex]
2) Ar = 40g/mol
3) He = 4 g/mol
So, the gases which have the highest molecular mass will have the lowest rate of effusion.
Hence, the decreasing order of rate of effusion will be:
[tex]He>C_3H_3>Ar[/tex]
The decreasing order of rate of effusion of given gases is,
[tex]\boxed{{\text{He}}>{\text{Ar}}>{{\text{C}}_3}{{\text{H}}_8}}[/tex]
Further Explanation:
Effusion is the process by which molecules of gas is traveled through a small hole from high pressure to the low pressure. According to graham’s law, effusion rate of a gas is inversely proportional to the square root of the molar mass of gas.
[tex]{\text{Rate of effusion}}\left({\text{R}}\right\propto\frac{1}{{\sqrt{{\mu}}}}[/tex]
Where [tex]{{\mu }}[/tex] is the molar mass of a gas.
The atomic mass of argon gas (Ar) is 40 g/mol.
The atomic mass of helium gas (He) is 4 g/mol.
The molar mass of propane gas [tex]\left({{{\text{C}}_3}{{\text{H}}_8}}\right)[/tex] is calculated as follows:
[tex]\begin{aligned}{\text{Molar mass}} &=\left[{\left( {\text{3}}\right)\left({{\text{atomic mass of carbon}}}\right)+\left({\text{8}}\right)\left({{\text{atomic mass ofhydrogen}}}\right)}\right]\\&=\left({\text{3}}\right)\left({{\text{12g/mol}}}\right)+\left({\text{8}}\right)\left({{\text{1g/mol}}}\right)\\&=\left({36{\text{g/mol}}}\right)+\left({8{\text{ g/mol}}}\right)\\&= 44{\text{ g/mol}}\\\end{aligned}[/tex]
The order of molar mass of gases is He < Ar < [tex]{{\text{C}}_3}{{\text{H}}_8}[/tex].
And, since the rate of effusion a gas is inversely proportional to the square root of the molar mass of gas, therefore, the decreasing order of rate of effusion of given gases is, He > Ar >[tex]{{\text{C}}_3}{{\text{H}}_8}[/tex]
Learn more:
1. Determine the Charles’s law.:https://brainly.com/question/1403211
2. Calculation of final volume of gas: https://brainly.com/question/6340739
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Ideal gas equation
Keywords: Effusion, rate of effusion, Ar, C3H3, He, molar mass, atomic mass, rate of effusion gases, atomic mass of argon, atomic mass of helium gas, molar mass of propane gas.
