Answers:
1. CO₂ < Ar < N₂ < He;
2. Cl₂ < CO₂ < Ar < N₂ < H₂
Step-by-step explanation:
Graham’s Law applies to the diffusion of gases:
The rate of diffusion (r) of a gas is inversely proportional to the square root of its molar mass (M).
[tex]r = \frac{1 }{\sqrt{M}}[/tex]
If you have two gases, the ratio of their rates of diffusion is
[tex]\frac{r_{2}}{r_{1}} = \sqrt{\frac{M_{1}}{M_{2}}}[/tex]
1. Order of diffusion rates
According to Graham's Law, the lightest gases will have the highest diffusion rates and the heavier gases the slowest.
The molecular masses of the gases are:
Ar 39.95; CO₂ 44.01; He 4.00; N₂ 28.02
Putting them in order,we get
44.01 > 39.95 > 28.02 > 4.00
CO₂ > Ar > N₂ > He
Thus, the relative rates of diffusion are
CO₂ < Ar < N₂ < He
2. Order of molecular speeds
A postulate of the Kinetic Molecular Theory is that at a given temperature, the average kinetic energy of the molecules is directly proportional to the Kelvin temperature.
KE = ½ mv² ∝ T
mv² ∝ T Divide each side by m
v² ∝ T/m
If T is constant.
v² ∝ 1/m Take the square root of each side
v ∝ 1/√m
This is an inverse relationship, so the molecules with the smallest molecular mass should have the highest average speeds.
The molecular masses of the gases are:
N₂ 28.02; H₂ 2.016; Cl₂ 70.91; CO₂ 44.01; Ar 39.95
Putting them in order. we get
70.91 > 44.01 > 39.95 > 28.02 > 2.016
Cl₂ > CO₂ > Ar > N₂ > H₂
Thus, the relative molecular speeds are
Cl₂ < CO₂ < Ar < N₂ < H₂
The order of increasing rates of effusion are:
Effusion refers to the movement of gas particles through a small hole. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. That is, the more massive is a molecule, the slower it effuses under the same conditions.
[tex]r = \frac{1}{\sqrt{M} }[/tex]
where,
First part
Let's consider the increasing order of molar masses of the first set of gases:
M(He) < M(Ar) < M(N₂) < M(CO₂)
4 g/mol < 18 g/mol < 28 g/mol < 44 g/mol
Considering the inverse relationship, the expected order of increasing rates of effusion is:
M(CO₂) < M(N₂) < M(Ar) < M(He)
Second part
Let's consider the increasing order of molar masses of the second set of gases:
M(H₂) < M(Ar) < M(N₂) < M(CO₂) < M(Cl₂)
2 g/mol < 18 g/mol < 28 g/mol < 44 g/mol < 71 g/mol
Considering the inverse relationship, the expected order of increasing rates of effusion is:
M(Cl₂) < M(CO₂) < M(N₂) < M(Ar) < M(H₂)
You can learn more about effusion here: https://brainly.com/question/8804761
