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).
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If you have two gases, the ratio of their rates of diffusion is
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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