3. Rank each of the following in order of DECREASING atomic radius a. Cl, Br, Ga
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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).
If you have two gases, the ratio of their rates of diffusion is
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