Question

(~40 Points, Please answer and explain)

Answer 1

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).

$r = \frac{1 }{\sqrt{M}}$

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

$\frac{r_{2}}{r_{1}} = \sqrt{\frac{M_{1}}{M_{2}}}$

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