Which gas in each of the following pairs diffuses more...

Which gas in each of the following pairs diffuses more rapidly, and what are the relative rates of diffusion?
(a) Krand $\mathrm{O}_{2} \quad$ (b) $\mathrm{N}_{2}$ and acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$

Key Concepts

Graham's Law of Diffusion

Graham's Law states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases (with lower molar masses) diffuse faster than heavier gases, which is the fundamental principle used to compare diffusion rates between gases.

Molar Mass and Its Influence on Diffusion

The molar mass of a gas directly affects how quickly its molecules move. Since the diffusion rate is inversely related to the square root of the molar mass, comparing the molar masses of different gases allows one to predict which gas will diffuse more rapidly.

Kinetic Molecular Theory

Kinetic Molecular Theory explains the behavior of gas particles, including their speeds, collisions, and energy distribution. It provides the framework for understanding why lighter molecules, which possess higher average speeds at a given temperature, tend to diffuse more quickly than heavier molecules.

Transcript

00:04 So this question is about graham's law of effusion.

00:08 And we're asked in two pairs of gases, which of them is going to effuse faster? and also are asked how much faster? so the first step, the principle behind it is that the smaller molecule is going to effuse faster, whichever one has a lower mass is going to effuse faster than the one that has a higher mass.

00:33 And we'll look at the equation in a moment.

00:35 But the first thing i'd like to do is come up with the molar masses for each of these.

00:41 So if we look at our periodic table, the molar mass for krypton is 84.

00:49 The molar mass for oxygen, a single oxygen atom is 16, but of course this is 02, so it's going to be 32.

00:59 Moving down to the second part, for nitrogen, a single nitrogen, is 14, but this is n2, so it's going to be 28.

01:09 And acetylene here, so carbon is 12, but there are two of them, so that's 24, and hydrogen is one, but there are two of them, so that's two, so 24 plus 2, is 26.

01:26 So in both pairs, we are going to want the smaller of the two.

01:34 So between krypton and oxygen, oxygen is considerably smaller than the krypton, considerably lighter, so we know that that one is going to be the faster one.

01:43 And then between the nitrogen and the acetylene, the acetylene is slightly smaller, so it's going to be slightly faster.

01:52 Now let's look at the equation.

01:54 So graham's law of afusion says that the ratio of the rates of effusion is equal to the square root of the ratio of the masses.

02:13 And you'll notice that we inverted it...

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