Chemistry 5070/12 — October/November 2016

Walkthrough

The question asks about how quickly gases diffuse. Gases diffuse because their particles move freely. Under the same conditions, the rate of diffusion of a gas is related to the mass of its particles: lighter gases diffuse more quickly, and heavier gases diffuse more slowly. At O Level it is enough to know that gases with the same relative molecular mass diffuse at the same rate.

Nitrogen is a diatomic molecule, $\text{N}_2$. Since one nitrogen atom has relative atomic mass 14, nitrogen's relative molecular mass is $2 \times 14 = 28$.

Now look for the gas whose relative molecular mass is also 28.

Carbon monoxide, $\text{CO}$, has one carbon atom ($12$) and one oxygen atom ($16$), so it has $\text{M}_r = 12 + 16 = 28$. That exactly matches nitrogen, so carbon monoxide diffuses at the same rate as nitrogen.

The other gases do not match:

• ammonia, $\text{NH}_3$, has $\text{M}_r = 17$, so it is lighter and diffuses more quickly;
• ethane, $\text{C}_2\text{H}_6$, has $\text{M}_r = 30$, so it is heavier and diffuses more slowly;
• oxygen, $\text{O}_2$, has $\text{M}_r = 32$, so it is heavier and diffuses more slowly.

Key Takeaways

• A gas diffuses faster when its particles are lighter.
• Under the same conditions, two gases with the same relative molecular mass diffuse at the same rate.
• Remember that many common gases are diatomic. Nitrogen is $\text{N}_2$, not N.
• Carbon monoxide is an important case because $\text{CO}$ and $\text{N}_2$ both have $\text{M}_r = 28$.

Common Mistakes

• Using the mass of a single nitrogen atom instead of the nitrogen molecule. Nitrogen is $\text{N}_2$, so its relative molecular mass is 28, not 14.
• Comparing the number of atoms in a formula rather than the total relative molecular mass. Ethane has 8 atoms, but it is heavier than nitrogen because carbon atoms are quite heavy.
• Forgetting the relative atomic masses of common elements: H = 1, C = 12, N = 14, O = 16.
• Thinking a smaller formula always means a lighter gas. For example, ammonia has only 4 atoms and is lighter, but oxygen has 2 atoms and is heavier. Actual $\text{M}_r$ matters.

Things to Be Careful About

• The phrase “under the same conditions” means the same temperature and pressure. This makes the comparison fair and allows us to compare rates by relative molecular mass directly.
• Use the correct formula of each gas. In particular, nitrogen is $\text{N}_2$, not N, because nitrogen is diatomic.
• Relative molecular mass has no unit. Do not write grams per mole for $\text{M}_r$; it is simply a number.
• If you use Graham’s law, remember that the rate of diffusion is inversely proportional to the square root of $\text{M}_r$. A gear with the same $\text{M}_r$ as nitrogen therefore diffuses at the same rate.