Video: Difference between Diatomic Gases (N_2 and Cl_2)

Which of the following statements correctly describes a difference between two diatomic gases, nitrogen (N₂) and chlorine (Cl₂)? [A] Nitrogen diffuses more slowly than chlorine as its molecular mass is smaller. [B] Nitrogen diffuses more slowly than chlorine as it is less reactive. [C] Nitrogen diffuses more quickly than chlorine as its molecular mass is bigger. [D] Nitrogen and chlorine diffuse at the same speed. (E) Nitrogen diffuses more quickly than chlorine as its molecular mass is smaller.

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Video Transcript

Which of the following statements correctly describes a difference between two diatomic gases, nitrogen N2 and chlorine Cl2? (A) Nitrogen diffuses more slowly than chlorine as its molecular mass is smaller. (B) Nitrogen diffuses more slowly than chlorine as it is less reactive. (C) Nitrogen diffuses more quickly than chlorine as its molecular mass is bigger. (D) Nitrogen and chlorine diffuse at the same speed. Or (E) nitrogen diffuses more quickly than chlorine as its molecular mass is smaller.

The five statements contain references to diffusion, molecular mass, and reactivity. Let’s have a look at what these mean. Diffusion is the overall movement of particles from an area where they’re at high concentration to an area where they’re at low concentration. You can see diffusion happening when you add ink to water. The individual particles of ink spread out until all the water is the same color.

The molecular mass is simply the mass of a single molecule. And it’s usually measured in unified atomic mass units.

And lastly, reactivity is the measure of the potential of substance to react. Reactivity isn’t generally given a number. It usually depends on the context. But there are substances like chlorine which are generally described as more reactive than nitrogen.

So statement (B) suggests that nitrogen diffuses more slowly because of its lower reactivity. Nitrogen is less reactive than chlorine because nitrogen has a strong triple bond. Whereas chlorine has a weaker single bond and it reacts readily to form chloride ions. But the question is, does the lower reactivity of nitrogen make it diffuse more slowly?

We’ll come back to that in a moment. First, let’s have a look at molecular mass. We can see the atomic mass of nitrogen from our periodic table is 14.007 unified atomic mass units. And we can calculate the molecular mass of nitrogen by multiplying that by two, giving us 28.014 unified atomic mass units. Again, going back to our periodic table, we can see the atomic mass of chlorine is 35.45 unified atomic mass units. Therefore, the molecular mass of chlorine, Cl2, is 70.90 unified atomic mass units. We can see from these numbers that the molecular mass of chlorine is much greater than the molecular mass of nitrogen.

Statement (C) says that nitrogen diffuses more quickly than chlorine as its molecular mass is bigger. We can dismiss this option straightaway because we know nitrogen has a smaller molecular mass than chlorine. This just leaves us a simple question. How do molecular mass or reactivity affect diffusion?

Well, diffusion is driven by Brownian motion. Brownian motion is a seemingly random movement of a particle in a sea of other particles. Every time the particle changes direction and speed, it’s because it’s collided with another particle. And it’s very difficult to predict how these collisions will occur and the consequence on the path of the particle. But what we’re talking about is diffusion, not Brownian motion. So what’s the importance of Brownian motion to diffusion?

Well, simply because of probabilities, it’s more likely for particles to spread out than it is for them to come together because of Brownian motion. So if we have two tiny pockets, one of pure nitrogen gas and one of pure chlorine gas, in another gas, we would expect those pockets to expand and for the particles to intermingle with the surrounding gas. The question is, which one would diffuse the fastest?

Well, there’s a simple principle. If a particle is lighter and it has the same amount of kinetic energy, it must be moving faster. If a particle is moving faster overall, it will diffuse more quickly. It will still follow Brownian motion, but it will move between each collision more quickly. From this, under the same conditions, we’d expect a molecule of nitrogen to move faster and diffuse faster than a molecule of chlorine. So we can eliminate option (D) because nitrogen and chlorine will diffuse at different speeds, nitrogen faster than chlorine.

We can also dismiss option (B) because, a, nitrogen diffuses more quickly than chlorine and the reactivity of nitrogen relative to chlorine doesn’t affect how it diffuses. Diffusion is about motion of individual particles, not how they react. Option (A) says that nitrogen diffuses more slowly than chlorine as its molecular mass is smaller. The molecular mass of nitrogen is smaller than chlorine, but that makes it diffuse faster, not more slowly. And what we’re left with is the correct answer. Nitrogen diffuses more quickly than chlorine as its molecular mass is smaller.

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