What is Graham's Law of Diffusion?

S7-SA5-0293

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

Graham's Law of Diffusion tells us how fast gases spread out or mix with other gases. It states that lighter gases spread faster than heavier gases at the same temperature and pressure. Think of it like a race where the lighter runners always win!

Simple Example

Quick Example

Imagine two balloons, one filled with hydrogen gas (very light) and another with oxygen gas (heavier). If both balloons have tiny holes, the hydrogen gas will leak out and mix with the air much, much faster than the oxygen gas. This is because hydrogen molecules are lighter.

Worked Example

Step-by-Step

QUESTION: Gas A has a molecular weight of 4 g/mol and Gas B has a molecular weight of 16 g/mol. How many times faster does Gas A diffuse compared to Gas B?

Step 1: Understand Graham's Law formula. Rate of diffusion is inversely proportional to the square root of molecular weight. So, (Rate A / Rate B) = sqrt(Molecular Weight B / Molecular Weight A).
---Step 2: Identify the given values. Molecular Weight A = 4 g/mol. Molecular Weight B = 16 g/mol.
---Step 3: Plug the values into the formula. (Rate A / Rate B) = sqrt(16 / 4).
---Step 4: Calculate the ratio inside the square root. (Rate A / Rate B) = sqrt(4).
---Step 5: Calculate the square root. (Rate A / Rate B) = 2.
---Answer: Gas A diffuses 2 times faster than Gas B.

Why It Matters

Understanding gas diffusion is crucial in fields like medicine for delivering medicines through inhalers, and in engineering for designing efficient ventilation systems in buildings. It's also vital in climate science to study how pollutants spread in the atmosphere, helping scientists predict air quality.

Common Mistakes

MISTAKE: Thinking heavier gases diffuse faster. | CORRECTION: Remember, lighter gases always diffuse faster. It's an inverse relationship – as molecular weight increases, diffusion rate decreases.

MISTAKE: Forgetting to take the square root of the molecular weights. | CORRECTION: The law involves the square root of the molecular weights, not just the molecular weights themselves.

MISTAKE: Mixing up the order of the gases in the formula (e.g., putting Molecular Weight A on top for Rate A). | CORRECTION: The ratio of rates (Rate A / Rate B) is equal to the square root of the *inverse* ratio of molecular weights (sqrt(Molecular Weight B / Molecular Weight A)).

Practice Questions

Try It Yourself

QUESTION: Which gas would diffuse faster: Methane (CH4, molecular weight = 16 g/mol) or Carbon Dioxide (CO2, molecular weight = 44 g/mol)? | ANSWER: Methane (CH4) would diffuse faster because it has a lower molecular weight.

QUESTION: If Gas X has a molecular weight of 9 g/mol and diffuses at 3 cm/s, what is the diffusion rate of Gas Y with a molecular weight of 36 g/mol? | ANSWER: Let Rate X = 3 cm/s, MW X = 9. Let MW Y = 36. (Rate X / Rate Y) = sqrt(MW Y / MW X). (3 / Rate Y) = sqrt(36 / 9) = sqrt(4) = 2. So, Rate Y = 3 / 2 = 1.5 cm/s.

QUESTION: Two gases, P and Q, have diffusion rates in the ratio of 4:1. If the molecular weight of Gas P is 4 g/mol, what is the molecular weight of Gas Q? | ANSWER: (Rate P / Rate Q) = sqrt(MW Q / MW P). (4 / 1) = sqrt(MW Q / 4). Squaring both sides: 16 = MW Q / 4. So, MW Q = 16 * 4 = 64 g/mol.

MCQ

Quick Quiz

According to Graham's Law, if Gas A is four times heavier than Gas B, how much faster will Gas B diffuse compared to Gas A?

2 times faster

4 times faster

16 times faster

It will diffuse slower

The Correct Answer Is:

If Gas A is 4 times heavier, its molecular weight is 4 times that of Gas B. The ratio of rates is sqrt(MW A / MW B) = sqrt(4/1) = 2. So, Gas B diffuses 2 times faster than Gas A.

Real World Connection

In the Real World

This law helps in processes like enriching uranium for nuclear power, where lighter isotopes are separated from heavier ones by making them diffuse through porous barriers. It's also used in perfume manufacturing to understand how different fragrance molecules spread in the air, creating a long-lasting scent.

Key Vocabulary

Key Terms

DIFFUSION: The spreading of particles from an area of higher concentration to an area of lower concentration | EFFUSION: The movement of gas particles through a tiny hole into a vacuum | MOLECULAR WEIGHT: The mass of one molecule of a substance | INVERSELY PROPORTIONAL: When one value increases, the other decreases proportionally

What's Next

What to Learn Next

Next, you can explore the Kinetic Molecular Theory of Gases. It explains why gases behave the way they do, including why lighter gases move faster, which will help you understand Graham's Law even better!