Effusion and Diffusion of Gases with Examples

Effusion and Diffusion of Gases with Examples

Diffusion:

Mixing molecules of one gas with molecules of another gas is called diffusion . Smell of a perfume or meal in a room are some common examples of diffusion of gases. Gases have different diffusion rates at different temperatures. Following formula shows ratio of diffusion rates of two gases at same temperature.

Diffusion rate (r) is directly proportional to average molecular velocity.

Where; r₁ and r₂are diffusion rates of gas 1 and gas 2, V₁ and V₂ are average molecular velocities of gases and M₁ and M₂ are molecular masses of gases.

Equation given above is called also “Graham’s Diffusion Law”.

Now, we will give diffusion ratio of two different gases at different temperatures. Let T₁ and T₂ are absolute temperatures of gases.

To sum up;

Speed of gas diffusion;

• is inversely proportional to square root of molar mass
• is directly proportional to square root of absolute temperature

Thus;

If gases have same temperature, one of them having smaller molar mass has greater diffusion rate. If gases have equal molar mass, one of them having higher temperature has greater diffusion rate.

Effusion:

As you can see from the picture given above, motion of the gases from one container to another by passing through small hole is called effusion (as given in the picture, in general second container is empty, or vacuum).Diffusion takes place under constant pressure on the contrary effusion takes place under pressure difference between containers. Effusion rates of gases changes according  to Graham’s diffusion law. Now we solve some examples related to diffusion and effusion of gases.

Example: If gases X and SO₂ are send out at same time from points A and B, they meet at point 20 cm away from B. Which one of the following statements are true? (SO₂=64)

I. Molar mass of X is 4

II. If we increase  absolute temperature of SO₂ and keep temperature of X constant, meeting point of gases get closer to A.

III. If we decrease absolute temperatures of gases at same amount, meeting point does not change.

Solution:

I. Since meeting point of gases is 20 cm away from B, molecules of X move 4 times faster than molecules of SO₂.

I is true

II. SO₂ moves slower than X, if we increase temperature of SO₂, its speed increases and meeting point get closer point A. II is also true.

III. Decreasing temperatures of gases at same amount, does not affect meeting point. III is true

Example: Which one of the following statements are true for average molecular velocity of H₂ and N₂ molecules. (H=1, N=14)

I. N₂ molecules at 40 ⁰C are slower than H₂ molecules at 40 ⁰C.

II. H₂ molecules at 80 ⁰C are slower than N₂ molecules at 40 ⁰C.

III. N₂ molecules at 80 ⁰C are faster than H₂ molecules at 40 ⁰C.

Solution:

Molar mass of H₂=2 g/mol, Molar mass of N₂=28 g/mol.

I. Since molar mass of N₂ is larger than H₂, molecules of N₂ move slower than H₂. I is true

II. Average molecular speed is directly proportional to square root of absolute temperature. Thus, molecules of H₂ are faster than molecules of N₂. II is true

III. Molecules of N₂ at 80 ⁰C are faster than molecules of H₂ at 40 ⁰C. III is true.

Example: Under constant temperature, when we open the taps gases meet at point A. Find molecular mass of X(gas).

Solution:

Since they meet at point A, molecules of He are faster than molecules of X.During same time He takes 4 unit distance, X takes 1 unit distance.

Gases Exams and  Problem Solutions