Calculating the Rate of Diffusion

Oct 13, 2025 by miodeya.com 143 views

Introduction

The rate of diffusion is a fundamental concept in chemistry that describes the movement of molecules from an area of higher concentration to an area of lower concentration. In this article, we will explore the rate of diffusion of hydrogen and oxygen through a porous pot under the same conditions. We will examine the factors that influence the rate of diffusion and compare the results to determine how long it will take for the same volume of oxygen to diffuse through the same pot.

The Rate of Diffusion

The rate of diffusion is influenced by several factors, including the concentration gradient, temperature, pressure, and the size and shape of the molecules. In this case, we are comparing the diffusion of hydrogen (H-1) and oxygen (O-16) through a porous pot under the same conditions.

The Graham's Law of Diffusion

The Graham's Law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight. This means that lighter molecules will diffuse faster than heavier molecules.

Calculating the Rate of Diffusion

To calculate the rate of diffusion, we need to know the molecular weight of hydrogen and oxygen. The molecular weight of hydrogen is 2 g/mol, and the molecular weight of oxygen is 32 g/mol.

We are given that 100 cm^3 of hydrogen diffused through a porous pot in 1.0 s. We can use this information to calculate the rate of diffusion of hydrogen.

Rate of Diffusion of Hydrogen

The rate of diffusion of hydrogen can be calculated using the following formula:

Rate of diffusion = Volume of gas / Time

Substituting the values, we get:

Rate of diffusion of hydrogen = 100 cm^3 / 1.0 s = 100 cm^3/s

Calculating the Rate of Diffusion of Oxygen

Now that we have the rate of diffusion of hydrogen, we can use the Graham's Law of diffusion to calculate the rate of diffusion of oxygen.

The Graham's Law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight. We can write this as:

Rate of diffusion of oxygen / Rate of diffusion of hydrogen = √(Molecular weight of hydrogen / Molecular weight of oxygen)

Substituting the values, we get:

Rate of diffusion of oxygen / 100 cm^3/s = √(2 g/mol / 32 g/mol)

Simplifying, we get:

Rate of diffusion of oxygen = 100 cm^3/s × √(1/16) = 100 cm^3/s × 1/4 = 25 cm^3/s

Time Required for Oxygen to Diffuse Through the Pot

Now that we have the rate of diffusion of oxygen, we can calculate the time required for the same volume of oxygen to diffuse through the same pot.

We are given that 100 cm^3 of hydrogen diffused through the pot in 1.0 s. We can use this information to calculate the time required for 100 cm^3 of oxygen to diffuse through the pot.

Time required = Volume of gas / Rate of diffusion

Substituting the values, we get:

Time required = 100 cm^3 / 25 cm^3/s = 4.0 s

Conclusion

In conclusion, we have compared the rate of diffusion of hydrogen and oxygen through a porous pot under the same conditions. We have used the Graham's Law of diffusion to calculate the rate of diffusion of oxygen and have found that it is 1/4 of the rate of diffusion of hydrogen. We have also calculated the time required for the same volume of oxygen to diffuse through the same pot and have found that it is 4.0 s.

References

Graham, T. (1833). "On the diffusion of gases." Transactions of the Royal Society of Edinburgh, 7, 1-22.
Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.

Q: What is the rate of diffusion of hydrogen and oxygen through a porous pot?

A: The rate of diffusion of hydrogen is 100 cm^3/s, and the rate of diffusion of oxygen is 25 cm^3/s.

Q: Why is the rate of diffusion of oxygen slower than the rate of diffusion of hydrogen?

A: The rate of diffusion of a gas is inversely proportional to the square root of its molecular weight. Oxygen has a molecular weight of 32 g/mol, which is 16 times greater than the molecular weight of hydrogen (2 g/mol). Therefore, the rate of diffusion of oxygen is slower than the rate of diffusion of hydrogen.

Q: How long will it take for the same volume of oxygen to diffuse through the same pot?

A: It will take 4.0 s for the same volume of oxygen to diffuse through the same pot.

Q: What factors influence the rate of diffusion of gases?

A: The rate of diffusion of gases is influenced by several factors, including the concentration gradient, temperature, pressure, and the size and shape of the molecules.

Q: What is the Graham's Law of diffusion?

A: The Graham's Law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.

Q: How can the rate of diffusion of a gas be calculated?

A: The rate of diffusion of a gas can be calculated using the following formula:

Rate of diffusion = Volume of gas / Time

Q: What is the molecular weight of hydrogen and oxygen?

A: The molecular weight of hydrogen is 2 g/mol, and the molecular weight of oxygen is 32 g/mol.

Q: Why is the rate of diffusion of hydrogen faster than the rate of diffusion of oxygen?

A: The rate of diffusion of hydrogen is faster than the rate of diffusion of oxygen because hydrogen has a smaller molecular weight than oxygen.

Q: Can the rate of diffusion of gases be affected by other factors?

A: Yes, the rate of diffusion of gases can be affected by other factors, including the concentration gradient, temperature, pressure, and the size and shape of the molecules.

Q: What is the significance of the rate of diffusion of gases?

A: The rate of diffusion of gases is significant in many fields, including chemistry, physics, and engineering. It is used to understand the behavior of gases and to design systems that involve the diffusion of gases.

Q: How can the rate of diffusion of gases be measured?

A: The rate of diffusion of gases can be measured using various techniques, including the use of porous pots, diffusion cells, and gas chromatography.

Q: What are some real-world applications of the rate of diffusion of gases?

A: Some real-world applications of the rate of diffusion of gases include the design of gas separation systems, the development of new materials, and the understanding of atmospheric phenomena.

Q: Can the rate of diffusion of gases be affected by the presence of other substances?

A: Yes, the rate of diffusion of gases can be affected by the presence of other substances. For example, the presence of a catalyst can increase the rate of diffusion of a gas.

Q: How can the rate of diffusion of gases be used to understand chemical reactions?

A: The rate of diffusion of gases can be used to understand chemical reactions by studying the rate of diffusion of reactants and products. This can provide insights into the mechanisms of chemical reactions and the factors that influence them.