Calculate the ratio of the rate of diffusion of oxygen to the rate of diffusion of hydrogen at constant temperature and pressure.

To determine the ratio of the rate of diffusion of oxygen to that of hydrogen, we can use Graham's Law of Effusion. This law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. In simpler terms, lighter gases diffuse faster than heavier gases. Let's break this down step by step.

Understanding Graham's Law

Graham's Law can be mathematically expressed as:

Rate of diffusion of gas 1 / Rate of diffusion of gas 2 = √(Molar mass of gas 2 / Molar mass of gas 1)

Identifying the Gases

In this case, we are comparing oxygen (O₂) and hydrogen (H₂). The molar masses of these gases are:

• Molar mass of oxygen (O₂): approximately 32 g/mol
• Molar mass of hydrogen (H₂): approximately 2 g/mol

Applying the Formula

Now, we can plug these values into Graham's Law:

Rate of diffusion of O₂ / Rate of diffusion of H₂ = √(Molar mass of H₂ / Molar mass of O₂)

Substituting the molar masses:

Rate of diffusion of O₂ / Rate of diffusion of H₂ = √(2 g/mol / 32 g/mol)

Calculating the Ratio

Now, let's simplify the fraction inside the square root:

Rate of diffusion of O₂ / Rate of diffusion of H₂ = √(1/16)

Taking the square root gives us:

Rate of diffusion of O₂ / Rate of diffusion of H₂ = 1/4

Final Result

This means that the rate of diffusion of oxygen is one-fourth that of hydrogen. In other words, hydrogen diffuses four times faster than oxygen under the same conditions of temperature and pressure.

Real-World Implications

This principle has practical applications in various fields, such as in the design of gas separation processes and understanding how gases behave in different environments. For instance, in the context of respiratory physiology, the faster diffusion of oxygen compared to heavier gases can influence how efficiently gases are exchanged in the lungs.

In summary, the ratio of the rate of diffusion of oxygen to that of hydrogen is 1:4, highlighting the significant impact of molar mass on the diffusion rates of gases.