Question

Which pair of the gaseous species diffuses through a small jet with the same rate of diffusion at same pressure and temperature? (1) \(\mathrm{NO}, \mathrm{CO}\) (2) \(\mathrm{NO}, \mathrm{CO}_{2}\) (3) \(\mathrm{NH}_{3}, \mathrm{PH}_{3}\) (4) \(\mathrm{NO}, \mathrm{C}_{2} \mathrm{H}_{6}\)

Short answer

NO and C2H6 have the same rate of diffusion due to having the same molar mass.

Step-by-step solution

- Identify the Principle

According to Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, gases with the same rate of diffusion must have equal molar masses.

- List the Molar Masses

Calculate the molar mass of each gas species: - NO: 14 amu (N) + 16 amu (O) = 30 amu- CO: 12 amu (C) + 16 amu (O) = 28 amu- CO2: 12 amu (C) + 2 * 16 amu (O) = 44 amu- NH3: 14 amu (N) + 3 * 1 amu (H) = 17 amu- PH3: 31 amu (P) + 3 * 1 amu (H) = 34 amu- C2H6: 2 * 12 amu (C) + 6 * 1 amu (H) = 30 amu

- Compare the Molar Masses

Evaluate the obtained molar masses to identify pairs with the same molar mass:- NO and CO: 30 amu and 28 amu, respectively- NO and CO2: 30 amu and 44 amu, respectively- NH3 and PH3: 17 amu and 34 amu, respectively- NO and C2H6: 30 amu and 30 amu, respectively

- Conclusion

The pair with the same molar mass and therefore the same rate of diffusion is NO (30 amu) and C2H6 (30 amu).

Key concepts

rate of diffusion

Graham's law of diffusion provides a critical insight into understanding how different gases spread. It states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Put simply, lighter gases diffuse faster than heavier ones. For example, consider two gases, A and B. If gas A has a smaller molar mass than gas B, gas A will diffuse more quickly. This fundamental principle is essential for comparing how different gases will behave under identical conditions.

molar mass

Molar mass plays a central role in determining the rate of diffusion for gases. The molar mass is essentially the weight of one mole of a given substance measured in atomic mass units (amu) or grams per mole (g/mol). To find the molar mass of a compound, you sum the atomic masses of all the elements in the molecule. For instance:

• The molar mass of nitric oxide (NO) is 14 (N) + 16 (O) = 30 amu
• The molar mass of carbon monoxide (CO) is 12 (C) + 16 (O) = 28 amu
• The molar mass of carbon dioxide (CO2) is 12 (C) + 2 * 16 (O) = 44 amu

Understanding the molar mass enables you to predict and compare how quickly different gases will diffuse.

gas species comparison

To directly compare the rate of diffusion between different gas species, you can use their molar masses. Graham's law tells us that gases with the same molar mass will diffuse at the same rate under identical conditions. Let's see this in action with the given gases:

• o: 30 amu
• CO: 28 amuo2: 44 amu
• h: 17 amu
• h3: 34 amu
• C2H6: 30 amuo and C2H6 both have molar masses of 30 amu. Therefore, according to Graham's law, they will diffuse at the same rate.
  This principle is extremely useful for predicting gas behaviors in various scientific and industrial applications, like chemical engineering and environmental science.') }]} ] } } } } '] } ]ặng.