Problem 10 - A Complete Resource Book in Chemistry for JEE Main

Question

Which pair of the gases diffuses with the same rate at same temperature and pressure? (a) \(\mathrm{CO}\) and \(\mathrm{NO}\) (b) \(\mathrm{NO}_{2}\) and \(\mathrm{CO}_{2}\) (c) \(\mathrm{NH}_{3}\) and \(\mathrm{PH}_{3}\) (d) \(\mathrm{NO}\) and \(\mathrm{C}_{2} \mathrm{H}_{6}\)

Step-by-Step Solution

Answer

The pair NO and C₂H₆ (option d) diffuse at the same rate.

Step 1: Identify the Diffusion 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. This means that for two gases to diffuse at the same rate under the same conditions, their molar masses must be equal.

Step 2: Calculate Molar Masses of Gases

We need to calculate the molar masses of each gas in the given options: - CO: Molar mass = 12 (C) + 16 (O) = 28 g/mol - NO: Molar mass = 14 (N) + 16 (O) = 30 g/mol - NO₂: Molar mass = 14 (N) + 2×16 (O) = 46 g/mol - CO₂: Molar mass = 12 (C) + 2×16 (O) = 44 g/mol - NH₃: Molar mass = 14 (N) + 3×1 (H) = 17 g/mol - PH₃: Molar mass = 31 (P) + 3×1 (H) = 34 g/mol - C₂H₆: Molar mass = 2×12 (C) + 6×1 (H) = 30 g/mol

Step 3: Compare Pairs on Molar Masses

Now, compare the molar masses of the pairs given: - (a) CO vs NO: 28 vs 30 g/mol - (b) NO₂ vs CO₂: 46 vs 44 g/mol - (c) NH₃ vs PH₃: 17 vs 34 g/mol - (d) NO vs C₂H₆: 30 vs 30 g/mol The pair with the same molar mass should diffuse at the same rate.

Step 4: Determine the Pair with Equal Molar Masses

From the comparison, we see that the pair NO and C₂H₆ both have molar masses of 30 g/mol. Therefore, this pair will diffuse at the same rate under the same temperature and pressure conditions.

Key Concepts

Molar Mass Calculation

The molar mass of a substance is essential for understanding its chemical properties and behavior, such as the rate of diffusion. To calculate the molar mass, simply sum up the atomic masses of all the atoms in the molecule. These atomic masses can be found on the periodic table.
For instance:

• For carbon monoxide (CO), you add the atomic mass of carbon (12) and oxygen (16), resulting in a molar mass of 28 g/mol.
• For nitric oxide (NO), you combine the atomic mass of nitrogen (14) and oxygen (16) to get 30 g/mol.

Repeated practice in calculating molar masses will make it simpler to predict other properties, such as the rate of diffusion of gases. Understanding how to accurately calculate molar masses is a foundational skill in chemistry.
It helps to visualize molecules and anticipate their behavior during chemical reactions or as they interact with their environment.

Rate of Diffusion

Graham's Law of Diffusion is a central principle for understanding how gases move. It states that the rate at which two gases diffuse is inversely proportional to the square root of their molar masses. Simply put, the lighter the gas, the faster it will diffuse.

1. This principle means if you compare two different gases, the one with the lower molar mass will have a higher rate of diffusion.
2. According to this law, \[ r_1 / r_2 = \sqrt{M_2 / M_1} \]where:
   • \(r_1\) and \(r_2\) are the rates of diffusion for gas 1 and gas 2, respectively.
   • \(M_1\) and \(M_2\) are the molar masses of gas 1 and gas 2.

This formula becomes useful when determining which gases from a selection will diffuse at the same rates under similar conditions.
Understanding the rate of diffusion is crucial for applications in industries like chemical engineering, where gas diffusion can impact product safety and effectiveness.

Gas Diffusion

Gas diffusion is the process through which gas molecules spread from an area of high concentration to an area of lower concentration. This natural movement continues until equilibrium is reached. Several factors affect diffusion in gases, with temperature and pressure being significant players.

The Factors Affecting Gas Diffusion

• **Temperature:** Higher temperatures provide more kinetic energy to gas molecules, increasing their movement speed and thereby their diffusion rates.
• **Pressure:** High pressure confines more gas molecules in the same space, potentially speeding up diffusion as there are more collisions and movement.
• **Molar Mass:** As Graham's Law states, gases with lower molar masses diffuse faster than those with higher molar masses.

Diffusion ensures even distribution of gases, which is vital in various scientific and practical applications, including respiratory processes and industrial gas treatments.
By understanding gas diffusion and its influencing factors, scientists and engineers can more accurately design processes and predict the behavior of gases in different environments.