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Which of the following gases have same r...

Which of the following gases have same rate of diffusion at constant P and T ?

A

`C_(2)H_(6)`

B

`C_(2)H_(4)`

C

`N_(2)`

D

CO

Text Solution

AI Generated Solution

The correct Answer is:
To determine which gases have the same rate of diffusion at constant pressure and temperature, we can use Graham's law of diffusion. This law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, gases with the same molar mass will diffuse at the same rate. ### Step-by-Step Solution: 1. **Identify the Gases**: First, we need to identify the gases given in the question. Let's assume we have the following gases: Ethane (C2H6), Ethylene (C2H4), Nitrogen (N2), and Carbon Monoxide (CO). 2. **Calculate Molar Masses**: - **Ethane (C2H6)**: - Carbon (C) has a molar mass of approximately 12 g/mol. - Hydrogen (H) has a molar mass of approximately 1 g/mol. - Molar mass of C2H6 = (2 × 12) + (6 × 1) = 24 + 6 = **30 g/mol**. - **Ethylene (C2H4)**: - Molar mass of C2H4 = (2 × 12) + (4 × 1) = 24 + 4 = **28 g/mol**. - **Nitrogen (N2)**: - Molar mass of N2 = (2 × 14) = **28 g/mol**. - **Carbon Monoxide (CO)**: - Molar mass of CO = 12 + 16 = **28 g/mol**. 3. **Compare Molar Masses**: - Ethane (C2H6) has a molar mass of 30 g/mol. - Ethylene (C2H4), Nitrogen (N2), and Carbon Monoxide (CO) all have a molar mass of 28 g/mol. 4. **Identify Gases with Same Molar Mass**: - The gases that have the same molar mass (28 g/mol) are Ethylene (C2H4), Nitrogen (N2), and Carbon Monoxide (CO). 5. **Conclusion**: - Therefore, the gases that will have the same rate of diffusion at constant pressure and temperature are Nitrogen (N2), Ethylene (C2H4), and Carbon Monoxide (CO). ### Final Answer: The gases that have the same rate of diffusion at constant P and T are Nitrogen (N2), Ethylene (C2H4), and Carbon Monoxide (CO). ---
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