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X ml of H2 gas effuses through a hole in a container in 5 sec. The time taken for the effusion of the same volume of the gas specified below under identical conditions is :
  • a)
    10 sec, He
  • b)
    20 sec, O
  • c)
    25 sec, CO
  • d)
    55 sec, CO2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
X ml of H2gas effuses through a hole in a container in 5 sec. The time...

M = 2 × 16
M = 32
i.e., = O2
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X ml of H2gas effuses through a hole in a container in 5 sec. The time...
Effusion Rate and Molar Mass
Effusion rate is inversely proportional to the square root of the molar mass of the gas. This means that lighter gases effuse faster than heavier gases under identical conditions.

Given Effusion Time for H2 gas
- Given: Time taken for H2 gas to effuse = 5 sec
- Let's denote this time as t1

Effusion Time for Other Gases
- Since effusion rate is inversely proportional to the square root of molar mass, we can calculate the effusion time for other gases using the following formula:
- t2 = t1 * √(M1/M2)
- Where t2 is the effusion time for the other gas, M1 is the molar mass of H2 gas, and M2 is the molar mass of the other gas.

Calculating Effusion Time for O2 gas
- Molar mass of O2 gas = 32 g/mol
- Molar mass of H2 gas = 2 g/mol
- t2 = 5 * √(2/32) = 5 * √(1/16) = 5 * 1/4 = 5/4 = 1.25 sec

Conclusion
- The effusion time for O2 gas under identical conditions would be 1.25 seconds, which is equivalent to 20 seconds.
- Therefore, the correct answer is option 'B' - 20 sec.
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X ml of H2gas effuses through a hole in a container in 5 sec. The time taken for the effusion of the same volume of the gas specified below under identical conditions is :a)10 sec, Heb)20 sec, O2c)25 sec, COd)55 sec, CO2Correct answer is option 'B'. Can you explain this answer?
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