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A bulb contains 1 mole of hydrogen and 1 mole of oxygen at temperature T. The ratio of rms values of velocity of hydrogen molecules to that of oxygen molecule is
  • a)
    1 : 4
  • b)
    4 :1
  • c)
    16 : 1
  • d)
    1 : 16
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A bulb contains 1 mole of hydrogen and 1 mole of oxygen at temperature...
Explanation:

  • The rms velocity of a gas molecule is given by the formula :


    • v(rms) = sqrt(3kT/m)


  • where k is Boltzmann constant, T is temperature and m is the mass of the molecule

  • Let us consider the case of a bulb containing 1 mole of hydrogen and 1 mole of oxygen

  • Since the number of moles is the same, the total number of molecules is the same for both gases

  • The mass of an oxygen molecule (O2) is 32 g/mol and that of a hydrogen molecule (H2) is 2 g/mol

  • So, the mass of an oxygen molecule is 16 times that of a hydrogen molecule

  • Using the formula for rms velocity, we get:


    • For hydrogen molecule: v(rms) = sqrt(3kT/2)

    • For oxygen molecule: v(rms) = sqrt(3kT/32)


  • Dividing the two equations, we get:


    • v(rms) of hydrogen / v(rms) of oxygen = sqrt((3kT/2) / (3kT/32))

    • v(rms) of hydrogen / v(rms) of oxygen = sqrt(32/2) = 4


  • Therefore, the ratio of rms values of velocity of hydrogen molecules to that of oxygen molecules is 4:1

  • Hence, the correct option is (B) 4:1

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A bulb contains 1 mole of hydrogen and 1 mole of oxygen at temperature...
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A bulb contains 1 mole of hydrogen and 1 mole of oxygen at temperature T. The ratio of rms values of velocity of hydrogen molecules to that of oxygen molecule isa)1 : 4 b)4 :1c)16 : 1d) 1 : 16Correct answer is option 'B'. Can you explain this answer?
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