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At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.
Correct answer is '22'. Can you explain this answer?
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Verified Answer
At what temperature (in Kelvin) will the average speed of hydrogen mol...
If 
are the average speeds of hydrogen and nitrogen molecules at temperatures T1K and T2K respectively, we have
...(i)
...(ii)
where m1 and m2 are the masses of hydrogen and nitrogen molecules respectively.
Dividing eq. (1) and (2), we get
...(iii)
Given when
and
Substituting these values in (3), we get
or
The most probable speed of nitrogen at temperature T is given by
Here k = 1.38 * 10-23 joule per degree, T = 22 K
and m = 28 a.m.u. =
∴
= 1.14 * 102m/s.
are the average speeds of hydrogen and nitrogen molecules at temperatures T1K and T2K respectively, we have ...(i) ...(ii)where m1 and m2 are the masses of hydrogen and nitrogen molecules respectively.
Dividing eq. (1) and (2), we get
...(iii)Given when
and
Substituting these values in (3), we get
or
The most probable speed of nitrogen at temperature T is given by
Here k = 1.38 * 10-23 joule per degree, T = 22 K
and m = 28 a.m.u. =
∴
= 1.14 * 102m/s.
Most Upvoted Answer
At what temperature (in Kelvin) will the average speed of hydrogen mol...
To find the temperature at which the average speed of hydrogen molecules is the same as that of nitrogen molecules, we can use the equation for average speed:
v = sqrt((3*k*T)/m)
where v is the average speed, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the molecular mass.
For nitrogen, m = 28 atomic mass units = 28 * 1.66 x 10^-27 kg.
For hydrogen, m = 2 atomic mass units = 2 * 1.66 x 10^-27 kg.
Let's set the average speeds of the two molecules equal to each other:
sqrt((3*k*T_nitrogen)/m_nitrogen) = sqrt((3*k*T_hydrogen)/m_hydrogen)
Simplifying, we can cancel out the square root and the Boltzmann constant:
sqrt(T_nitrogen/m_nitrogen) = sqrt(T_hydrogen/m_hydrogen)
Squaring both sides, we get:
T_nitrogen/m_nitrogen = T_hydrogen/m_hydrogen
Plugging in the values for m_nitrogen, m_hydrogen, and T_nitrogen = 35 + 273.15 K, we can solve for T_hydrogen:
(35 + 273.15) / 28 = T_hydrogen / 2
308.15 / 28 = T_hydrogen / 2
10.72 = T_hydrogen / 2
T_hydrogen = 10.72 * 2
T_hydrogen = 21.44 K
Therefore, the temperature at which the average speed of hydrogen molecules is the same as that of nitrogen molecules kept at 35°C is approximately 21.44 Kelvin.
v = sqrt((3*k*T)/m)
where v is the average speed, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the molecular mass.
For nitrogen, m = 28 atomic mass units = 28 * 1.66 x 10^-27 kg.
For hydrogen, m = 2 atomic mass units = 2 * 1.66 x 10^-27 kg.
Let's set the average speeds of the two molecules equal to each other:
sqrt((3*k*T_nitrogen)/m_nitrogen) = sqrt((3*k*T_hydrogen)/m_hydrogen)
Simplifying, we can cancel out the square root and the Boltzmann constant:
sqrt(T_nitrogen/m_nitrogen) = sqrt(T_hydrogen/m_hydrogen)
Squaring both sides, we get:
T_nitrogen/m_nitrogen = T_hydrogen/m_hydrogen
Plugging in the values for m_nitrogen, m_hydrogen, and T_nitrogen = 35 + 273.15 K, we can solve for T_hydrogen:
(35 + 273.15) / 28 = T_hydrogen / 2
308.15 / 28 = T_hydrogen / 2
10.72 = T_hydrogen / 2
T_hydrogen = 10.72 * 2
T_hydrogen = 21.44 K
Therefore, the temperature at which the average speed of hydrogen molecules is the same as that of nitrogen molecules kept at 35°C is approximately 21.44 Kelvin.
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At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer?
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At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer?.
At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what temperature (in Kelvin) will the average speed of hydrogen molecules be the same as that of nitrogen molecules kept at 35oC. Molecular weights of nitrogen and hydrogen are 28 and 2 atomic mass units respectively. Given Boltzmann’s constraint = 1.38 * 10-23 joule per degree.Correct answer is '22'. Can you explain this answer?.
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