A levels average kinetic energy problem

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tahmidbro
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a) what is the rms speed of four hydrogen molecules with the speeds of 890, 755, 902, 866m/s?

Ans : 855m/s

My problem is part b)

b) at what temperature would these hydrogen molecules be?
( Mass of H atom = 1.67 x 10^(-27) kg )

Now, in 1/2m<c^2> = (3/2)kt, should I use the mass for only 1 hydrogen atom, or mass of 2 hydrogen atoms, or the mass for all 8 atoms in 4 molecules?

the answer in the solution book is 29K which only comes if I use mass for only one atom. ( They did not show any working )

The confusion arises when I tried the following question:

Q. Estimate the rms speed of the molecules of air in this room.

The answer given in the solution book :

Estimate of 20 °C (T = 293 K); assume all molecules are dinitrogen, so m = 4.676 × 10^(–26) kg; gives rms = 509m/s.
( They have used mass of two nitrogen atoms here )

Please help :-)
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Stonebridge
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tahmidbro
You only need the mass of one hydrogen atom in your first question.
The temperature of the room would be the same for any number of hydrogen atoms in the room, so long as the rms speed is the same.
So m is the mas of one hydrogen atom.

The mass used is always that of a single molecule of the gas. Hydrogen is just one atom.

In the second question it says dinitrogen. That means, you are dealing with a molecule that is made up of two nitrogen atoms.
That is why they use the mass of 2 atoms.
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golgiapparatus31
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(Original post by Stonebridge)
So m is the mas of one hydrogen atom.

The mass used is always that of a single molecule of the gas. Hydrogen is just one atom.
But hydrogen molecule is mentioned in the question. Hydrogen molecule is H2, according to the link below:
https://www.britannica.com/science/hydrogen
"...hydrogen molecules, each consisting of a pair of atoms, a diatomic molecule, H2"
:/
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tahmidbro
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(Original post by Stonebridge)
tahmidbro
You only need the mass of one hydrogen atom in your first question.
The temperature of the room would be the same for any number of hydrogen atoms in the room, so long as the rms speed is the same.
So m is the mas of one hydrogen atom.

The mass used is always that of a single molecule of the gas. Hydrogen is just one atom.

In the second question it says dinitrogen. That means, you are dealing with a molecule that is made up of two nitrogen atoms.
That is why they use the mass of 2 atoms.
''dinitrogen'' is not part of the second question. It was part of the answer from the solution book.

And why should I not consider dihydrogen for hydrogen case also?
Last edited by tahmidbro; 1 month ago
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Stonebridge
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golgiapparatus31
Yes, sorry, I misread your question. I don't know why they used the mass of a hydrogen atom in that first part. The mass should be that of the molecule, as I said later. Hence why also dinitrogen uses the mass of 2 atoms of hydrogen.
I can only assume the mark scheme has made a mistake. It happens.
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tahmidbro
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(Original post by Stonebridge)
tahmidbro
golgiapparatus31
Yes, sorry, I misread your question. I don't know why they used the mass of a hydrogen atom in that first part. The mass should be that of the molecule, as I said later. Hence why also dinitrogen uses the mass of 2 atoms of hydrogen.
I can only assume the mark scheme has made a mistake. It happens.
You can see this :
https://www.thestudentroom.co.uk/sho...4#post92419724

All right, Thanks a lot for the help!
Last edited by tahmidbro; 1 month ago
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