How to prove M = 2.016 X D (M = 2D)

[Indranil]

Homework Statement

How to prove M = 2.016 X D (M = 2D) if the atomic weight of Hydrogen is 1.008

Homework Equations

How to prove M = 2.016 X D (M = 2D).if the atomic weight of Hydrogen is 1.008

The Attempt at a Solution

As I know,
D = the mass of one molecule of gas / the mass of one molecule of H2
= the mass of one molecule of gas / the mass of 2 molecules of H atoms
= 1/2 X the mass of one molecule of gas / the mass of one H atom
= 1/2 X the molecular mass of gas
= 1/2 X M
If I put the value in the equation above I get
D = one molecule of gas / 2 molecules of H atoms
= 2.016 / 1.008 X 1.008
= 2.016 / 2.016
= 1

 

[DrClaude]

Homework Statement

How to prove M = 2.016 X D (M = 2D) if the atomic weight of Hydrogen is 1.008

Is that the actual statement of the problem? What are M and D? And you have two equations there, which is the correct one?

 

[Indranil]

Is that the actual statement of the problem? What are M and D? And you have two equations there, which is the correct one?

Yes
'M' means 'molecular mass' and 'D' means 'vapour density'
The two equations are correct
D = the mass of one molecule of gas / the mass of one molecule of H2
= the mass of one molecule of gas / the mass of 2 molecules of H atoms
= 1/2 X the mass of one molecule of gas / the mass of one H atom
= 1/2 X the molecular mass of gas
= 1/2 X M
2D = M
if the atomic weight of Hydrogen is 1.008, then how to get M = 2.016 X D, I tried below but did not get
If I put the value in the equation above I get
D = one molecule of gas / 2 molecules of H atoms
= 2.016 / 1.008 X 1.008
= 2.016 / 2.016
= 1

 

[mjc123]

The problem is that M is not the mass of one molecule of gas/ the mass of one H atom. It is the mass of one molecule of gas/(1/12)*the mass of one ¹²C atom. On the carbon-12 scale, the atomic weight of hydrogen is 1.008.

 

[Borek]

'D' means 'vapour density'

D = the mass of one molecule of gas / the mass of one molecule of H2

Ratio of masses is not the vapor density, vapor density is mass/volume. Something is very wrong here.

 

[Indranil]

Ratio of masses is not the vapor density, vapor density is mass/volume. Something is very wrong here.

only density = mass / volume but vapour density or relative density D = M / 2

 

[Borek]

Relative density is unitles, vapor density has units of mass/volume. These are two completely different properties.

It is still not clear what the question really is.

 

[Indranil]

Relative density is unitles, vapor density has units of mass/volume. These are two completely different properties.

It is still not clear what the question really is.

How to get molecular weight of Hydrogen from this formula 2D = M, If atomic weight of hydrogen is 1.008? (where 'D' is vapor density, and 'M' is molecular weight)