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

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Discussion Overview

The discussion revolves around proving the relationship M = 2.016 X D (where M = 2D) in the context of molecular mass and vapor density, particularly using the atomic weight of Hydrogen as 1.008. Participants explore the definitions of M and D, and the implications of these definitions on the equations presented.

Discussion Character

  • Homework-related
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that D represents the vapor density, defined as the mass of one molecule of gas divided by the mass of one molecule of H2.
  • Others question the clarity of the problem statement, asking for definitions of M and D, and whether both equations presented are correct.
  • One participant states that M is not simply the mass of one molecule of gas divided by the mass of one H atom, but rather it should be related to the carbon-12 scale, where the atomic weight of hydrogen is 1.008.
  • There is a contention regarding the definition of vapor density, with some arguing that it is not simply a ratio of masses, while others maintain that relative density is defined as M/2.
  • Participants express confusion over the distinction between relative density and vapor density, noting that they are fundamentally different properties.
  • One participant seeks clarification on how to derive the molecular weight of Hydrogen from the formula 2D = M, given the atomic weight of hydrogen.

Areas of Agreement / Disagreement

Participants do not reach consensus on the definitions of M and D, nor on the validity of the equations presented. Multiple competing views remain regarding the interpretation of vapor density and its relationship to molecular mass.

Contextual Notes

There are unresolved assumptions regarding the definitions of terms used in the equations, and the discussion reflects a lack of clarity in the problem statement itself.

Indranil
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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
 
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Indranil said:

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?
 
DrClaude said:
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
 
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.
 
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Indranil said:
'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.
 
Borek said:
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
 
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.
 
Borek said:
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)
 

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