Why is the molar mass of a molecule defined as the the sum of molar mass of all the atoms present in the molecule?

For example, suppose we have to calculate the molar mass of $\ce{H_2O} $ molecule.

Then, $$\text{Molar mass of a } \ce{H_2O}\text{ molecule} = 2 \times \text{Molar mass of }\ce{H} + \text{Molar mass of }\ce{O}$$ = 2 * 1g/mol of H + 16g/mol of O

= 2g/mol of H + 16g/mol of O

As you can see we get two contrasting results - "1g/mol of H" and "2g/mol of H atoms)

How can both "1g" and "2g" form 1 mole of Hydrogen?

I think that the confusion is with the use of units. I have represented one mole of H like this = 18 g/1 mole of H But when I multiply with 2 then also I get the same denominator,the result I get is 36 g/1 mole of H

Why am I getting the same denominator (1 mole of H) ?

I have one more question

Why $6.022 \times 10^{23}$ atoms of different elements (constituents of molecule) form $6.022 \times 10^{23}$ molecules of the substance?

  • $\begingroup$ make your question more elaborate and you're right ? what doubt do you have ? $\endgroup$ – Physicsapproval Mar 7 '17 at 9:24
  • $\begingroup$ My question is that how both 1 g and 2 g form 1 mole of H? $\endgroup$ – user42209 Mar 7 '17 at 14:58
  • $\begingroup$ I am still not clear with your language . Although 1 mole of H atom would weigh about 1g . $\endgroup$ – Physicsapproval Mar 7 '17 at 15:02
  • $\begingroup$ In your units manipulation you're missing that it is 2 atoms of hydrogen per molecule of water. $\endgroup$ – MaxW Mar 7 '17 at 16:31
  • $\begingroup$ @MaxW why is the relative atomic mass of an atom numerically equal to it's gram atomic mass? $\endgroup$ – user42209 Mar 10 '17 at 17:40

Stoichiometry will decide how many moles of each element forms how many moles of the product. Hence, in your equation, 2 moles or 2x6.023x10^23 atoms of H will combine with 1 mole or 6.023x10^23 atoms of Oxygen to form 1 mole or 6.023x10^23 molecules of water. I hope this clears your confusion.

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  • $\begingroup$ You can format mathematical and chemical expressions on Chemistry.SE using MathJax; this post contains further details. $\endgroup$ – orthocresol Mar 7 '17 at 14:47
  • $\begingroup$ @orthocresol thanks for letting me know! I was wondering how other people do the formatting here :) $\endgroup$ – Mrityunjay Gupta Mar 7 '17 at 15:39
  • $\begingroup$ No problem. There are a number of resources scattered on Chemistry Meta, feel free to drop me a line if you need anything. $\endgroup$ – orthocresol Mar 7 '17 at 15:54
  • $\begingroup$ @MrityunjayGupta why is the relative atomic mass of an atom numerically equal to it's gram atomic mass? $\endgroup$ – user42209 Mar 10 '17 at 17:39

The mole is simply a way of counting things, but you have to be careful what you are counting. Molar mass is just a way of counting the mass of one mole of something.

If you are counting atoms then 3 moles of atoms (two moles of hydrogen atoms and one of oxygen atoms) come together to make one mole of water molecules. Moles are not additive because they count different things on the two sides of the equation (atoms on one side, molecules on the other). But mass is additive so the total mass of one mole of water is the sum of the masses of the three moles of its components. So the molar mass of water is about 18g/mole.

The molar counts (and masses) depend on what we are counting. If we count hydrogen and oxygen molecules then there would be 1 mole of hydrogen molecules (H2) and half a mole of oxygen molecules. The one mole of water would still weight the same if we count and weigh correctly.

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  • $\begingroup$ why is the relative atomic mass of an atom numerically equal to it's gram atomic mass? $\endgroup$ – user42209 Mar 10 '17 at 17:41

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