What is the difference betweet molecular mass (Mr) and molar mass (M)?

1 Answer
Aug 15, 2016

Answer:

See explanation.

Explanation:

Molecular mass is a term used to denote the mass of a single molecule and is measured in unified atomic mass units, #"u"#, much like atomic mass, which denotes the mass of a single atom.

Now, a unified atomic mass unit, which is defined as #1/12"th"# of the mass of a single, unbound carbon-12 atom, is equal to

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 u" ~~ 1.660539 * 10^(-24)"g")color(white)(a/a)|)))#

Let's take water, #"H"_2"O"#, as an example of how molecular mass works.

The molecular mass of water is equal to #"18.015 u"#, which means that a single water molecule has a mass of

#18.015 color(red)(cancel(color(black)("u"))) * (1.660539 * 10^(-24)"g")/(1color(red)(cancel(color(black)("u")))) = 2.99146 * 10^(-23)"g"#

So, if one molecule of water has a mass of #2.99146 * 10^(-23)"g"#, it follows that one mole of water, which contains #6.022 * 10^(23)# molecules of water as given by Avogadro's number, will have a mass of

#2.99146 * 10^(-23)"g"/(1color(red)(cancel(color(black)("molec.")))) * (6.022 * 10^(23)color(red)(cancel(color(black)("molec."))))/("1 mole H"_2"O") ~~ "18.015 g mol"^(-1)#

This represents water's molar mass, which denotes the mass of one mole of water molecules.

As you can see, you have

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 u " = " 1 g mol"^(-1))color(white)(a/a)|)))#

Long story short, for a given compound, molecular mass tells you the mass of single molecule, while molar mass tells you the mass of a mole of said compound.

#color(white)(a/a)#

SIDE NOTE

As given to you, the molecular mass, #M_r#, is most likely the relative molecular mass, sometimes called molecular weight, which is defined as molecular mass divided by #1/12"th"# of the mass of a single, unbound carbon-12 atom.

#"relative molecular mass" = "molecular mass"/"1 u"#

For water, the relative molecular mass is

#M_r = (18.015 color(red)(cancel(color(black)("u"))))/(1color(red)(cancel(color(black)("u")))) = 18.015#

When given to you as #M_r#, the molar mass is actually the relative molecular mass, a unitless quantity.

In order to avoid confusion, keep in mind that molecular mass tells you the mass of a single molecule and relative molecular mass tells you the mass of a single molecule relative to #1/12"th"# of the mass of a single, unbound carbon-12 atom.