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

Aug 15, 2016

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, $\text{u}$, much like atomic mass, which denotes the mass of a single atom.

Now, a unified atomic mass unit, which is defined as $\frac{1}{12} \text{th}$ of the mass of a single, unbound carbon-12 atom, is equal to

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 u" ~~ 1.660539 * 10^(-24)"g}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Let's take water, $\text{H"_2"O}$, as an example of how molecular mass works.

The molecular mass of water is equal to $\text{18.015 u}$, 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 $2.99146 \cdot {10}^{- 23} \text{g}$, it follows that one mole of water, which contains $6.022 \cdot {10}^{23}$ molecules of water as given by Avogadro's number, will have a mass of

$2.99146 \cdot {10}^{- 23} {\text{g"/(1color(red)(cancel(color(black)("molec.")))) * (6.022 * 10^(23)color(red)(cancel(color(black)("molec."))))/("1 mole H"_2"O") ~~ "18.015 g mol}}^{- 1}$

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

As you can see, you have

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\text{1 u " = " 1 g mol}}^{- 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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.

$\textcolor{w h i t e}{\frac{a}{a}}$

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 $\frac{1}{12} \text{th}$ of the mass of a single, unbound carbon-12 atom.

$\text{relative molecular mass" = "molecular mass"/"1 u}$

For water, the relative molecular mass is

${M}_{r} = \left(18.015 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{u"))))/(1color(red)(cancel(color(black)("u}}}}\right) = 18.015$

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 $\frac{1}{12} \text{th}$ of the mass of a single, unbound carbon-12 atom.