# 3.1 Molar mass

The mass of one mole of a substance is the relative mass of that substance expressed in grams. This is true whether you are talking about relative atomic masses for elements, relative molecular masses for covalent compounds, or relative formula masses for ionic compounds.

The mass of one mole of a substance is called the **molar mass**; it has units of grams per mole (g mol^{-1}).

What is the difference between a molar mass and the relative mass?

The former has units, the latter does not.

However the actual number *is *the same.

Thus helium has a relative mass of 4 (no units), meaning the helium atom is, relatively speaking, 4 times heavier than a hydrogen atom. Helium has a molar mass of 4 g mol^{-1}, meaning that each mole of helium atoms has a mass of 4 g.

What is the molar mass of water (H

_{2}O)?The RMM of H

_{2}O is 18.02 so, Molar mass of H_{2}O = 18.0 g mol^{-1}

The definition of molar mass leads to two simple mathematical equations which help in performing calculations involving moles (they are in fact two forms of the same equation):

Mass of a substance = (number of moles of substance) × (molar mass of substance)

**(1)**Number of moles of a substance = mass of substance /molar mass of substance

**(2)**

If you were asked to find the number of moles of water in 100 g, this is one way you might go about it.

Choose which form of the equation you need to use.

As you want to find the number of moles, you should use equation **2**:

You have previously worked out the molar mass of H_{2}O = 18.0 g mol ^{−}^{1}, so putting the numbers and units in the equation you get:

Number of moles of water = 100 g/18.0 g mol−1 = 5.56 mol

Account for the unit mol in the above calculation?

The units can be found using the following sequence:

g /g mol

^{−}^{1}= 1 mol^{−}^{1}= mol

Now have a go at the following calculations.

How many moles are there in 0.769 g of CaF

_{2}, given RAM (Ca) = 40.08 and RAM (F) = 19.00?RFM CaF

_{2}= 40.08 + (19.00 x 2)= 78.08

Molar Mass CaF

_{2}= 78.08 g mol^{-1}Number of moles of CaF

_{2}= 0.769/78.08

= 0.01 mol.

What is the mass of 0.140 mol of C

_{6}H_{12}O_{6}(glucose)?RAMs: C (12.01), H(1.01) and O (15.99).

RFM C

_{6}H_{12}O_{6}= (12.01 x 6) + (1.01 x 12) + (15.99 x 6)= 72.06 + 12.12 + 95.94

= 180.12

Mass of C

_{6}H_{12}O_{6}= 0.140 x 180.12