Mole calculations and Avogadro's constant

In a nutshell

The number of moles of a substance is a certain number of the particles within that substance. The number of particles is known as Avogadro's constant.

Equations

$number\,of molecules/atoms/ions=number\,of\,moles\times avogadro's\,constant\,(6.02\times10^{23})$

$number\,of\,moles=\frac{mass\,of\,element/compound}{A_r/M_r}$

Note: To calculate the number of moles of an element, the relative atomic mass must be used. Where as, to calculate the number of moles of a compound, the relative formula mass must be used.

Variable Units

VARIABLE	UNIT name	unit
$number\,of\,moles$	$mole$	$mol$
$mass\,of\,element/compound$	$gram$	$g$

All other variables discussed in this summary do not have a unit.

The mole and Avogadro's constant

One mole is the number of particles equal to the value of Avogadro's constant.

Avogadro's constant has a value of $6.02\times10^{23}$ .

For an element, one mole of particles will have a mass (in grams) equal to the weight of the relative atomic mass ( $A_r$ ).
For a compound, one mole of particles will have a mass (in grams) equal to the weight of the relative formula mass ( $M_r$ ).

Equation linking moles and Avogadro's constant:

$number\,of molecules/atoms/ions=number\,of\,moles\times avogadro's\,constant\,(6.02\times10^{23})$

Tip: To find the number of moles from a given number of particles, divide the number of particles by Avogadro's constant.

$number\,of\,moles=\frac{number\,of molecules/atoms/ions}{avogadro's\,constant\,(6.02\times10^{23})}$ 

Example

How many atoms are there in $15$ moles of a hydrogen molecule?

Multiply the number of moles of hydrogen ( $15 \space moles$ ) by Avogadro's constant $(6.02\times10^{23})$ :

$15\times(6.02\times10^{23})=9.03\times10^{24}$

There are two atoms of hydrogen in one molecule ( $H_2$ ), so the answer is multiplied by two:

$(9.03\times10^{24})\times2=1.81\times10^{25}\,atoms$

In $15$  moles of a hydrogen molecule, there is $\underline{1.81\times10^{25}\,} \ atoms$ .

The mole

Definition

One mole of molecules/atoms/ions of any substance will have a mass (in grams) that is equal to the relative mass ( $M_r$ / $A_r$ ) of the substance.

Equation for the number of moles

This equation can be used to calculate the number of moles of a substance using the mass and relative mass of the substance.

$number\,of\,moles=\frac{mass\,of\,element/compound}{A_r\,or\,M_r}$

The equation can be rearranged, to work out the unknown mass of a substance given its number of moles and relative mass.

$mass=moles\times M_r$

$M_r=\frac{Mass}{Moles}$

Example 1

A molecule of hydrogen has a mass of $4 \space g$  . How many moles of hydrogen are there?

First calculate the relative formula mass ( $M_r$ ) of a hydrogen molecule ( $H_2$ ):

$M_r(H_2)=1+1=2$

Take the mass of hydrogen ( $4 \space g$ ) and divide this by the relative formula mass ( $M_r$ ) to find the number of moles:

$number\,of\,moles=\frac{4}{2}=2\,mol$

There are $\underline{2 \ moles}$ of hydrogen gas.

Example 2

There are $6 \space moles$  of nitrogen gas. What is the mass of the nitrogen gas?

First calculate the relative formula mass ( $M_r$ ) of a nitrogen molecule ( $N_2$ ):

$M_r(N_2)=14+14=28$

Take the moles of nitrogen gas ( $6 \space moles$ ) and multiply this by the relative formula mass ( $M_r$ ) to find the mass of nitrogen:

$mass=28\times6=168\,grams$

There is $\underline{168 \ grams}$  of nitrogen gas in $6 \ moles$ .

Using masses and moles to work out the empirical formula

PROCEDURE

1.

Work out the number of moles for each element in the compound using given masses.

$moles = \frac{mass}{A_r}$

2.

Divide the number of moles for each element by the smallest value for the number of moles.

3.

This will leave the smallest whole number ratio for each type of element in the compound and therefore, the empirical formula for the compound.

Example

A hydrocarbon contains $60 \space g$ of carbon and $10 \space g$ of hydrogen. What is the empirical formula for this hydrocarbon?

First work out the number of moles of carbon ( $A_r = 12$ ) and hydrogen ( $A_r = 1$ ):

$C = \frac{60}{12} = 5\,moles$

$H = \frac{10}{1} = 10\,moles$

The ratio is $C:H=5:10$ . Divide the ratio by the smallest value ( $5 \space moles$ ):

$C:H=1:2$

The empirical formula is $\underline{CH_2}$ .