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

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:

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

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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

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 $$\underline{CH_2}$$.