//Stoichiometry- Chemical Calculations: Relative Atomic Mass and Reacting Mass ## Stoichiometry- Chemical Calculations

###### Learning outcome:
1. Relative Atomic Mass
2. Reacting Mass

#### Relative Atomic Mass

At present we know there are 118 different elements know in the earth. The atoms of these elements differ in mass because of having different numbers of electrons, protons and neutrons in them. You know the actual mass of one atom is very small. As for example, the mass of a single atom of sulfur is around

0.000 000 000 000 000 000 000 053 16 g

Obviously, this small quantity is not easy to work with so, a scale called the ‘relative atomic mass scale’ is used. In this scale an atom of carbon is given a relative atomic mass, Ar, of 12.00 and all other atoms of the other elements are given a relative atomic mass compared to that of carbon.

#### Reacting Masses

Chemist often needs to be able to show the relative masses of the atoms involved in a chemical process.

For example, if 6 g of carbon was completely combusted then what mass of carbon dioxide would be produced? To answer this type of question instead of using the actual masses of atoms we use the relative atomic mass. the relative formula mass (RFM) is the sum of the relative atomic masses of all those elements shown in the formula of the substance.  In the above example, we can work out the relative formula mass of molecules such as O2 and CO2 using the relative atomic masses of the atoms they are made of. Here,

O2 has a relative formula mass of 2 × 16 = 32 where CO2 has a relative formula mass of 12 + (2 × 16) = 44. So we can now use this equation to answer the question asked above. Hence, converting these relative masses to actual masses by adding mass units, g, would give: The above calculation is showing that if we burn 12 g of carbon (C) completely then it will produce 44 g of carbon dioxide (CO2) gas. So we get 6 g of carbon burning will result in the formation of 22 g of carbon dioxide gas.

Let’s have a look at another example. What mass of hydrogen gas will be produced if 46 g of sodium is reacted with water?

Firstly we will write down the balanced chemical equation: Secondly, we have to find the relative atomic mass of sodium from the Periodic Table then work out the relative formula masses of water, sodium hydroxide and hydrogen gas.

Relative atomic mass of sodium is 23. Relative formula mass of water, sodium Hydroxide and hydrogen gas are , (2 × 1) + 16 = 18 (H2O), 23 + 16 + 1 = 40 (NaOH) and 2 × 1 = 2 (H2) respectively.

Now, you can write these masses under the balanced chemical equation taking into account the numbers used to balance the equation as follows. You can convert these relative masses into actual or reacting masses by putting in mass units, for example, grams (g) as follows, Thus we get the answer to the question of what mass of hydrogen would be produced if 46 g of sodium was reacted with water will be 2 g hydrogen.

In the chemical industry it is is particularly important to know how much of a substance has been formed or used up during a chemical reaction where the substances being reacted (reactants) and the substances being produced (products) are worth thousands of pounds. Waste costs money!

To solve this great problem they need a way of counting atoms, ions or molecules. Since they are very tiny particles and it is impossible to measure out a dozen or even a hundred of them. Instead of its, chemists weigh out a very large number of particles.

Here, this number is 6 × 1023 atoms, ions or molecules and is called Avogadro’s constant after the famous Italian scientist Amedeo Avogadro (1776–1856). And An amount of substance that containing 6 × 1023 particles is called a mole (often abbreviated to mol).

For example, a mole of the element magnesium will be 6 × 1023 atoms of magnesium.

`Source- Cambridge IGCSE; Chemistry 3rd Edition`