Relative Formula Mass

Calculating Relative Formula Mass

Percentage by Mass

By using formula mass and atomic mass, we can work out what percentage of a molecule’s mass a given element makes up. All we have to do is take the formula and atomic masses, and substitute them into the formula below:

\% \text{ Mass of Element } =\frac{\text{Relative Atomic Mass of Element}}{\text{Relative Formula of Compound}} \times 100

Example

The relative formula mass of the molybdenum compound MoOCl₄ is 254. Calculate the percent by mass of Molybdenum ,  (\text{Mo, A}_r 96) in this compound.

\% \text{ Mo } = \text{Atomic Mass Mo} \div \text{Formula Mass}\text{ Molybdenum}\text{ Compound}\\ =\frac{96}{254} \times 100\\ = 0.38 \times 100 = 38 \%

Conservation of Mass

Conservation of mass is an important principle in chemistry, as well as in science more broadly. The principle of the conservation of mass states that:

Mass is neither created nor destroyed in a chemical reaction. The mass of  reactant used and the mass of  products formed are equal. 

In simple terms, what goes in must come out. Atoms can’t simply disappear, as such neither can the mass they account for. Take for example the reaction of 3\text{ g} of sodium with 3\text{ g} of chlorine to form sodium chloride. The mass of the NaCl produced must be 6\text{ g} as no other products are formed, and 6\text{ g} of reactant was used. 

Though the total mass of products should always be roughly equal to the mass of reactant used, the masses measured in experiments are not always exactly equal. In some cases, product may be lost in some way (loss of gaseous products is discussed below). In these cases the mass of the products will seem to be as less than the mass of the reactants used. 

In other cases, unaccounted for impurities in reactants or reaction vessels may take place in the reaction, creating unexpected products. In these cases the mass of the products will seem to be more than that of the reactant used. It is important to remember that in both cases, the actual mass of reactants (be they intended or accidental) and of the products (gaseous, liquid, or solid) will always be equal once everything has been accounted for.

Balancing Equations

One important consequence of the conservation of mass is that it allows us to write balanced chemical equations for reactions. As mass is conserved in a chemical reaction, so are atoms. The number of reactant atoms used will always be equal to atoms of product produced. If 6 atoms worth of reactant are used, then 6 atoms worth of product must be formed. 

Some chemical equations do not require any work to be balanced as they already are. For example, sodium hydroxide reacting with hydrochloric acid:

\text{NaOH + HCl } \rarr \text{ NaCl + H}_2\text{O}

On the left hand side of the equation there is 1 sodium atom, 1 oxygen atom, 1 chlorine atom, and 2 hydrogen atoms. On the left hand side there is 1 sodium atom, 1 oxygen atom, 1 chlorine atom, and 2 hydrogen atoms. As such, we do not need to do anything to balance this equation, the numbers of atoms are equal.

In many cases however, we need to work to make an equation balanced. Take for example the reaction of magnesium hydroxide and hydrochloric acid:

\text{Mg(OH)}_2 \text{ + HCl} \rarr \text{MgCl}_2 \text{ + H}_2 \text{O}

Here, the number of atoms on each side are not equal. On the right hand side we have 1 atom of magnesium, 2 atoms of oxygen, 3 atoms of hydrogen, and 1 atom of chlorine. On the right we have 1 atom of magnesium, 1 atoms of oxygen, 2 atoms of hydrogen, and 2 atom of chlorine.

To get to equal number of atoms on both sides we need to multiply one or more of the molecules in the reaction. We start by multiplying HCl by 2. This means that there are two molecules of HCl reacting with every one of magnesium hydroxide. This gives us 2 chlorine atoms on the right, equaling 2 on the left. Chlorine is now balanced

\text{Mg(OH)}_2 \text{  + } 2 \text{HCl} \rarr \text{MgCl}_2  \text{ + H}_2 \text{O}

However, we now have 4 hydrogen atoms on the left and only 2 on the right. To balance the hydrogen, we need to double the number on the right. To do this, we double the molecules of water formed:

\text{Mg(OH)}_2 \text{ + } 2 \text{HCl} \rarr \text{MgCl}_2 \text{ + } 2 \text{H}_2 \text{O}

This also gives us another oxygen, meaning there are now 2 atoms both left and right. The equation is fully balanced. 

Reactions forming gasses

In many reactions, the principle of the conservation of mass seems to be violated. It is not uncommon to find that, after a reaction has taken place, the measured mass of the product formed is not equal to the mass of the reactant used. Though it may seem that this mass has been destroyed, in reality it has simply not been measured. This tends to happen when one or more of the products formed in a reaction is a gas. Take the reaction of bicarbonate of soda and hydrochloric acid.

\text{NaHCO}_{3 (s)}+\text{HCl}_{ (aq)}\rarr\text{NaCl}_{ (s)}+\text{H}_2\text{O}_{ (l)}+\text{CO}_{2 (g)}

This reaction has three products; sodium chloride, water, and carbon dioxide. If this experiment were to be carried out in an open container, the mass of the products would not be equal to that of the reactants. This is not because any mass has been destroyed. Instead, the mass of the products that has been measured is only that of sodium chloride and water.

Because carbon dioxide is a gas, it is able to escape the container, and so is not present when we measure the mass of the products. If we were to calculate the mass of carbon dioxide released, and add this back to the mass of the products, the result should equal the mass of the reactants used.