Conservation of Mass, Relative Formula Mass and Moles

Why mass is conserved

In a chemical reaction, reactants become products because their atoms are rearranged. Bonds between atoms change, but the atoms themselves are neither created nor destroyed. Because all the original atoms are still present, their total mass stays the same. This is the law of conservation of mass:

$$\text{total mass of reactants}=\text{total mass of products}$$

The word total matters: every substance involved must be included, even a gas that is difficult to see or collect. If 10 g of reactants form two products and one product has a mass of 6 g, the other must have a mass of 4 g, provided these are the only products.

A closed system allows no substances to enter or leave. If a reaction takes place in a closed container, the mass of the container and its contents remains constant, even if a gas or a solid forms.

Why an open reaction can appear to lose or gain mass

A balance measures the container and the substances remaining on it, not necessarily every substance involved in the reaction. In a non-enclosed system, matter can move between the reaction mixture and its surroundings.

When magnesium reacts with hydrochloric acid, hydrogen gas is produced:

$$\mathrm{Mg + 2HCl \rightarrow MgCl_2 + H_2}$$

In an open flask, the hydrogen particles move freely and escape into the air. They carry mass away from the flask, so the balance reading decreases. No atoms have disappeared: some are now outside the system being weighed. Including the escaped hydrogen would give the same total mass as before.

The opposite happens when a metal reacts with oxygen from the air. For example, magnesium forms magnesium oxide:

$$\mathrm{2Mg + O_2 \rightarrow 2MgO}$$

Oxygen particles enter from the surroundings, and their atoms become part of the solid oxide. The oxide therefore has a greater mass than the magnesium alone. The increase is the mass of oxygen added; it is not newly created matter.

The particle model explains both observations: gases consist of particles that have mass and can move across the boundary of an open system. Mass is still conserved when the substances in the surroundings are included.

Calculating relative formula mass

Chemists use relative atomic mass, $A_r$, to compare the masses of atoms. These values are found in the periodic table. To find relative formula mass, $M_r$, add the relative atomic masses of every atom shown in the formula:

$$M_r=\text{sum of the }A_r\text{ values of all atoms in the formula}$$

The formula tells you how many atoms of each element to count. For calcium chloride, $\mathrm{CaCl_2}$, there is one calcium atom for every two chlorine atoms. Using $A_r(\mathrm{Ca})=40$ and :

$$M_r(\mathrm{CaCl_2})=40+(2\times35.5)=111$$

For nitrogen gas, $\mathrm{N_2}$, using $A_r(\mathrm{N})=14$ gives $M_r=2\times$. An element can therefore have a formula mass different from its atomic mass if its particles contain more than one atom.

Neither $A_r$ nor $M_r$ has units: each is a relative comparison, not a mass measured in grams.

Relative masses in a balanced equation

A balanced equation contains the same number of each type of atom on both sides. Consequently, the total relative masses also match, once the balancing numbers are included.

For $\mathrm{2Mg+O_2\rightarrow2MgO}$, use $A_r(\mathrm{Mg})=24$ and . The relative masses are 24 for Mg, 32 for and 40 for MgO. Including the balancing numbers:

$$\text{reactants: }(2\times24)+32=80$$ $$\text{products: }2\times40=80$$

The two sides agree because the same atoms are present. The 2 before MgO counts two lots of MgO; the $M_r$ of MgO itself remains 40.

The mole: counting enormous numbers of particles — Higher Tier

Atoms are too small and numerous to count individually in an ordinary sample. Chemists therefore measure amount of substance in moles, symbol mol. A mole is a counting unit, rather like a dozen, but represents an enormously larger number.

One mole contains approximately $6.0\times10^{23}$ specified particles. The number of particles per mole is the Avogadro constant, approximately . A more precise rounded value commonly used is ; use the value supplied in a calculation.

It matters which particles are being counted. One mole of sodium contains one mole of sodium atoms; one mole of hydrogen gas contains one mole of $\mathrm{H_2}$ molecules. For an ionic compound such as sodium chloride, we count formula units: each NaCl formula unit represents one sodium ion and one chloride ion.

Equal amounts in moles contain equal numbers of the specified particles. They need not have equal masses, because the particles of different substances have different masses.

Linking mass and moles — Higher Tier

The mass of one mole in grams is numerically equal to the substance’s relative formula mass. For individual atoms of an element, use its relative atomic mass. For example, one mole of iron atoms has a mass of 56 g, whereas one mole of nitrogen molecules has a mass of 28 g.

This mass per mole is called molar mass, measured in $\text{g mol}^{-1}$. Dividing a sample’s mass by its mass per mole tells you how many moles it contains. The GCSE relationship is:

$$\text{number of moles}=\frac{\text{mass of substance in g}}{\text{relative formula mass}}$$

For example, carbon has $A_r=12$, so each mole of carbon atoms has a mass of 12 g. A 42 g sample contains:

$$n=\frac{42}{12}=3.5\ \text{mol}$$

The sample contains three and a half times the number of atoms in one mole.

Rearranging the mass–mole equation — Higher Tier

Writing mass as $m$ and amount in moles as $n$, the GCSE numerical relationship is $$, with mass in grams. Multiply both sides by to make mass the subject:

$$m=nM_r$$

For example, $0.50\ \text{mol}$ of nitrogen gas, with $M_r=28$, has a mass of $0.50\times28=14\ \text{g}$.

To make $M_r$ the subject, divide $m=nM_r$ by $n$:

$$M_r=\frac{m}{n}$$

For the same substance, mass and amount in moles are directly proportional: doubling the mass doubles the number of moles.

Using the Avogadro constant in standard form — Higher Tier

Standard form writes a number as , where and is an integer. For example, . Positive powers of ten represent large numbers; negative powers represent small numbers, such as .

To convert moles to a number of particles, multiply by the Avogadro constant:

$$N=nN_A$$

Here $N$ is the number of specified particles and $N_A$ is the Avogadro constant. Suppose a sample contains $0.50\ \text{mol}$ of sodium atoms. Using $N_A=6.0\times10^{23}\ \text{mol}^{-1}$:

$$N=0.50\times6.0\times10^{23}=3.0\times10^{23}\text{ atoms}$$

To work in the opposite direction, rearrange to $n=N/N_A$. A sample containing $1.2\times10^{24}$ sodium atoms therefore contains:

$$n=\frac{1.2\times10^{24}}{6.0\times10^{23}}=0.20\times10^1=2.0\ \text{mol}$$

When dividing powers of ten, subtract their exponents: $10^{24}/10^{23}=10^1$. The final answer means the sample contains twice the number of atoms in one mole.

Conservation and apparent mass changes

• Atoms are rearranged, not created or destroyed: total reactant mass = total product mass.
• Closed system: no matter enters or leaves, so total measured mass stays constant.
• Open system: escaping gas lowers the measured mass; gas entering and reacting can increase it. Include the gas to account for the conserved total mass.

Relative formula mass

$$M_r=\sum A_r\text{ for all atoms in the formula}$$