0620 · 3.2Relative masses of atoms and molecules

Relative atomic mass

0:00When heated strongly, fifty grams of calcium carbonate decomposes into twenty-eight grams of calcium oxide and twenty-two grams of carbon dioxide. These amounts follow a pattern set by the atoms involved. By understanding relative masses, you can work out that pattern before carrying out the reaction. We will connect atomic masses, chemical formulae and reacting masses without using the mole concept. We need three starting ideas from earlier topics. Elements contain atoms, and isotopes of an element have different numbers of neutrons.

0:28Chemical formulae tell us the proportions of atoms or ions in substances. A balanced equation shows the relative numbers of particles involved, while keeping the number of atoms of each element unchanged. Individual atoms are far too small for their masses in grams to be convenient. Instead, chemists compare them with an agreed reference. That reference is one twelfth of the mass of a carbon-twelve atom. Imagine it as a standard measuring block against which atomic masses can be compared, rather than a physical piece removed from an atom.

0:58Relative atomic mass is the average mass of the isotopes of an element compared to one twelfth of the mass of a carbon-twelve atom. The word relative tells us that this is a comparison. A value of twenty-four means that the average atomic mass is twenty-four times the reference mass. It does not mean that an atom has a mass of twenty-four grams. Relative atomic mass has no unit because it compares one mass with another.

1:20Dividing quantities measured in the same units leaves a number rather than a mass measurement. This is like comparing two lengths and saying one is twice the other. The comparison is two, not two centimetres, even if both lengths were measured in centimetres. The word average matters because an element can contain a mixture of isotopes. Their atoms have different masses because they contain different numbers of neutrons. The average takes account of how common each isotope is.

1:44A more abundant isotope contributes more strongly, so the result is not necessarily halfway between the individual isotope masses. For example, the relative atomic mass of chlorine used in these calculations is thirty-five point five. This does not mean that a chlorine atom contains half a neutron. Mass number counts the protons and neutrons in one atom, so it is a whole number. Relative atomic mass describes an average across the isotopes, which can be a decimal.

2:11For calculations, use the relative atomic masses given in the question or Periodic Table. We will use hydrogen as one, carbon as twelve, oxygen as sixteen and calcium as forty. These numbers describe comparisons on the same scale. That shared scale allows us to add atomic contributions when we know a substance’s formula.

Molecular and formula mass

2:30Relative molecular mass is the sum of the relative atomic masses of all the atoms in a molecule. A molecule contains a particular combination of atoms, so we add their contributions. Water provides a simple worked example. Its formula tells us that each molecule contains two hydrogen atoms and one oxygen atom. Each hydrogen atom contributes one, so the hydrogen contribution is two multiplied by one, giving two. Oxygen adds sixteen for its single atom.

2:57Adding two and sixteen gives a relative molecular mass of eighteen. There is no unit, because we have added relative values rather than masses measured in grams. Carbon dioxide contains one carbon atom and two oxygen atoms in each molecule. Carbon contributes twelve, and the oxygen contribution is two multiplied by sixteen, giving thirty-two. Twelve plus thirty-two gives a relative molecular mass of forty-four. The small number after oxygen applies only to that element, not to the whole formula.

3:25A useful habit is to count the atoms before adding any masses. Otherwise, it is easy to include each element just once and overlook repeated atoms. For carbon dioxide, twelve plus sixteen would describe only one carbon and one oxygen. That combination does not match the formula, so it cannot give the correct answer. Ionic compounds need slightly different language because they do not consist of separate molecules. Their ions form a continuous lattice, and the formula gives the simplest ratio of those ions.

3:52We therefore use the term relative formula mass. The calculation still adds the relative atomic masses represented in the formula, but calling the result molecular mass would suggest molecules that are not present. Sodium chloride has one sodium ion for every chloride ion in its formula ratio. Using twenty-three for sodium and thirty-five point five for chlorine, we add those contributions. Twenty-three plus thirty-five point five gives fifty-eight point five.

4:18This is the relative formula mass of sodium chloride, and it has no unit. Calcium carbonate gives us another worked example. Its formula contains one calcium ion and one carbonate ion, and the carbonate ion contains one carbon and three oxygen. The oxygen contribution is three multiplied by sixteen, giving forty-eight. Adding forty, twelve and forty-eight gives a relative formula mass of one hundred.

Reacting masses: calcium carbonate

4:42Relative masses become especially useful when connected to a balanced equation. The equation fixes the proportions of particles, while their relative masses tell us how much each contributes. Scaling up the number of particles preserves that mass ratio. This is why a microscopic formula can help predict masses measured on a laboratory balance. When heated, calcium carbonate decomposes to give calcium oxide plus carbon dioxide. The balanced symbol equation is on the board, and every coefficient is one.

5:10Calcium carbonate has a relative formula mass of one hundred. For calcium oxide, forty plus sixteen gives fifty-six, while carbon dioxide has a relative molecular mass of forty-four. These values establish the mass proportion for the reaction. One hundred grams of calcium carbonate gives fifty-six grams of calcium oxide and forty-four grams of carbon dioxide. Fifty-six plus forty-four equals one hundred grams, which agrees with conservation of mass. The gas still counts as a product, even if it escapes from the container.

5:41Suppose fifty grams of calcium carbonate decomposes completely. Divide fifty grams by the reference amount of one hundred grams to obtain a scale factor of zero point five. Multiplying fifty-six grams by zero point five gives twenty-eight grams of calcium oxide. For carbon dioxide, forty-four grams multiplied by zero point five gives twenty-two grams. The products total twenty-eight plus twenty-two, giving fifty grams. Halving the starting amount has halved both product masses because the reaction proportions remain unchanged.

6:10These calculations assume that the calcium carbonate reacts completely and the products are accounted for. We are scaling a fixed relationship, not changing the chemical formulae.

Reacting masses: magnesium oxide

6:19An exam question could ask you to calculate the mass of magnesium oxide formed from twelve grams of magnesium with excess oxygen. Magnesium plus oxygen gives magnesium oxide. The balanced symbol equation is on the board. Two magnesium atoms react with one oxygen molecule to form two formula units of magnesium oxide. Magnesium oxide has a relative formula mass of twenty-four plus sixteen, giving forty. The coefficients give a mass proportion of two multiplied by twenty-four to two multiplied by forty, or forty-eight to eighty.

6:49Twelve grams divided by forty-eight grams gives a scale factor of zero point two five. Multiplying eighty grams by zero point two five gives twenty grams of magnesium oxide. The product is heavier than the magnesium because oxygen has been added. Subtracting twelve grams from twenty grams shows that eight grams of oxygen reacted. Never assume that reactant and product masses must be equal individually. Conservation of mass compares the total mass of all reactants with the total mass of all products.

7:16One common mistake is reading the coefficients in an equation as gram amounts. Coefficients describe particle proportions, so you must include the relative masses. Another is changing formula subscripts while scaling, but subscripts count atoms and must stay fixed. Also, give units for reacting masses, but never attach grams to relative atomic, molecular or formula masses. If an exam asks you to describe relative atomic mass, include the isotope average and the carbon-twelve reference.

7:43Define relative molecular mass as the sum of the relative atomic masses of all atoms in a molecule. For an ionic compound, use relative formula mass instead. In calculations, show the atom count or reaction proportion before giving your final answer. Relative atomic mass compares an isotope average with a fixed reference. Adding the atomic contributions gives relative molecular mass for molecules or relative formula mass for ionic compounds. A balanced equation then connects those values to reacting mass proportions.

8:14Once that relationship is established, you can scale it to any starting mass without changing the chemistry.