Relative masses of atoms and molecules Revision Notes

Relative atomic mass (symbol A_r) is the average mass of the atoms of an element, taking into account the masses of its isotopes and their relative abundances, compared to 1/12th the mass of a carbon-12 atom.

It is a dimensionless quantity because it is a ratio of masses.

The standard reference is the carbon-12 isotope, which is assigned exactly 12 atomic mass units (u).

• Relative atomic mass is an average value.
• It is relative to 1/12th the mass of a carbon-12 atom.
• It reflects natural isotopic composition.

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, resulting in different mass numbers.

For example, chlorine has two main isotopes: chlorine-35 and chlorine-37.

Because isotopes have different masses, the relative atomic mass of an element is a weighted average based on the percentage abundance of each isotope in nature.

• Isotopes differ in neutron number.
• Isotopes have different masses but same chemical properties.
• Natural abundance affects the average atomic mass.

The relative atomic mass scale is based on the carbon-12 isotope, which is assigned a mass of exactly 12 atomic mass units (u).

One atomic mass unit is defined as 1/12th of the mass of a carbon-12 atom.

This provides a standard reference for comparing atomic masses of all elements.

• Carbon-12 isotope mass = exactly 12 u.
• 1 u = 1/12th mass of carbon-12 atom.
• All relative atomic masses are ratios to this standard.

The relative atomic mass is calculated by multiplying the mass of each isotope by its relative abundance (expressed as a decimal), then summing these values.

For example, chlorine has two isotopes: chlorine-35 (mass = 35 u, abundance = 75%) and chlorine-37 (mass = 37 u, abundance = 25%).

Calculation: A_r = (35 × 0.75) + (37 × 0.25) = 26.25 + 9.25 = 35.5 u.

• Multiply isotope mass by fractional abundance.
• Sum all contributions to get average.
• Result is the relative atomic mass.

An element X has two isotopes: X-10 with mass 10 u and abundance 20%, and X-11 with mass 11 u and abundance 80%. Calculate the relative atomic mass of element X.

Step 1: Convert percentages to decimals: 20% = 0.20, 80% = 0.80.

Step 2: Multiply each isotope mass by its abundance: (10 × 0.20) = 2.0, (11 × 0.80) = 8.8. Step 3: Add the results: 2.0 + 8.8 = 10.8 u, which is the relative atomic mass of element X.

• Convert percentage to decimal.
• Multiply isotope mass by abundance.
• Add results for average atomic mass.

Relative atomic mass (Ar) is the weighted average mass of an atom of an element compared to 1/12th the mass of a carbon-12 atom. It is a dimensionless quantity used as the basis for calculating molecular and formula masses. For example, the relative atomic mass of hydrogen is approximately 1, oxygen is approximately 16, and carbon is approximately 12.

• Ar is a ratio, not a mass in grams.
• It accounts for isotopic abundance of the element.
• Used as the building block for molecular and formula mass calculations.

Relative molecular mass (Mr) is the sum of the relative atomic masses of all atoms in a molecule. It is a dimensionless quantity that represents the mass of one molecule relative to 1/12th the mass of a carbon-12 atom.

For example, water (H₂O) consists of 2 hydrogen atoms and 1 oxygen atom:

Mr(H₂O) = (2 × Ar(H)) + (1 × Ar(O)) = (2 × 1) + (1 × 16) = 18

• Mr is used for covalent molecular substances.
• Calculated by adding Ar values of each atom in the molecular formula.
• No units are used since it is a relative value.

Ionic compounds do not exist as discrete molecules but as giant lattice structures composed of ions. Therefore, the term relative formula mass (Mr) is used instead of relative molecular mass.

Relative formula mass is calculated by adding the relative atomic masses of all atoms in the empirical formula (simplest ratio) of the ionic compound.

For example, sodium chloride (NaCl) consists of sodium ions (Na⁺) and chloride ions (Cl⁻): Mr(NaCl) = Ar(Na) + Ar(Cl) = 23 + 35.5 = 58.5

• Mr for ionic compounds is based on the formula unit, not a molecule.
• Reflects the simplest whole-number ratio of ions.
• Used because ionic compounds form lattices, not molecules.

Calculate the relative formula mass of magnesium chloride, MgCl₂.

Step 1: Identify the relative atomic masses: Ar(Mg) = 24, Ar(Cl) = 35.5

Step 2: Use the formula MgCl₂, which contains 1 magnesium atom and 2 chlorine atoms: Mr = (1 × 24) + (2 × 35.5) = 24 + 71 = 95

• Write the formula clearly.
• Multiply Ar by the number of each atom.
• Add all contributions to find Mr.
• Answer: Mr(MgCl₂) = 95

A common mistake is to confuse relative molecular mass with relative formula mass. Remember to use relative molecular mass for molecules and relative formula mass for ionic compounds.

Another error is neglecting to multiply the relative atomic mass by the number of atoms of that element in the formula.

Always check the chemical formula carefully before calculating.

• Use correct term depending on compound type.
• Multiply Ar by atom count correctly.
• Check formula and arithmetic carefully.

In any chemical reaction, the total mass of the reactants equals the total mass of the products. This is known as the law of conservation of mass. It means that atoms are neither created nor destroyed during a reaction; they are simply rearranged to form new substances.

Because of this, if the mass of some reactants is known, the mass of the products or other reactants can be calculated by ensuring the total mass remains constant. This principle is fundamental when determining masses in chemical reactions without using the mole concept.

• Total mass of reactants = Total mass of products
• Atoms are conserved and rearranged during reactions

A balanced chemical equation shows the relative numbers of atoms or molecules of each substance involved in a reaction. These ratios can be used to find the relative masses of reactants and products.

For example, consider the reaction between hydrogen and oxygen to form water:

2H₂(g) + O₂(g) → 2H₂O(l) (balanced equation) This equation shows that 2 molecules of hydrogen react with 1 molecule of oxygen to produce 2 molecules of water.

• Balanced equations give mole ratios which correspond to fixed mass ratios
• Use relative atomic masses to find relative molecular masses if needed
• Mass ratios can be derived directly from balanced equations for calculations

To calculate the mass of an unknown reactant or product, use the mass ratios from the balanced equation and the known mass of another substance.

Step 1: Write the balanced equation for the reaction.

Step 2: Calculate the relative molecular masses (Mr) of the substances involved if needed, or use given mass ratios directly if provided in the question (without mole concept). Step 3: Set up a proportion comparing the known mass to the unknown mass using the ratio of relative molecular masses or given mass ratios from the equation. Step 4: Solve the proportion to find the unknown mass.

• Identify known and unknown masses
• Use balanced equation to find mass ratio
• Set up and solve proportion to find unknown mass

Magnesium reacts with oxygen to form magnesium oxide. The balanced equation is:

2Mg(s) + O₂(g) → 2MgO(s) Relative atomic masses: Mg = 24, O = 16

Calculate the mass of magnesium oxide formed when 48 g of magnesium reacts completely with oxygen.

• Step 1: Balanced equation shows 2 moles Mg react with 1 mole O₂ to form 2 moles MgO
• Step 2: Calculate relative formula masses: Mg = 24, MgO = 24 + 16 = 40
• Step 3: Mass ratio of Mg to MgO is 48 g Mg corresponds to x g MgO
• Step 4: Using ratio 2 × 24 g Mg → 2 × 40 g MgO, so 48 g Mg → x g MgO
• Set up proportion: 48 g Mg / x g MgO = 48 g Mg / 80 g MgO
• Solve: x = (48 × 80) / 48 = 80 g MgO
• Answer: 80 g of magnesium oxide is formed

A common mistake is to forget that the total mass of reactants equals the total mass of products, leading to incorrect mass calculations.

Another error is using unbalanced equations, which gives wrong mass ratios.

Also, confusing relative atomic mass with actual mass can cause mistakes in proportional calculations.

• Always balance chemical equations before calculations
• Remember total mass of reactants = total mass of products
• Use relative atomic or formula masses correctly in ratios
• Check units and ensure consistent use of grams