Comparing Masses of Substances

Relative Atomic Mass (Ar)

The concept of relative atomic mass allows chemists to compare the masses of different atoms using a standard reference. The modern standard is the 12C isotope of carbon.

• Definition: The weighted mean (average) mass of an atom compared to 1/12 of the mass of a 12C atom.

• Expression:

• Values are typically found on the Periodic Table, often to one decimal place for lighter elements.

• Example: Nitrogen has a relative atomic mass of 14, meaning it is 14 times heavier than hydrogen (Ar = 1).

Relative Molecular Mass (Mr)

Relative molecular mass is used for molecules and is calculated by summing the relative atomic masses of all atoms in the molecule.

• Formula:

• Example 1: For CO2:

• Example 2: For H2SO4:

• Relative atomic and molecular masses have no units.

Relative Formula Mass (Mr)

This term is used for ionic compounds and compounds with giant structures, where the concept of a molecule does not apply.

• Example: For hydrated copper(II) sulfate, CuSO4·5H2O:

Molar Mass (M)

Molar mass is the mass per mole of a substance, measured in g mol-1. It applies to both molecular and ionic substances.

• Formula: where n = amount in moles, m = mass in grams, M = molar mass in g mol-1.

• Example Table:

Calculations Using the Avogadro Constant

The Avogadro Constant (L)

The Avogadro constant (L) is the number of particles (atoms, molecules, or ions) in one mole of a substance.

• Value:

• Used to convert between number of particles and amount in moles.

Calculating Number of Particles

• Formula:

• Example: How many H2O molecules in 1.25 g of water?

  • mol

  • Number of molecules =

Calculating Mass from Number of Particles

• Formula:

• Example: What is the mass of 100 million atoms of gold?

  • mol

  • g

Calculations Involving Moles

The Mole

The mole (mol) is the SI unit for the amount of substance. It is defined as the amount of substance that contains as many particles as there are atoms in exactly 12 g of the 12C isotope.

• 1 mol = particles

• Used to count atoms, molecules, ions, electrons, etc.

Calculating Moles

• Formula:

• Rearrangements:

• Example 1: Amount in 6.51 g of NaCl ( g mol-1): mol

• Example 2: Mass of 0.263 mol of HI ( g mol-1): g

• Example 3: Molar mass from 0.284 mol and 17.8 g: g mol-1

Calculations Using Reacting Masses

Stoichiometry and Balanced Equations

A balanced chemical equation shows the ratio of moles and masses of reactants and products. This allows calculation of the required or produced mass of a substance in a reaction.

• Example:

  • 1 mol N2 reacts with 3 mol H2 to form 2 mol NH3

  • 28.0 g N2 reacts with 6.0 g H2 to form 34.0 g NH3

Calculating Reacting Masses

• Stepwise Method:

  1. Calculate molar masses of relevant substances.

  2. Calculate the amount (in mol) of the known substance.

  3. Use the stoichiometric ratio to find the amount of the unknown.

  4. Calculate the mass of the unknown using .

• Example: What mass of SO3 is needed to form 75.0 g of H2SO4?

  • g mol-1, g mol-1

  • mol

  • Ratio is 1:1, so mol

  • g

Determining Formulae and Equations from Reacting Masses

• Experimental data can be used to deduce the formula of a compound or the correct equation for a reaction.

• Example: Heating 16.7 g Na2CO3·10H2O yields 3.15 g H2O. The ratio of moles gives the equation:

  • Na2CO3·10H2O → Na2CO3·7H2O + 3H2O

The Yield of a Reaction

Theoretical Yield, Actual Yield, and Percentage Yield

Theoretical yield is the maximum possible mass of product, calculated from the balanced equation, assuming complete reaction and no losses. Actual yield is the mass actually obtained. Percentage yield compares these two values.

• Formula:

• Example: If theoretical yield is 26.7 tonnes and actual yield is 18.5 tonnes:

• Low yields can result from incomplete reactions, side reactions, or product loss during purification.

Atom Economy

Definition and Importance

Atom economy measures the efficiency of a reaction in terms of how many atoms from the reactants end up in the desired product. It is important for sustainability and waste reduction in industrial processes.

• Formula:

• Example: For CaCO3 + 2NaCl → Na2CO3 + CaCl2:

  • Atom economy =

• Generalizations:

  • Addition reactions: 100% atom economy

  • Elimination and substitution reactions: lower atom economies

  • Multistep reactions: may have even lower atom economies

Worked Example Table: Atom Economy

Key Terms

• Molar mass (M): Mass per mole of a substance (g mol-1).

• Avogadro constant (L): mol-1, the number of particles in one mole.

• Mole: The amount of substance containing as many particles as there are atoms in 12 g of 12C.

• Theoretical yield: Maximum possible mass of product, assuming complete reaction.

• Actual yield: Mass of product actually obtained.

• Percentage yield: Actual yield divided by theoretical yield, as a percentage.

• Atom economy: Molar mass of desired product divided by sum of molar masses of all products, as a percentage.

• Hydrate: Compound containing water of crystallization, e.g., CuSO4·5H2O.