Chapter 4Stoichiometry

Barium forms the cation Ba²⁺ and nitrogen forms the nitride anion N³⁻. Applying the criss-cross method, the numerical value of each ion's charge becomes the subscript of the other ion and the signs are dropped:

Check: 3 × (+2) = +6 and 2 × (−3) = −6, so the compound is electrically neutral.

Molecular formula = n (empirical formula), where n = molar mass ÷ empirical formula mass.

So a mole is the amount, and Avogadro's number is how many particles that amount contains.

Check: Cu 1 = 1; S 2 = 1 + 1; H 4 = 4; O 8 = 4 + 2 + 2. The acid must be hot and concentrated: copper does not react with dilute sulphuric acid.

The formula of an element contains only one kind of atom: either the symbol alone for elements that exist as an aggregate of atoms (Na, Fe, C) or a symbol with a subscript for molecular elements (O₂, N₂, O₃). The formula of a compound contains two or more kinds of atoms bonded together (H₂O, NaCl, NH₃, CH₄).

Water (H₂O) and carbon dioxide (CO₂): the ratios 2 : 1 and 1 : 2 cannot be simplified, so n = 1. Methane (CH₄) and ammonia (NH₃) are other examples.

Empirical formula mass = 30; n = 60 ÷ 30 = 2; molecular formula = (CH₂O)₂ = C₂H₄O₂ (acetic acid, CH₃COOH).

Count the atoms: 3 H, 1 P and 4 O. Molecular formula H₃PO₄.

C: 1 + 1 + 1 = 3; H: 3 + 2 + 2 + 1 = 8; O: 1. Molecular formula C₃H₈O, usually written C₃H₇OH to show the OH group.

The structure has one Ca²⁺ ion and one carbonate ion CO₃²⁻ (one C bonded to three O atoms). The charges balance 1 : 1, so the formula is CaCO₃.

A chemical formula represents an element or a compound by symbols, with subscripts showing the number of atoms of each kind. H₂O shows that in one molecule of water two atoms of hydrogen are bonded to one atom of oxygen.

A formula unit is the formula of an ionic compound showing the minimum ratio between its ions. Sodium chloride exists as ions bonded together in a crystal, not as molecules; since the ratio between its ions is 1 : 1, it is represented by the formula unit NaCl.

A molecular formula shows all the types of atoms bonded together in one molecule of a compound and their actual numbers. Examples: H₂O, NH₃, CH₄, H₂O₂, C₆H₆.

In ozone three atoms of oxygen are bonded to each other in one molecule, so its formula is O₃. Sodium exists as an aggregate of atoms, not molecules, so it is represented by its symbol alone.

Empirical formula of a compound shows the simplest whole number ratio of atoms present in that compound. All ionic compounds are represented by their empirical formulas.

An empirical formula shows only the simplest ratio, not the actual numbers. C₆H₆ and C₂H₂ both have C : H = 1 : 1, so both have the empirical formula CH.

For H₂O₂: n = 34 ÷ 17 = 2, so (HO)₂ = H₂O₂. If n = 1 the two formulas are the same.

Empirical formula mass = 13; n = 78 ÷ 13 = 6; molecular formula = (CH)₆ = C₆H₆.

Experimental data on the mass percent composition of the compound: the percentage of each element is divided by its atomic mass to get the mole ratio, which is then reduced to the simplest whole numbers.

In this method, the numerical value of each of the ion charges is crossed over to become the subscript of the other ion. Signs of the charges are then dropped. Li⁺ and O²⁻ give Li₂O.

Some metals (Cu, Fe, Sn) can lose different numbers of electrons and so show variable valency. Their compounds are named with Roman numerals: copper(I) oxide Cu₂O, copper(II) oxide CuO; iron(II) chloride FeCl₂, iron(III) chloride FeCl₃.

The number 6.022 × 10²³ is called Avogadro's number after the name of the Italian chemist Amedeo Avogadro. Avogadro's number is the number of units in one mole of a substance. It is represented as Nᴀ.

The quantity of a substance containing Avogadro's number of particles (Nᴀ) is called a mole. A mole of carbon atoms contains 6.022 × 10²³ atoms and weighs 12 g; a mole of O₂ contains 6.022 × 10²³ molecules and weighs 32 g; a mole of NaCl has 6.022 × 10²³ formula units and weighs 58.5 g.

The mass of one mole of a substance is called its molar mass. The molar mass of hydrogen atoms is 1.008 g; that of hydrogen molecules (H₂) is 2.016 g.

Because 1.00 g = 6.022 × 10²³ amu. Taking this many particles turns a mass in amu into the same number in grams: one C atom is 12 amu, so 6.022 × 10²³ C atoms weigh 12 g.

A mole of hydrogen atoms (1.008 g) and a mole of hydrogen molecules (2.016 g) are different amounts. When we use the term mole of a substance, we must also refer to what type of particles (atoms, molecules or ions) are present.

M(CO₂) = 12 + 32 = 44 g mol⁻¹. n = 88 ÷ 44 = 2 mol. Molecules = 2 × 6.022 × 10²³ = 1.204 × 10²⁴.

m = n × M = 0.5 × 58.5 = 29.25 g.

Molecules = 0.25 × 6.022 × 10²³ = 1.506 × 10²³. Each CH₄ has 5 atoms: atoms = 5 × 1.506 × 10²³ = 7.53 × 10²³.

Atoms and molecules are so small that they cannot be counted. The mole concept allows us to count atoms and molecules by weighing macroscopic amounts of matter, and it turns the ratio in an equation into a mass ratio we can weigh out in the laboratory.

Representing a chemical change in terms of symbols of elements and formulas of compounds is called a chemical equation. It tells us the elements or compounds which are reacting (reactants, on the left) and those being produced (products, on the right).

One mole of zinc reacts with one mole of sulphuric acid to produce one mole of zinc sulphate and one mole of hydrogen gas: 1 : 1 : 1 : 1.

Sometimes a chemical reaction moves both ways: the reactants react to give the products and the products, in turn, react to give the reactants back. Such reactions are called reversible reactions and are shown by ⇌.

Symbols written after formulas to show physical states: (s) solid, (l) liquid, (g) gas and (aq) aqueous (dissolved in water). Example: Zn(s) + H₂SO₄(aq) → ZnSO₄(aq) + H₂(g).

AgCl being insoluble comes out of the aqueous solution in the form of a precipitate; Na⁺ and NO₃⁻ are spectator ions.

Al: 4 = 2 × 2; O: 3 × 2 = 6 = 2 × 3.

A chemical equation can only be written if all the points are experimentally verified. The nature of the products and their correct formulas must first be ascertained. An equation cannot be invented on paper: copper with dilute H₂SO₄ gives no reaction at all, though one could balance an equation for it.

One mole (100 g) of calcium carbonate reacts with two moles (73 g) of hydrochloric acid to produce one mole (111 g) of CaCl₂, one mole (18 g) of water and one mole (44 g) of carbon dioxide. 100 + 73 = 173 g = 111 + 18 + 44: the total mass of the reactants equals that of the products.

1 mol of alcohol gives 2 mol CO₂, so 1.8 mol gives 2 × 1.8 = 3.6 mol CO₂ (and uses 5.4 mol O₂).

5 g of H₂ gives 36 ÷ 4 × 5 = 45 g of water.

More of that reactant is present than the equation needs, so it is left over at the end. The other reactant is used up completely and decides how much product forms; that is why calculations start from the reactant that is not in excess.

The percentage by mass of each element in a compound: mass of the element in one mole ÷ molar mass × 100. For CO₂: 12 ÷ 44 × 100 = 27.3 % carbon (and 72.7 % oxygen).

Same empirical formula

An empirical formula does not tell us the actual number of atoms present in a compound; rather it represents the simplest ratio between atoms. It is possible that some compounds may have the same empirical formula. Benzene (C₆H₆) and acetylene (C₂H₂) both have C : H = 1 : 1, so both are CH. Glucose (C₆H₁₂O₆), acetic acid (C₂H₄O₂) and formaldehyde (CH₂O) are all CH₂O.

Different molecular formulas

The molecular formula shows the actual number of atoms in one molecule, n × (empirical formula). Compounds with the same empirical formula but different molar masses have different values of n, and so different molecular formulas.

Each is found by criss-crossing the charges; a polyatomic ion taken more than once goes in brackets, and Al³⁺/N³⁻ cancel 1 : 1.

Avogadro's number has an immense significance in Chemistry, and the quantity of a substance containing Avogadro's number of particles is called a mole.

Check: 5.217 + 0.962 + 2.478 = 8.657 g, and 60.26 + 11.11 + 28.62 = 99.99 % ≈ 100 % (rounding).

A reversible reaction never goes to completion: at any time all the reactants and products are present together. So the balanced equation gives only the maximum (theoretical) mass of product that would form if the reaction went to completion; the actual mass is less.

What a chemical equation is

Representing a chemical change in terms of symbols of elements and formulas of compounds is called a chemical equation. It tells us the reactants (written on the left) and the products (written on the right); an arrow from reactants to products separates the two.

1. Law of conservation of mass

A chemical equation must obey the law of conservation of mass. No atom should be destroyed or produced during a chemical change. The total number and the type of atoms must remain the same, so the total number and kind of atoms on both sides of the equation must be equal: the chemical equation must be balanced.

2. Correct formulas

The formulas of elements and compounds must be written correctly. A wrong formula cannot be fixed by changing coefficients: water is always H₂O, never HO or H₂O₂.

3. Correct mole ratio

A chemical equation must determine the correct mole ratio among the reactants, the products and between the reactants and the products.

4. Direction of change

A chemical equation must also point out the direction in which the change is proceeding: → for a reaction that goes one way, ⇌ for a reversible reaction.

5. Physical states

It is a usual practice to show the normal physical states of reactants and products as a subscript. Solid, liquid and gas are symbolized as s, l and g; aqueous (aq) represents the solvated ion.

Experimental verification

A chemical equation can only be written if all the above points are experimentally verified. The nature of the products and their correct formulas must first be ascertained.

Example

Zinc reacts with sulphuric acid to give zinc sulphate and hydrogen gas. One mole of zinc reacts with one mole of sulphuric acid to produce one mole of zinc sulphate and one mole of hydrogen gas. The equation is balanced (1 Zn, 2 H, 1 S, 4 O on each side), has correct formulas, a 1 : 1 : 1 : 1 mole ratio, a forward arrow and state symbols.

The problem

In a chemical reaction a large number of atoms or molecules of reactants react to give the products. We would like to know the mass ratio in which the reactants react, and to express these masses in grams. It is not possible to weigh individual atoms or molecules because they are very small.

Building up to Avogadro's number

Consider 2C + O₂ → 2CO. Increasing the number of reacting species (2 × 100 atoms with 100 molecules, 2 × 10 000 atoms with 10 000 molecules) does not change the ratio in which they react, but the numbers are still far too small to weigh. We increase them to 6.022 × 10²³, because 1.00 g = 6.022 × 10²³ amu:

Starting from a simple equation we now have a mass ratio, 24 g : 32 g : 56 g, which can conveniently be used in the laboratory.

The mole

Mole is a number like a dozen or a gross. A dozen of oranges means 12 oranges; similarly a mole of a substance means its 6.022 × 10²³ particles, which can be atoms, molecules or ions. We must say which particles we mean.

Molar mass

The mass of one mole of a substance is called molar mass. Hydrogen atoms 1.008 g; hydrogen molecules 2.016 g.

The equation read in moles

Structure of sand

Sand is mostly silicon dioxide (silica). It is a giant covalent (network) structure, not a collection of small molecules. Each silicon atom is bonded to four oxygen atoms (at the corners of a tetrahedron), and each oxygen atom is shared between two silicon atoms, so the network runs on through the whole crystal.

Finding the ratio

The formula is an empirical formula

Like the formula units of ionic compounds, SiO₂ is an empirical formula: it shows the simplest whole number ratio of atoms in the network, not a molecule. It can also be found by analysis: silica contains 46.7 % Si and 53.3 % O by mass; 46.7 ÷ 28 = 1.67 and 53.3 ÷ 16 = 3.33, a 1 : 2 ratio.

Empirical formula

Empirical formula of a compound shows the simplest whole number ratio of atoms present in that compound. All the ionic compounds are represented by their empirical formulas, which show the simplest ratio between their ions: the empirical formula of calcium fluoride is CaF₂.

Molecular formula

A molecular formula shows all the types of atoms bonded together in one molecule of the compound, with their actual numbers: H₂O₂, C₆H₆, C₆H₁₂O₆.

Relation between the two

If for a compound the value of n is one, its molecular formula is the same as its empirical formula (H₂O, CO₂, CH₄).

Example 1: hydrogen peroxide

Example 2: benzene

Example 3: glucose

Same empirical formula, different compounds

Principle

In order to write down the formula of an ionic compound, first identify the cations and anions and the number of charges present on them. Finally combine the two ions together to form an electrically neutral compound.

Steps

Example 1: lithium oxide

Cation Li⁺, anion O²⁻. Crossing over gives Li₂O₁ → Li₂O (2 × +1 = +2; −2).

Example 2: aluminium oxide

Cation Al³⁺, anion O²⁻. Crossing over gives Al₂O₃ (+6, −6).

Example 3: magnesium nitride

Cation Mg²⁺, anion N³⁻. Crossing over gives Mg₃N₂ (+6, −6).

More examples

Definition

Representing a chemical change in terms of symbols of elements and formulas of compounds is called a chemical equation. It tells us the elements or compounds which are reacting and those which are being produced. The reacting substances are called reactants and those produced are called products. Reactants are written on the left, products on the right, separated by an arrow.

Information from a balanced equation

Reversible reactions

Sometimes a reaction moves both ways: the reactants react to give the products and the products, in turn, react to give the reactants back. Such reactions are called reversible reactions and are indicated by the sign ⇌.

Ionic equations

Reactions involving ions may also be shown as chemical equations. Both AgNO₃ and NaCl are ionic compounds and are soluble in water. When they are mixed in water they react; AgCl, being insoluble, comes out of the aqueous solution as a precipitate.

Basis

A complete and balanced chemical equation tells us the mole ratio or molar mass ratio between the reactants and the products. With the help of this ratio we can find the masses of the products if we know the masses of the reactants, and vice versa.

The total masses of the reactants are equal to the total masses of the products (173 g).

Mass-mass: Example 1

Mole-mole: Example 2

Mole-mass: Example 3

Mass-particles: Example 4

Steps

Example 1: sulphuric acid

H–O–S(=O)(=O)–O–H has 2 H, 1 S and 4 O atoms. Molecular formula H₂SO₄.

Example 2: phosphoric acid

Phosphorus bonded to three OH groups and one =O: 3 H, 1 P, 4 O. Molecular formula H₃PO₄.

Example 3: n-propyl alcohol

CH₃–CH₂–CH₂–OH: 3 C, 8 H, 1 O. Molecular formula C₃H₈O (C₃H₇OH).

Example 4: calcium carbonate

One Ca²⁺ and one carbonate ion (C bonded to three O): CaCO₃. Being ionic, this is a formula unit.