How Much? The Amount Of Chemical Change

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Balancing Equations

A symbol equation uses chemical symbols to show the number and type of atoms in reactants and products; a word equation uses only words.
Atoms cannot be created or destroyed in a chemical reaction, so the number of each atom must be the same on both sides — the equation must be balanced.
When balancing: do not change any formulae; place coefficients in front of formulae; do not split polyatomic ions (e.g., SO₄²⁻, NO₃⁻) unless needed.
For combustion of organic compounds, balance carbon first, then hydrogen, then oxygen.
Use state symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous.
Some elements are diatomic in their natural state and must be written with a subscript 2: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂.

A balanced chemical equation

Reacting Mass Calculations

The number of moles is calculated using: number of moles = mass of substance (g) / molar mass (g mol⁻¹).
Be clear about the particle type: 1 mole of CaF₂ contains 1 mole of CaF₂ formula units, but 1 mole of Ca²⁺ ions and 2 moles of F⁻ ions.
The stoichiometry (mole ratio) from the balanced equation links the amounts of reactants and products.
To find the mass of product: calculate moles of reactant, use the mole ratio, then convert moles to mass using mass = moles × molar mass.
In reacting mass calculations, you can work in any mass unit (g, tonnes, etc.) as long as you are consistent, because masses are in proportion to the balanced equation.
Example: burning 6.0 g of Mg (M = 24.31) gives 0.25 mol Mg, which produces 0.25 mol MgO (M = 40.31), mass = 10.08 g.

Avogadro's Law & Molar Volume of Gas

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules.
At standard temperature and pressure (STP) — 0 °C (273 K) and 100 kPa — one mole of any gas occupies 22.7 dm³ mol⁻¹.
Volume of gas = amount of gas (mol) × 22.7 dm³ mol⁻¹; amount of gas (mol) = volume of gas (dm³) / 22.7 dm³ mol⁻¹.
The stoichiometry of a reaction and Avogadro's Law allow deduction of exact volumes of gaseous reactants and products, e.g., 50 cm³ propane requires 250 cm³ O₂ and forms 150 cm³ CO₂ (ratio 1:5:3).
If gas volumes are not in the same ratio as the coefficients, the limiting reactant determines the amount of product.
To find the limiting reactant with gas volumes, divide each volume by its coefficient; the smallest result is the limiting reactant.

Concentration Calculations

Volumetric analysis uses the volume and concentration of a standard solution to find the concentration of an unknown solution, commonly via titration.
In a titration, a known volume (e.g., 20 or 25 cm³) is measured with a pipette into a conical flask; the other solution is added from a burette until the indicator changes colour; concordant results are needed.
Problem-solving steps: write the balanced equation; determine moles of the known substance; use the mole ratio; calculate the unknown quantity.
Moles = volume (dm³) × concentration (mol dm⁻³); concentration = moles / volume (dm³); volume = moles / concentration.
For monoprotic acid–base reactions (one H⁺ or one OH⁻ per formula unit), the shortcut C₁V₁ = C₂V₂ can be used, and volumes may be in cm³ as units cancel.
Back titration finds an unknown indirectly: react it with excess reagent, then titrate the excess; use mole ratios to deduce the amount of the original substance.

Concentration, moles and volume

Limiting & Excess Reactants

The limiting reactant is the reactant that is not in excess and determines how much product can form; the excess reactant is left over.
To identify the limiting reactant: calculate moles of each reactant, divide each by its coefficient from the balanced equation, and the smallest result is limiting.
Example: 10 mol C with 3 mol H₂ for C + 2H₂ → CH₄: H₂ is limiting because 3 mol H₂ requires only 1.5 mol C, leaving C in excess.
Example: 9.2 g Na (0.40 mol) and 8.0 g S (0.25 mol) for 2Na + S → Na₂S: Na gives 0.40/2 = 0.20 (lowest), so Na is limiting and S is in excess.

Percentage Yield Calculations

The theoretical yield is the maximum amount of product possible from the limiting reactant, assuming perfect conversion with no losses.
The experimental (actual) yield is the amount of product actually collected; differences arise from side reactions, loss during transfer or purification, and incomplete reaction.
Percentage yield = (actual yield / theoretical yield) × 100.
Ensure actual and theoretical yields have the same unit before applying the formula.
Example: theoretical yield 6.5 g, actual 5.8 g gives (5.8 / 6.5) × 100 = 89.2%.
Example: 6.5 g Zn (0.10 mol) with excess CuSO₄ gives theoretical 6.4 g Cu; actual 4.8 g gives (4.8 / 6.4) × 100 = 75%.

Atom Economy

Atom economy measures how efficiently reactants are converted into the desired product; higher atom economy means less waste and a more sustainable process.
Atom economy = (molecular mass of desired product / sum of molecular masses of ALL reactants) × 100.
Alternatively, atom economy = (mass of desired product / total mass of all products) × 100.
In addition reactions, atom economy is always 100% because all atoms end up in the single product, e.g., CH₂=CH₂ + Br₂ → CH₂BrCH₂Br.
A low atom economy means more resources are needed and more waste must be managed, increasing environmental and economic costs.
Other factors for process efficiency include rate, quantities of catalysts and solvents, energy use, and economic efficiency.
Example: Fe₂O₃ + 3CO → 2Fe + 3CO₂ has atom economy = (2 × 55.8) / [159.6 + (3 × 28.0)] × 100 = 45.8%.

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1.Which statement best defines a symbol equation?
Easy
- AA shorthand way of describing a chemical reaction using chemical symbols to show the number and type of each atom
- BA longer way of describing a chemical reaction using only words to show the reactants and products
- CA diagram showing the physical states of reactants and products
- DA list of the molar masses of all substances in a reaction
2.During a chemical reaction, atoms can be created or destroyed.
Easy
True or false?
3.Which state symbol represents a substance dissolved in water?
Easy
- A(s)
- B(l)
- C(g)
- D(aq)
4.Which of the following elements are diatomic in their natural state and must be written with a subscript 2 in equations? (select all that apply)
Easy
- AHydrogen
- BNitrogen
- CCarbon
- DOxygen
- ESulfur
5.Which one of the following is the correct net ionic equation for the reaction between CaCl2 and AgNO3?
Easy
- ACa2+ (aq) + 2AgNO3 (aq) → 2Ag+ (s) + Ca(NO3)2 (aq)
- BCaCl2 (aq) + 2Ag+ (aq) → 2AgCl (s) + Ca2+ (aq)
- CCa2+ (aq) + 2NO3- (aq) → Ca(NO3)2 (aq)
- DAg+ (aq) + Cl- (aq) → AgCl (s)
6.When the following equation is balanced correctly, using the smallest whole number coefficients, which row represents the coefficients? _ Mg3N2 (s) + _ H2O (l) → _ Mg(OH)2 (aq) + _ NH3 (aq)
Easy
- A1, 6, 3, 2
- B1, 3, 3, 1
- C2, 6, 2, 2
- D2, 6, 3, 2
7.Which one of the following is the correct net ionic equation for the reaction between NaC2H3O2 (aq) and HCl (aq)?
Easy
- AC2H3O2- (aq) + HCl (aq) → CCl (aq) + 2H+ (aq) + CO2 (aq)
- BC2H3O2- (aq) + H+ (aq) → HC2H3O2 (aq)
- CNa+ (aq) + Cl- (aq) → NaCl (aq)
- DNaC2H3O2 (aq) + H+ (aq) → HC2H3O2 (aq) + Na+ (aq)
8.When calcium carbonate is heated it decomposes according to the following equation: CaCO3 (s) → CaO(s) + CO2 (g) If 6.00 g of calcium carbonate is heated and produces 2.73 g of calcium oxide, what is the percentage yield of calcium oxide? (Mr CaCO3 = 100.09; CaO = 56.08)
Medium
- A18%
- B81%
- C90%
- D0.81%

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9.Hydrogen and chlorine react according to the following equation: H2 (g) + Cl2 (g) → 2HCl (g) When 1.5 moles of chlorine reacts with 2.0 moles of hydrogen, what will be the result?
Medium
- A3.5 mol of HCl
- B1.5 mol of HCl and 0.5 mol of H2
- C2.0 mol of HCl and 0.5 mol of Cl2
- D3.0 mol of HCl and 0.5 mol of H2
10.A solution of sodium chloride is made by adding 300 cm3 of water to a flask containing 200 cm3 of 0.50 mol dm-3 sodium chloride. What is the concentration of the resulting solution?
Medium
- A0.05 mol dm-3
- B0.1 mol dm-3
- C0.2 mol dm-3
- D0.3 mol dm-3
11.What is the number of molecules in 500 cm3 of oxygen under standard conditions?
Medium
- A3.01 x 10²³
- B1.33 x 10²⁵
- C2.73 x 10²⁴
- D1.33 x 10²²
12.Oxidation of ammonia by oxygen is the first step in the manufacture of nitric acid, which is used in the production of the synthetic material nylon. wO2 (g) + xNH3 (g) → yNO (g) + zH2O (g) Which values for w, x, y and z balance this equation?
Medium
- Aw=5, x=4, y=4, z=6
- Bw=6, x=4, y=4, z=5
- Cw=6, x=5, y=5, z=4
- Dw=5, x=6, y=6, z=4
13.When heated, anhydrous magnesium nitrate, Mg(NO3)2, will decompose into magnesium oxide and a mixture of gases shown in the following equation: 2Mg(NO3)2 (s) → 2MgO (s) + 4NO2 (g) + O2 (g) 1.48 g of anhydrous magnesium nitrate is heated until no further reaction takes place. What mass of nitrogen dioxide is produced?
Medium
- A0.92 g
- B0.46 g
- C1.48 g
- D1.84 g
14.A hydrocarbon, X, was burned in excess oxygen to give carbon dioxide and water as the only products. 0.1 mol of X produced 9.08 dm3 of carbon dioxide at standard conditions. What is the molecular formula of X?
Medium
- ACH4
- BC2H6
- CC3H8
- DC4H10
15.A Group II metal of mass 0.33 g reacted with 154.0 cm3 of oxygen at 273 K and 100 kPa pressure, to form an oxide which contains O2- ions. What is the molar mass of the metal?
Hard
- A0.02 g mol-1
- B24.32 g mol-1
- C17.38 g mol-1
- D211.95 g mol-1
16.A compound is made of sulfur and oxygen only. A sample of the compound has a mass of 8.0 g and consists of 3.2 g of sulfur and 4.8 g of oxygen. What is the empirical formula? (Ar S = 32.07, O = 16.00)
Medium
- ASO
- BSO2
- CSO3
- DS2O3
17.Which of the following samples has the largest mass? (Ar values: H = 1.01, N = 14.01, O = 16.00, S = 32.07)
Medium
- A2.0 mol of NH4+
- B1.0 mol of H2S
- C1.0 mol of H2O2
- D2.0 mol of OH-
18.The coefficient for copper when the following equation is balanced is: _Cu + _HNO3 → _Cu(NO3)2 + _NO + _H2O
Medium
- A1
- B2
- C3
- D4
19.Excess dilute hydrochloric acid is added separately to equal masses of the four metals, calcium, zinc, magnesium and strontium. Which metal will give off the largest volume of hydrogen gas in the reaction?
Hard
- Acalcium
- Bzinc
- Cmagnesium
- Dstrontium
20.Which statement correctly defines the limiting reactant?
Medium
- AThe reactant that is in excess
- BThe reactant that determines how much product can be made
- CThe reactant that has the largest number of moles
- DThe reactant that is left over after the reaction
21.The theoretical yield is the maximum amount of product that can be formed from a given amount of reactants, assuming perfect conversion with no losses.
Easy
True or false?
22.Which formula correctly represents percentage yield?
Medium
- Apercentage yield = (theoretical yield / actual yield) × 100
- Bpercentage yield = (actual yield / theoretical yield) × 100
- Cpercentage yield = (actual yield × theoretical yield) × 100
- Dpercentage yield = (theoretical yield - actual yield) × 100
23.Which of the following statements about atom economy is correct?
Medium
- AAtom economy is calculated from experimental data
- BA higher atom economy means more waste is produced
- CIn addition reactions, atom economy is always 100%
- DAtom economy is the same as percentage yield
24.Match each term with its correct definition.
Medium
- Limiting reactant
- Excess reactant
- Theoretical yield
- Actual yield
- The reactant that is not in excess and determines the amount of product
- The reactant that is left over after the reaction
- The maximum amount of product that can be formed from a given amount of reactants
- The amount of product actually collected in the lab
25.Arrange the steps for balancing a chemical equation in the correct order.
Medium
- Write the formulae of the reactants and products
- Count the numbers of atoms in each reactant and product
- Balance the atoms one at a time until all the atoms are balanced
- Use appropriate state symbols in the equation
26.Match each quantity with the correct formula.
Medium
- Number of moles from mass
- Number of moles of a gas at STP
- Concentration of a solution
- Percentage yield
- n = m / M
- n = V / 22.7
- c = n / V
- actual / theoretical × 100
27.Place the steps of a titration in the correct order.
Medium
- Measure a known volume of one solution with a pipette and place it in a conical flask
- Fill the burette with the other solution
- Add a few drops of indicator to the conical flask
- Open the burette tap and add solution until the indicator just changes colour
- Repeat until concordant results are obtained
28.Which of the following are reasons why the actual yield is less than the theoretical yield? (select all that apply)
Medium
- ASide reactions occur
- BProduct is lost during transfer or purification
- CThe reaction is incomplete
- DThe limiting reactant is in excess
- EThe molar mass of the product is too high
29.Which of the following statements about atom economy are correct? (select all that apply)
Medium
- AIt is calculated from the balanced chemical equation
- BA higher atom economy means less waste
- CAddition reactions always have 100% atom economy
- DIt depends on the actual yield obtained in the lab
- EIt is always equal to the percentage yield
30.Which of the following are correct about a back titration? (select all that apply)
Medium
- AIt is used to find the concentration or amount of an unknown substance indirectly
- BIt involves reacting the unknown with an excess of a further reactant
- CThe excess reactant is then analysed by titration
- DIt can be used to determine the percentage by mass of calcium carbonate in marble
- EIt requires no indicator
31.In a titration, concordant results are obtained by carrying out multiple trials.
Easy
True or false?
32.When balancing a chemical equation, you may change the formulae of the substances to make it balance.
Medium
True or false?
33.In an addition reaction, the atom economy is always 100%.
Medium
True or false?
34.The limiting reactant is the reactant that is present in excess.
Medium
True or false?
35.A gas sample contains 0.50 mol of methane, CH4, and 0.50 mol of carbon dioxide, CO2. Which of the following statements about this sample are correct? (select all that apply)
Medium
- AThe sample contains a total of 1.00 mol of gas molecules
- BThe sample contains 1.00 mol of carbon atoms in total
- CThe sample contains 1.00 mol of hydrogen atoms in total
- DThe sample contains 3.01 x 10²³ molecules of methane
- EThe two gases occupy equal volumes under the same conditions of temperature and pressure
36.A gaseous hydrocarbon CxHy burns completely in excess oxygen. 20 cm3 of the hydrocarbon reacts with exactly 100 cm3 of oxygen to produce 60 cm3 of carbon dioxide, with all gas volumes measured at the same temperature and pressure. What is the molecular formula of the hydrocarbon?
Medium
- AC2H4
- BC3H8
- CC3H6
- DC2H6
37.A 25.0 cm3 portion of a 0.200 mol dm-3 solution of a metal chloride, MCl2, is treated with excess silver nitrate solution. The mass of silver chloride precipitated is 1.435 g. What is the concentration of chloride ions in the original solution? (Mr of AgCl = 143.5)
Medium
- A0.200 mol dm-3
- B0.400 mol dm-3
- C0.100 mol dm-3
- D0.800 mol dm-3
38.In an experiment, 2.00 g of magnesium ribbon is added to 100 cm3 of 0.500 mol dm-3 hydrochloric acid. Which statement about this reaction is correct? (Ar: Mg = 24.31)
Medium
- AMagnesium is the limiting reactant
- BHydrochloric acid is the limiting reactant
- CNeither reactant is limiting; both are used up exactly
- DThere is not enough information to identify the limiting reactant
39.A student heats 5.00 g of a hydrated salt, Na2CO3.xH2O, until the mass is constant. The mass falls to 1.85 g. What is the value of x? (Mr: Na2CO3 = 106.0, H2O = 18.0)
Medium
- A1
- B5
- C10
- D2
40.A 1.00 g sample of an impure carbonate, MCO3, is treated with excess dilute hydrochloric acid. The carbon dioxide evolved occupies 224 cm3 at STP (molar volume = 22.7 dm3 mol-1). What is the percentage by mass of MCO3 in the sample? (Mr of MCO3 = 100.0)
Hard
- A22.4%
- B50.0%
- C98.7%
- D10.0%
41.Silicon reacts with chlorine gas to produce silicon chloride, SiCl4. How many moles of chlorine gas are needed to react with 1 mole of silicon?
Medium
42.25.0 cm3 of hydrochloric acid solution reacts with 36.2 cm3 of 0.225 mol dm-3 sodium hydroxide solution. What is the concentration of the acid in mol dm-3?
Medium
43.A 2.27 dm3 sample of nitrogen gas, measured under standard conditions, reacted with a large excess volume of hydrogen gas to produce ammonia. Only 20.0% of the nitrogen gas reacted to produce ammonia. What mass of ammonia was made?
Medium
44.When 0.10 mol of chlorine gas, Cl2, reacts with excess cold sodium hydroxide, sodium chlorate(I) is formed as one of the products according to the equation: Cl2 (g) + 2NaOH (aq) → NaCl (aq) + NaClO (aq) + H2O (l) What mass of sodium chlorate(I), NaClO, is formed?
Medium
45.Solid fertilisers are often rated by their NPK mass ratio. A particular fertiliser has a ratio of 20 g (N) : 30 g (P) : 10 g (K) per 100 g of fertiliser. It is recommended that 14 g of this fertiliser is used per 5 dm3 of water. What is the concentration of nitrogen, in mol dm-3, in the solution? (Ar N = 14.01)
Medium
46.When lead sulfide reacts with oxygen it produces lead(II) oxide and sulfur dioxide according to the equation below: PbS (s) + O2 (g) → PbO (s) + SO2 (g) What is the whole number sum of the coefficients in the balanced equation?
Medium
47.Some coal contains as much as 3% sulfur. How much sulfur dioxide (Mr = 64.07 g mol-1) is produced by burning a lump of coal of mass 125 g? (Ar S = 32.07)
Medium
48.The conversion of toxic emissions into harmless products takes place in catalytic converters as follows: _CO (g) + _NO (g) → _CO2 (g) + _N2 (g) The sum of the coefficients is
Medium
49.Natural gas contains on average 5.5 mg / m3 of hydrogen sulfide, H2S (Mr = 34.09; Ar of S = 32.07). If a typical household in the UK consumes 0.198 m3 of gas per day, what is the average annual emission of sulfur in g per household?
Hard
50.When a 1.00 g sample of carbon is burned in a limited supply of oxygen, 0.72 g of the carbon combusts to form CO and the reaction also produces 0.28 g of CO2. These gases were passed through excess NaOH (aq) which absorbs the CO2, but not the CO. The remaining gas was then dried and collected. Assuming that all gas volumes were taken at 273.15 K and 100 kPa pressure, what was the volume of gas at the end of the reaction? (Molar volume of a gas at STP = 22.7 dm3 mol-1)
Hard
51.Chicken eggs are made up of 5.0% by mass of egg shell. The average egg has a mass of 50.0 g. Assume that chicken eggshell is pure calcium carbonate. How many complete chicken’s egg shells would need to neutralise 50.0 cm3 of 2.00 mol dm-3 ethanoic acid?
Challenge
52.When a sample of potassium oxide, K2O, is dissolved in 250 cm3 of distilled water, 25 cm3 of this solution is titrated against sulfuric acid with a concentration of 2.00 mol dm-3. Complete neutralisation takes place with 15 cm3 of sulfuric acid. What is the mass of the original sample of potassium oxide dissolved in 250 cm3 of distilled water?
Challenge
53.Explain why the hydration of ethene has a higher atom economy than the substitution of bromoethane to produce ethanol.
Hard
54.Explain the difference between the theoretical yield and the actual yield of a reaction, and give two reasons why they may differ.
Hard
55.A student predicts that the mass of copper obtained by displacement from copper(II) sulfate will equal the mass of zinc used. Explain why the actual mass of copper collected is usually less than the theoretical yield.
Hard
56.Silicon reacts with chlorine gas to produce silicon chloride, SiCl4. How many moles of chlorine gas are needed to react with 1 mole of silicon?
Medium
- A3 mol
- B1 mol
- C4 mol
- D2 mol
57.25.0 cm3 of hydrochloric acid solution reacts with 36.2 cm3 of 0.225 mol dm-3 sodium hydroxide solution. What is the concentration of the acid in mol dm-3?
Medium
- A1.326 mol dm-3
- B-0.674 mol dm-3
- C2.326 mol dm-3
- D0.326 mol dm-3
58.A 2.27 dm3 sample of nitrogen gas, measured under standard conditions, reacted with a large excess volume of hydrogen gas to produce ammonia. Only 20.0% of the nitrogen gas reacted to produce ammonia. What mass of ammonia was made?
Medium
- A2.68 g
- B1.68 g
- C0.68 g
- D-0.32 g
59.When 0.10 mol of chlorine gas, Cl2, reacts with excess cold sodium hydroxide, sodium chlorate(I) is formed as one of the products according to the equation: Cl2 (g) + 2NaOH (aq) → NaCl (aq) + NaClO (aq) + H2O (l) What mass of sodium chlorate(I), NaClO, is formed?
Medium
- A7.44 g
- B6.44 g
- C8.44 g
- D9.44 g
60.Solid fertilisers are often rated by their NPK mass ratio. A particular fertiliser has a ratio of 20 g (N) : 30 g (P) : 10 g (K) per 100 g of fertiliser. It is recommended that 14 g of this fertiliser is used per 5 dm3 of water. What is the concentration of nitrogen, in mol dm-3, in the solution? (Ar N = 14.01)
Medium
- A1.04 mol dm-3
- B-0.96 mol dm-3
- C0.04 mol dm-3
- D2.04 mol dm-3
61.When lead sulfide reacts with oxygen it produces lead(II) oxide and sulfur dioxide according to the equation below: PbS (s) + O2 (g) → PbO (s) + SO2 (g) What is the whole number sum of the coefficients in the balanced equation?
Medium
- A11
- B9
- C10
- D8
62.Some coal contains as much as 3% sulfur. How much sulfur dioxide (Mr = 64.07 g mol-1) is produced by burning a lump of coal of mass 125 g? (Ar S = 32.07)
Medium
- A9.49 g
- B6.49 g
- C7.49 g
- D8.49 g
63.The conversion of toxic emissions into harmless products takes place in catalytic converters as follows: _CO (g) + _NO (g) → _CO2 (g) + _N2 (g) The sum of the coefficients is
Medium
- A7
- B8
- C9
- D6
64.Natural gas contains on average 5.5 mg / m3 of hydrogen sulfide, H2S (Mr = 34.09; Ar of S = 32.07). If a typical household in the UK consumes 0.198 m3 of gas per day, what is the average annual emission of sulfur in g per household?
Hard
- A0.374 g
- B0.397 g
- C0.423 g
- D397 g
65.When a 1.00 g sample of carbon is burned in a limited supply of oxygen, 0.72 g of the carbon combusts to form CO and the reaction also produces 0.28 g of CO2. These gases were passed through excess NaOH (aq) which absorbs the CO2, but not the CO. The remaining gas was then dried and collected. Assuming that all gas volumes were taken at 273.15 K and 100 kPa pressure, what was the volume of gas at the end of the reaction? (Molar volume of a gas at STP = 22.7 dm3 mol-1)
Hard
- A3.36 dm3
- B1.36 dm3
- C0.36 dm3
- D2.36 dm3
66.Chicken eggs are made up of 5.0% by mass of egg shell. The average egg has a mass of 50.0 g. Assume that chicken eggshell is pure calcium carbonate. How many complete chicken’s egg shells would need to neutralise 50.0 cm3 of 2.00 mol dm-3 ethanoic acid?
Challenge
- A4
- B1
- C3
- D2
67.When a sample of potassium oxide, K2O, is dissolved in 250 cm3 of distilled water, 25 cm3 of this solution is titrated against sulfuric acid with a concentration of 2.00 mol dm-3. Complete neutralisation takes place with 15 cm3 of sulfuric acid. What is the mass of the original sample of potassium oxide dissolved in 250 cm3 of distilled water?
Challenge
- A25.43 g
- B33.92 g
- C28.26 g
- D31.09 g

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