Quantitative Chemistry
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Balanced chemical equations
A balanced equation has the same number of each type of atom on both sides. Only coefficients (numbers in front) are changed — never the chemical formulae themselves.
Balancing reflects conservation of mass — no atoms are created or destroyed.
Balanced chemical equations — Key Knowledge
- Balanced equation equal atoms on each side
- Coefficients numbers in front of formulae, adjusted to balance
Relative formula mass
Relative formula mass (Mr) is the sum of the relative atomic masses (Ar) of all atoms in a formula.
For example, CaCO₃: Mr = 40 + 12 + (16 × 3) = 100.
Relative formula mass — Key Knowledge
- Mr sum of all Ar values in the formula
- Ar relative atomic mass of an individual element, from the periodic table
Conservation of mass
No atoms are created or destroyed in a chemical reaction. The total mass of reactants always equals the total mass of products.
If the system is closed so no gas can escape, the balance reading stays the same.
Conservation of mass — Key Knowledge
- Conservation of mass total mass unchanged
- Apparent mass loss gas escapes an open container
- Apparent mass gain gas from the air is absorbed, e.g. combustion of metals
The mole (4.3.2) (HT)
One mole of any substance contains exactly 6.02 × 10²³ particles. The mass of one mole equals the Mr in grams.
moles = mass
g ÷ Mr
One mole of carbon-12 has a mass of exactly 12 g.
The mole (4.3.2) (HT) — Key Knowledge
- Mole unit for amount of substance
- Avogadro's constant 6.02 × 10²³ particles per mole
Using moles in equations (4.3.2) (HT)
Balanced equations show the ratio of moles of reactants and products. These ratios can be used to calculate masses.
If 2Mg + O₂ → 2MgO, the ratio is 2 : 1 : 2.
Using moles in equations (4.3.2) (HT) — Key Knowledge
- Mole ratio coefficients in a balanced equation give the ratio of moles
- Mass calculation convert mass → moles → use ratio → convert back to mass
Limiting reactants (4.3.2) (HT)
The limiting reactant is the one that is completely used up first in a reaction. It determines the maximum amount of product formed.
Adding more of the excess reactant will not increase the amount of product.
Limiting reactants (4.3.2) (HT) — Key Knowledge
- Limiting reactant completely used up, controls amount of product
- Excess reactant some is left over after the reaction
Concentration of solutions
Concentration measures how much solute is dissolved in a given volume of solution.
concentration
g/dm³ = mass of solute
1 dm³ = 1000 cm³. Always convert cm³ to dm³ before using the formula.
Concentration of solutions — Key Knowledge
- Concentration mass of solute per volume of solution
- Units g/dm³
Concentration in mol/dm³ (4.3.2) (HT)
Concentration can also be expressed in moles per decimetre cubed.
concentration
mol/dm³ = moles of solute ÷ volume of solution
To convert between g/dm³ and mol/dm³, divide the g/dm³ value by the Mr.
Concentration in mol/dm³ (4.3.2) (HT) — Key Knowledge
- Molar concentration mol/dm³
Percentage yield
Percentage yield compares the actual mass of product obtained with the maximum theoretical mass. It is always less than 100%.
percentage yield =
mass of product obtained ÷ maximum theoretical mass × 100
Yield can never genuinely exceed 100% — if the measured mass is too high, the product is likely impure.
Percentage yield — Key Knowledge
- Percentage yield actual vs theoretical
- Reasons yield is below 100% incomplete reaction, practical losses during transfer or filtering, side reactions
Atom economy
Atom economy measures what proportion of the reactant atoms end up in the useful product rather than in waste by-products.
atom economy =
Mr of desired product ÷ total Mr of all products × 100
A reaction can have high yield but low atom economy if it reliably makes the desired product alongside lots of waste.
Atom economy — Key Knowledge
- Atom economy proportion of atoms forming the desired product
- High atom economy less waste, better for environment and cost
- Difference from yield atom economy is about the equation; yield is about the practical outcome