Quantitative chemistry, Year 10: reacting masses, limiting reactants and concentration

6

HintThe big numbers in front of the formulae give the recipe.

The whyThe equation says that one mole of magnesium reacts with two moles of hydrochloric acid. Three moles of magnesium therefore need 3 × 2 moles of acid.

0.5; 0.5; 20

HintThree steps: grams to moles, then the ratio in the equation, then moles back to grams.

The whyMoles of Mg = 12 ÷ 24. The equation shows 2 mol of Mg making 2 mol of MgO, a 1 : 1 ratio. The Mr of MgO is 24 + 16 = 40, so the mass is the moles of MgO × 40.

6 g

Hint28 g is exactly one mole of N2, so read the amounts straight from the balancing numbers.

The whyOne mole of N2 has a mass of 2 × 14 = 28 g. It reacts with three moles of H2, and each mole of H2 has a mass of 2 × 1 = 2 g, so the mass of hydrogen is 3 × 2 g.

The 2 is a ratio of moles, not of masses

HintBalancing numbers count particles, and the particles of the two substances do not weigh the same.

The whyThe equation says 1 mol of Mg reacts with 2 mol of HCl. In grams that is 24 g of magnesium with 2 × 36.5 = 73 g of hydrogen chloride. Masses have to be turned into moles before the ratio can be used.

160 g

HintWork backwards: turn the product into moles first, then use the ratio to find the reactant.

The whyMoles of Fe = 112 ÷ 56 = 2. The equation shows 1 mol of Fe2O3 giving 2 mol of Fe, so 1 mol of Fe2O3 is needed. Its Mr is (2 × 56) + (3 × 16) = 160, so the mass is 160 g.

moles

HintBalancing numbers count particles, so you need the chemist's counting unit.

The whyDivide each mass by the relative formula mass of that substance. The amounts you get are then turned into the simplest whole-number ratio, and those whole numbers are the balancing numbers.

0.2; 0.6; 0.4; 3

HintDivide each mass by its Mr, then divide all three results by the smallest.

The whyMoles = mass ÷ Mr for each substance. Dividing the three amounts by the smallest gives the ratio 1 : 3 : 2, and these are the balancing numbers.

2 : 3

HintDividing by the smaller amount leaves a half in the ratio, so scale up once more.

The whyDividing both amounts by 0.4 gives 1 : 1.5. Balancing numbers must be whole, so multiply both by 2. The equation is 2Al + 3Cl2 → 2AlCl3.

To get the simplest whole-number ratio

HintAmounts such as 0.2 and 0.6 are in the right proportion, but an equation is never written with them.

The whyDividing by the smallest amount turns it into 1 and scales the others to match, which usually gives whole numbers straight away. If a half appears, doubling everything clears it.

44

HintRearrange moles = mass ÷ Mr so that Mr is the subject.

The whyMultiplying both sides of moles = mass ÷ Mr by Mr and then dividing by moles gives Mr = mass ÷ moles = 22 ÷ 0.5. The specification expects you to be able to change the subject of an equation like this.

The limiting reactant

HintIts name comes from the fact that it sets a ceiling on what can be made.

The whyOnce this reactant has run out, the reaction stops, however much of the other reactant is left. The amount of product therefore depends on how much of it there was at the start.

excess

HintIt means more than is needed.

The whyIf there is more than enough of one reactant, the other one is certain to react completely. The one that is used up is then the limiting reactant, and some of the other is left over at the end.

Magnesium: it needs only 0.2 mol of acid, so acid is left over

HintUse the ratio in the equation to see how much of one the other requires.

The why0.1 mol of magnesium reacts with 0.1 × 2 = 0.2 mol of acid. There is 0.3 mol of acid, more than enough, so the magnesium runs out first and 0.1 mol of acid is left unreacted.

It stays the same

HintAsk which substance runs out first, and whether that has changed.

The whyThe amount of product is set by the limiting reactant. The magnesium still runs out at the same point, so the same amount of hydrogen is made; there is simply more acid left over.

4.4

HintThe acid is plentiful, so only the solid decides the answer: grams to moles, ratio, moles to grams.

The whyCalcium carbonate is the limiting reactant. Its Mr is 40 + 12 + (3 × 16) = 100, so 10 g is 0.1 mol. The equation gives 1 mol of CO2 per mole of CaCO3, so 0.1 mol of CO2 forms, with a mass of 0.1 × 44.

volume

HintIt is the amount of space the solution takes up.

The whyConcentration says how much solute is packed into each unit of solution. More solute in the same space, or the same solute in less space, both give a more concentrated solution.

1000

HintA decimetre is 10 cm, and a cube has three dimensions.

The whyA cube 10 cm along each edge holds 10 × 10 × 10 cubic centimetres. One cubic decimetre is the same volume as one litre.

0.25; 15

HintConvert the volume first, then multiply by how much each whole cubic decimetre holds.

The whyDivide by 1000 to change cm³ into dm³. Then mass of solute = concentration × volume = 60 × 0.25. This is the concentration equation rearranged to make mass the subject.

40

HintChange the volume into cubic decimetres before you divide.

The why500 cm³ is 0.5 dm³, and 20 ÷ 0.5 = 40. Another way to see it: a whole cubic decimetre is twice as much solution, so it would hold twice as much sugar.

40 g/dm³: the same mass is in half the volume

HintThink about what happens to the result of a division when the number you divide by gets smaller.

The whyConcentration = mass ÷ volume. The mass of solute has not changed, but it is now divided by half the volume, so the answer doubles. In the same way, doubling the mass of solute in the same volume doubles the concentration.