For the same mass, powder has a larger surface area than lumps, so it reacts faster, but it does not make more product. A question that says “without changing the amount” is testing exactly that split.
This lesson belongs to rates of reaction. It uses the collision reasoning from concentration effects and the graph reading from reading a rate from a graph.
Why does surface area matter?
In a reaction between a solid and a liquid or solution, collisions can only happen at the surface of the solid. Particles buried inside a lump cannot meet the other reactant until the outer layer reacts away.
Crushing the solid exposes more of its particles. More exposed particles means more frequent collisions, so more successful collisions per second.
How big is the change in surface area?
Take a cube with sides of 2 cm. Its surface area is 6 × (2 × 2) = 24 cm², and its volume is 8 cm³.
Cut it into eight cubes of side 1 cm. The volume in total is still 8 cm³. Each small cube has surface area 6 × (1 × 1) = 6 cm², so the eight cubes give 8 × 6 = 48 cm².
The material is the same but the exposed surface has doubled. Real powder is split into far smaller pieces, so the increase is far greater.
Worked example
This is invented data. Two experiments each use 1.0 g of calcium carbonate with an excess of dilute hydrochloric acid. One uses lumps and the other powder. The equation is:
CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂
Step 1, find moles of CaCO₃. Mr = 40 + 12 + (3 × 16) = 100. Moles = 1.0 ÷ 100 = 0.010 mol.
Step 2, use the ratio. CaCO₃ : CO₂ is 1 : 1, so 0.010 mol of CO₂ forms.
Step 3, convert to volume. At room temperature and pressure 1 mol of gas occupies 24 dm³ (use the value your question gives). Volume = 0.010 × 24 = 0.24 dm³ = 240 cm³.
Step 4, compare. Both experiments end at 240 cm³, because the acid is in excess and the mass of CaCO₃ is the same. The powder curve rises more steeply and flattens earlier.
Step 5, explain. Powder has a larger surface area, so more particles are exposed to the acid, collisions are more frequent and the initial rate is higher.
What mistake should you watch for?
Mistaken answer: “The powder gives more carbon dioxide because there is more surface.”
Surface area changes the rate only. The amount of gas is fixed by the moles of the limiting reactant, here 0.010 mol of CaCO₃. On a graph the two lines must finish at the same height.
A second slip is to say the powder particles have more energy. Their energy has not changed, but more of them are exposed.
Check yourself
1. A 3 cm cube is cut into twenty-seven 1 cm cubes. By what factor does the total surface area increase?
Show answer
Before: 6 × 9 = 54 cm². After: 27 × 6 = 162 cm². 162 ÷ 54 = 3.
2. On a volume-time graph, how should the final volumes for powder and lumps of equal mass compare, and why?
Show answer
They should be equal, because the same mass of limiting reactant contains the same number of moles, so the same amount of product forms.
3. 2.0 g of CaCO₃ reacts with excess acid. What volume of CO₂ forms at room temperature and pressure, using 24 dm³ per mole?
Show answer
Moles = 2.0 ÷ 100 = 0.020 mol. CO₂ = 0.020 × 24 = 0.48 dm³ = 480 cm³.
Where does this lead next?
Next, look at a substance that changes the rate without being a reactant in a catalyst’s role. The mole and equation-ratio tutor is a good way to re-check the final volume in a question like this.
When a student knows the facts but mixes up rate and amount under exam pressure, a teacher can help in online one-to-one Chemistry tuition.