What happens to the surface area to volume ratio of a solid when it is broken into smaller pieces?

It increases, because cutting the solid creates new surfaces while the total volume stays the same.

A cube of side 3 cm is cut into twenty-seven cubes of side 1 cm. Calculate the new total surface area and the new surface area to volume ratio.

Each small cube has a surface area of 6 cm², so the total is 162 cm² for the same 27 cm³, giving a ratio of 6:1, three times the original.

A solid is ground until its pieces are one tenth of their original size in every direction. What happens to the surface area to volume ratio?

It becomes ten times greater, because the ratio for a cube is inversely proportional to the length of its side.

OCR GCSE Combined Science Chemistry J250

Chemical Reactions

Topic overview Writing formulae of elements and compounds Balanced equations, and deducing formulae from ions Ionic equations, and state symbols The mole and the Avogadro constant Conservation of mass, and changes of mass in open systems Stoichiometry, and calculating reacting masses Exothermic and endothermic reactions, and reaction profiles Activation energy, and bond energy calculations Oxidation and reduction, by oxygen and by electrons Acids, alkalis and neutralisation The ionic equation for neutralisation, and reactions of acids Dilute and concentrated, weak and strong The pH scale, and hydrogen ion concentration pH as a factor of ten, and measuring pH Products at the electrodes, and molten ionic compounds Electrolysis of aqueous solutions Inert and non-inert electrodes

Elements, Compounds and Mixtures

Topic overview Purity, and melting point data Relative formula mass and empirical formulae Formulations, and separating mixtures Paper and thin layer chromatography Interpreting chromatograms and Rf values Choosing a purification method Metals and non-metals in the Periodic Table Electron arrangement and position in the Periodic Table Ionic, covalent and metallic bonding compared Dot and cross diagrams, and the limits of models Reactions, electron arrangement and Mendeleev's table Carbon's four bonds, and the variety of organic compounds Diamond, graphite, fullerenes and graphene Bond strength, intermolecular forces and predicting state Bulk properties of ionic, molecular and giant structures

Global Challenges

Topic overview Extracting metals by reduction and by electrolysis Biological methods of metal extraction Life cycle assessment Recycling, and the decisions behind it Fractional distillation of crude oil The fractions, and crude oil as a feedstock Dependence on hydrocarbons, and cracking The Earth's early atmosphere, and how oxygen developed The greenhouse effect, and evidence for climate change Effects of carbon dioxide and methane, and air pollutants Producing potable water

Monitoring and Controlling Chemical Reactions

Topic overview Mass of solute, concentration and dilution calculations Measuring the rate of a reaction, and rate graphs Factors affecting rate, and collision theory Surface area and rate Catalysts and how they work Reversible reactions and dynamic equilibrium Changing the conditions of an equilibrium Activation energy, and enzymes as catalysts

Particles

Topic overview The particle model and changes of state Limitations of the particle model How the atomic model changed, and the structure of the atom The size of atoms, and the subatomic particles Calculating protons, neutrons and electrons

Predicting and Identifying Reactions

Topic overview Groups 1, 7 and 0, and why they behave as they do Predicting reactivity from the Periodic Table Reactivity of metals with water and acids Tests for oxygen, hydrogen, carbon dioxide and chlorine

Monitoring and Controlling Chemical Reactions

Surface area and rate

3 things to know
Paper 10 (Chemistry)

Overview

How breaking a solid up raises its surface area to volume ratio, why powders react faster, the cube calculations, the flour dust hazard, and comparing the graphs for powder and lumps.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Explain why a powdered solid reacts faster than the same mass of the solid in one large lump.

Key term

Which particles of a solid reactant are able to take part in a reaction with a solution?

Numbers

A cube of solid has sides of 3 cm. Calculate its surface area, its volume and its surface area to volume ratio.

Questions from this subtopic

Each one with the model answer underneath.

1
What happens to the surface area to volume ratio of a solid when it is broken into smaller pieces?
Model answer
It increases, because cutting the solid creates new surfaces while the total volume stays the same.
2
Explain why a powdered solid reacts faster than the same mass of the solid in one large lump.
Model answer
The powder has a much larger surface area to volume ratio, so many more of its particles are exposed and collisions with the other reactant are more frequent.
3
Which particles of a solid reactant are able to take part in a reaction with a solution?
Model answer
Only the particles on the surface, because the ones inside cannot be reached by the solution.
4
A cube of solid has sides of 3 cm. Calculate its surface area, its volume and its surface area to volume ratio.
Model answer
The surface area is 6 × 3 × 3 = 54 cm², the volume is 27 cm³, and the ratio is 54:27, which is 2:1.
5
A cube of side 3 cm is cut into twenty-seven cubes of side 1 cm. Calculate the new total surface area and the new surface area to volume ratio.
Model answer
Each small cube has a surface area of 6 cm², so the total is 162 cm² for the same 27 cm³, giving a ratio of 6:1, three times the original.
6
A solid is ground until its pieces are one tenth of their original size in every direction. What happens to the surface area to volume ratio?
Model answer
It becomes ten times greater, because the ratio for a cube is inversely proportional to the length of its side.

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Chemical Reactions

Elements, Compounds and Mixtures

Global Challenges

Monitoring and Controlling Chemical Reactions

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