A Kitchen Scale Can Be Perfectly Consistent and Still Wrong

Before you can balance an equation or count moles, you need to know what kind of substance you have and how reliably you have measured it. A wrong unit or a careless extra digit can spoil an otherwise perfect calculation.

Chemistry itself is everywhere — in the food we cook, the medicines we take and the fuel in our vehicles.

This part covers the role of chemistry and the classification of matter, SI units and unit conversion, and significant figures with accuracy and precision.

Chemistry studies the composition, properties and changes of matter, and matter is classified by physical state as solid, liquid or gas, and by composition as elements, compounds or mixtures.

Chemistry at work: fertilisers for crops, medicines, clean drinking water, fuels, soaps, cement and plastics all come from chemical processes. Traditional Indian knowledge applied chemistry too — in natural dyes such as indigo, metal extraction and working, glass and pigments, and herbal medicines.

By physical state:

- Solid — particles tightly packed, fixed shape and volume
- Liquid — particles close but free to move, fixed volume but no fixed shape
- Gas — particles far apart, no fixed shape or volume

By composition:

- Element — one kind of atom: copper, oxygen
- Compound — elements joined in a fixed ratio: water, common salt
- Homogeneous mixture — uniform throughout: sugar syrup, air, brass
- Heterogeneous mixture — visibly uneven: sand in water, dal and rice

Worked example — fixed ratio. Water always contains hydrogen and oxygen in a mass ratio of $1:8$, so $9$ g of water holds $1$ g of hydrogen and $8$ g of oxygen.

An everyday example. Sugar syrup for jalebis is a homogeneous mixture: you cannot see sugar and water separately, yet the sweetness depends on how much sugar you add.

The substance. A compound has a fixed composition and new properties; a mixture has a variable composition, and its parts keep their own properties.

Scientific measurements use the seven SI base units, including the kilogram, metre, second, kelvin and mole, and conversions are done by multiplying by unit factors — fractions equal to one — so that unwanted units cancel.

Common prefixes: milli ($10^{-3}$), centi ($10^{-2}$), kilo ($10^3$), micro ($10^{-6}$), nano ($10^{-9}$).

Worked example 1 — volume.

$$2\text{ L}\times \frac{1{\text{ m}}^3}{1000\text{ L}}=2\times 10^{-3}{\text{ m}}^3$$

Worked example 2 — density.

$$1.2\text{ g/mL}\times \frac{1\text{ kg}}{1000\text{ g}}\times \frac{10^6\text{ mL}}{1{\text{ m}}^3}=1200{\text{ kg/m}}^3$$

Worked example 3 — mass. A $500$ mg paracetamol tablet:

$$500\text{ mg}\times \frac{1\text{ g}}{1000\text{ mg}}\times \frac{1\text{ kg}}{1000\text{ g}}=5\times 10^{-4}\text{ kg}$$

Worked example 4 — time.

$$3\text{ days}\times \frac{24\text{ h}}{1\text{ day}}\times \frac{3600\text{ s}}{1\text{ h}}=259200\text{ s}$$

An everyday example. A petrol pump sells fuel in litres, but a refinery may track the same fuel in cubic metres or kilograms — the factor-label method moves between them.

The substance. Each unit factor equals one, so multiplying by it changes the units but never the actual quantity.

**Very large or small numbers are written in scientific notation, $N\times 10^n$; sums and differences keep the fewest decimal places, products and quotients keep the fewest significant figures; precision is how closely repeated readings agree, while accuracy is how close they are to the true value.

Scientific notation.** $0.000045=4.5\times 10^{-5}$ and $232.508=2.32508\times 10^2$.

Worked example 1 — addition.

$$12.11+18.0+1.012=31.122\to 31.1$$

Worked example 2 — multiplication.

$$(5.6\times 10^5)\times (6.9\times 10^8)=38.64\times 10^{13}=3.864\times 10^{14}\to 3.9\times 10^{14}$$

Worked example 3 — division.

$$\frac{2.7\times 10^{-3}}{5.5\times 10^4}\approx 0.491\times 10^{-7}\to 4.9\times 10^{-8}$$

Worked example 4 — accuracy versus precision. The true mass is $2.00$ g.

- Student A: $1.95$, $1.93$ g — close to each other, far from $2.00$: precise, not accurate
- Student B: $1.94$, $2.05$ g — average near $2.00$ but spread out: accurate on average, not precise
- Student C: $2.01$, $1.99$ g — close together and near $2.00$: accurate and precise

An everyday example. **A kitchen scale that always reads $20$ g too high gives the same reading every time — precise, but not accurate.

The substance. Carry extra digits through the working and round only the final answer**, or rounding errors pile up.