Class 8 Science Chapter 9: Solutes, Solvents and Solutions

Every Sip Tastes the Same

Anya had been given an oral rehydration drink when she was ill - sugar and salt stirred into water. What she noticed later was odd: every mouthful tasted exactly like the one before. Not sweet in one sip and salty in the next, which is what a glass with sugar at the bottom and salt at the top would give.

Evenly Spread, All Through

So the sugar and the salt had not settled anywhere. They had spread themselves out through the whole glass, in the same proportions everywhere. A mixture like that, with its parts evenly distributed throughout, is a uniform mixture.

Now Try Chalk Powder

Stir a spoon of chalk powder into water instead and watch. It clouds the water, then drifts down and gathers at the bottom. Sand does it faster and sawdust floats on top. In none of these is the mixture the same throughout: they are non-uniform mixtures.

You Can See the Parts

That is the practical difference. In a non-uniform mixture the parts can be told apart, by the naked eye or through a magnifying glass. In a uniform mixture they cannot: however closely the rehydration drink is examined, there is no grain of salt to be found in it.

A Uniform Mixture Has a Name

A uniform mixture is called a solution. So salt stirred into water until it disappears is a solution, and chalk powder in water is not. The word is narrower than "mixture", and that is the point of having it.

The Two Parts of a Solution

Mix a solid into a liquid and you get a solution. The liquid in it is the solvent, and the solid is the solute. The solute dissolves into the solvent. Salt and sugar were the solutes in Anya’s drink and water was the solvent.

Keeping the Two Names Apart

The solute is the part that goes in and disappears; the solvent is the part that does the dissolving. Solute and solid both begin with the same letter in that pairing, which is a crude aid but it works.

When Both Parts Are Liquids

Mix two liquids and the solid-and-liquid rule has nothing to grip. Here the substance present in the smaller amount is called the solute, and the one present in the larger amount is the solvent. It is a rule about quantity, not about what the substance is.

The Awkward Case of Sugar Syrup

The syrup a gulab jamun sits in is a great deal of sugar in rather little water. By the quantity rule you might call the sugar the solvent. You would be wrong: the sugar is a solid and the water is the liquid, so water is the solvent and sugar the solute. The quantity rule is only for two liquids.

Why Water Keeps Turning Up

Water dissolves a remarkable range of things, which is why it is the solvent in a rehydration drink, in syrup, in tea and in the sea. It is not the only solvent - oil, ghee and milk have all been used as solvents in Indian systems of medicine - but it is the one met most often.

Air Is a Solution Too

A solution need not have a liquid in it at all. Air is a mixture of gases, and those gases are evenly spread through it, so air is a uniform mixture as well. The idea is wider than a glass of salty water.

What Makes a Mixture, Not a Compound

In a solution the parts keep their own properties. The salt in the water is still salt, which is why the drink tastes salty; the water is still water. Nothing new has been made. That is what separates a mixture from a compound.

Reading a Label for the Solvent

Given a bottle and asked which part is the solvent, ask two questions in order. Is one part a liquid and the other a solid? Then the liquid is the solvent. Are both liquids? Then whichever there is more of is the solvent.

Where This Is Going

The next question is the obvious one: if salt dissolves in water, does it dissolve without limit? Keep spooning salt in and something must happen. That is the next topic, and the answer is what the words saturated and unsaturated are for.

What to Carry Forward

A uniform mixture, with its parts evenly spread throughout, is a solution. Mix a solid into a liquid and the solid is the solute, the liquid the solvent. Mix two liquids and the smaller amount is the solute. A non-uniform mixture, like chalk powder in water, is not a solution, and its parts can be seen. Air is a uniform mixture of gases.

Scenario:

A teacher sets out three glasses of water and gives three pupils a spoon of a different white powder each: common salt, powdered chalk and powdered sugar, though nobody is told which is which. Each pupil stirs their powder in and all three glasses look alike at first, cloudy and pale. The pupils are asked to write down which of the three mixtures are solutions. The first writes that all three are, since all three went cloudy. The second tastes her glass, finds it sweet, and concludes that only a mixture you can taste is a solution. The third says she cannot decide yet and asks to come back to the glasses after the lunch break.

Analysis:

The third pupil is the one working scientifically, and the break is exactly what the question needs. Cloudiness in the first few seconds is just stirring, so a judgement made then is a judgement about the stirring. After the break two of the glasses are clear and one has a white layer at the bottom: the chalk has settled and the salt and the sugar have not. So two of the three are solutions and the chalk mixture is a non-uniform mixture. The first pupil was wrong because she judged too early. The second was wrong for a different reason: taste shows that a solute has kept its properties, which is worth knowing. But the salt glass would also have tasted of something and a tasteless substance can dissolve perfectly well. Tasting is also not a thing to do with an unknown powder.

Activity:

Try it with three powders from your own kitchen - salt, sugar and flour - and write down what each glass looks like at once, after ten minutes and after an hour.

Title:

Try it at home: sort four powders into solutions and mixtures

Safety:

Do not taste any of the tumblers, and use clean drinking water rather than water from a tank or a drain.

What You Notice:

After an hour the salt and the sugar tumblers are clear. So each holds a solution in which the powder is the solute and the water is the solvent. The flour and the sand have settled at the bottom, so those two are non-uniform mixtures and their parts can still be seen. Judging at once rather than after an hour would have made all four look alike.

Water is not the only solvent used in India. Indian systems of medicine have long prepared formulations in oils, in ghee and in milk as well as in water.

A solution need not contain any liquid at all. Air is a mixture of gases spread evenly through one another, which makes it a uniform mixture.

The parts of a solution keep their own properties. The salt in a rehydration drink is still salt, which is exactly why you can taste it.

The solute is the one that vanishes — Whatever goes in and disappears from view is the solute. The liquid it disappears into is the solvent, and the two together make the solution.

Solid first, then quantity — Ask the questions in order. Is one part a solid and the other a liquid? Then the liquid is the solvent. Are both liquids? Only then does the smaller amount become the solute.

One Spoon at a Time

Half fill a clean glass tumbler with water and stir in one level spoon of salt. It goes. Add a second and stir, and that goes too. Keep going, one spoon at a time, stirring properly after each, and count. The question the counting answers is whether this can go on for ever.

It Cannot

At some point a spoonful stirs and stirs and does not disappear. A layer of white grains settles on the bottom of the tumbler and stays there however long you work at it. The water has stopped taking salt.

Two Names for the Two Stages

Up to that point the solution could still have taken more salt at that temperature, and a solution like that is called an unsaturated solution. Once the solute stops dissolving and begins settling on the bottom, the solution is a saturated solution at that temperature.

Why "At That Temperature" Keeps Being Said

Because it matters, and the next topic is about why. For now treat the phrase as part of the definition rather than as padding: a solution is saturated at a stated temperature, not saturated full stop.

A Different Question: How Much Is In There?

Saturated and unsaturated answer whether more can go in. A separate question is how much is already in, and that has its own word. Concentration is how much solute a fixed quantity of solution, or of solvent, is holding.

Dilute and Concentrated

A solution with little solute in a fixed quantity is called dilute; one with a lot is called concentrated. The pair of words is useful and slightly slippery, because both are relative. There is no spoon count at which dilute becomes concentrated.

Relative to What?

To the other solution you are comparing it with. One spoon of salt in a glass is dilute compared with two spoons in the same glass, and that same two-spoon solution is dilute compared with four. The words describe a comparison, not a fixed amount.

A Comparison That Needs Care

Which is more concentrated: two spoons of salt in a hundred millilitres of water, or four spoons in fifty millilitres? Count both parts. The second has twice the salt in half the water, so it is four times as concentrated. Looking only at the spoons would have said twice.

The Third Word: Solubility

Now the quantity that the saturation experiment actually measured. Solubility is the greatest quantity of a solute that a fixed amount of solvent will take. Count the spoons that went in before the settling started and you have measured it, roughly, for salt in water at room temperature.

Three Words, Three Jobs

Keep them apart. Saturated is a state - can any more go in or not. Concentration is an amount - how much is in there now. Solubility is a limit - the most that will ever go in, in that quantity of solvent at that temperature.

A Saturated Solution Need Not Be Concentrated

This sounds wrong and is worth sitting with. Some substances dissolve very poorly, so their saturated solution holds very little solute and is a dilute solution. Saturated means "no more will go in", not "a lot has gone in".

What the Settled Layer Tells You

The grains on the bottom are the sign that the limit has been passed. They are not part of the solution: a solution is a uniform mixture, and undissolved salt sitting on the bottom is very obviously not evenly spread. The solution above it is saturated and the extra salt is simply extra.

Measuring the Limit Honestly

To compare the solubility of two substances the conditions have to match: the same quantity of solvent, the same temperature, level spoons rather than heaped ones, and stirring until you are sure nothing more will go. Change any of those and you are measuring something else.

Back to the Tumbler

So the experiment that looked like a game of counting spoons was three ideas at once. It built unsaturated solutions, reached a saturated one, and the count where it stopped was the solubility of salt in that much water at that temperature.

What to Carry Forward

A solution that can still take more solute at that temperature is unsaturated; one in which the solute has ceased to dissolve and has begun to settle is saturated at that temperature. Concentration is the amount of solute in a fixed quantity, and dilute and concentrated are relative words. Solubility is the greatest quantity of a solute that a fixed amount of solvent will take.

Scenario:

Two pupils prepare sugar solutions for a science fair stall and label them. The first dissolves three level spoons of sugar in a tumbler of water and writes "concentrated". The second dissolves half a spoon of a different powder in an identical tumbler, finds that a second half-spoon will not go in at all however hard she stirs, and writes "saturated". A visitor reads both labels and says the first tumbler must be the saturated one. This is because it obviously holds more. One of the pupils then adds a fourth spoon of sugar to the first tumbler and it dissolves without trouble, which the visitor takes as proof that the label was simply wrong.

Analysis:

Both labels were right and the visitor is wrong twice over. The first tumbler is concentrated, because three spoons in a tumbler is a good deal of sugar. And it is also unsaturated, which is exactly what the fourth spoon dissolving proves. The second tumbler is saturated, because no more of that powder will dissolve at that temperature, and it is at the same time dilute, because only half a spoon went in. So the two labels are not answers to the same question. Concentrated reports how much is present, while saturated reports whether the limit has been reached. The visitor assumed they were the same question and read "holds more" as "nearer the limit", when the limit for sugar is far higher than the limit for the other powder.

Activity:

Find out at home how many level spoons of salt and how many of sugar a cup of water will take before grains stay on the bottom, and say which has the higher solubility.

Title:

Try it at home: measure the solubility of salt and of sugar

Safety:

Use clean drinking water and do not taste either tumbler. Use a kitchen spoon rather than anything from a laboratory.

What You Notice:

Both tumblers pass from unsaturated to saturated. And the count at which each stopped is the solubility of that solute in that much water at room temperature. Sugar usually gives much the larger count, so sugar has the higher solubility in water. If your two counts came out close, check that both spoons were level rather than heaped and that both tumblers held the same measured water.

Comparing the solubility of two substances means matching the conditions: the same quantity of solvent, the same temperature and level spoons rather than heaped ones.

A saturated solution can be a very weak one. If a substance dissolves poorly, the most that will go in is still hardly anything.

The grains on the bottom of the tumbler are not part of the solution at all, because a solution is a uniform mixture and a settled layer is plainly not evenly spread.

State, amount, limit — Three words and three jobs. Saturated is a STATE - can more go in? Concentration is an AMOUNT - how much is in now? Solubility is a LIMIT - the most that will ever go in.

Dilute is always dilute compared with something — There is no spoon count at which dilute becomes concentrated. Both words describe a comparison between two solutions, so ask "dilute compared with what?" every time.

The Phrase That Was Doing Work

Every definition in the last topic carried the words "at that temperature". A solution is saturated at that temperature; a solubility is measured at that temperature. This topic is what those words were protecting.

Warming a Saturated Solution

Take about fifty millilitres of water in a beaker, measure its temperature - say it reads twenty degrees Celsius - and stir in baking soda, spoonful by spoonful, until some will not dissolve and sits on the bottom. The solution is now saturated at twenty degrees. Then put the beaker over a flame and warm it, stirring, towards fifty degrees.

The Undissolved Powder Goes

The layer on the bottom disappears. Nothing was added, nothing was taken away, and the powder that had refused to dissolve at twenty degrees dissolves at fifty. So the limit itself has moved.

Keep Going and It Happens Again

Add more baking soda at fifty degrees until a layer settles again, then warm the beaker on towards seventy degrees. The new layer dissolves too. Water at seventy degrees takes more baking soda than water at fifty, which takes more than water at twenty.

The Rule, and Its Hedge

For most substances, the solubility in water increases as the temperature increases. "Most" is doing real work there: a handful of solids behave the other way, so the honest statement is about most of them rather than all.

Saying It the Other Way Round

Here is a neater way to put the same fact. A solution at its limit for one temperature acts like an unsaturated one once it is warmed, because the limit has gone up and there is now room for more.

Be Careful With the Heating

This is a demonstration rather than an activity to do alone, and the reason is the heating device. A beaker of water over a flame needs an adult beside it, and a thermometer belongs in the water rather than resting on the glass.

Now Ask About Gases

Solids are not the only solutes. Many gases dissolve in water, oxygen among them, though oxygen dissolves only to a small extent - there is very little of it in a glass of water compared with the water itself.

Why That Little Matters Enormously

That small dissolved quantity is what every fish, every water plant and every other water-living organism breathes. Aquatic life is supported by the oxygen dissolved in the water, not by the oxygen in the air above it.

Gases Dissolve Evenly Too

The gases dissolved in water are spread evenly through it, so the mixture is a uniform one. Dissolved gas in water is as much a solution as dissolved salt is, which is why the word is not restricted to solids.

The Surprise: Gases Go the Other Way

Ask whether warming the water helps a gas dissolve, as it helped the baking soda, and the answer is no. The solubility of gases in a liquid generally DECREASES as the temperature rises. Solids and gases disagree.

Cold Water Holds More Oxygen

So cold water carries more dissolved oxygen than warm water does, which is exactly what aquatic life needs from a cold stream or a deep lake. Warm the water and some of the dissolved oxygen leaves it.

Why This Is Worth Knowing Outside the Classroom

Water warmed by human activity holds less oxygen than it did, and fish in it have less to breathe. One fact about solubility turns into a reason to care what is poured into a river. It also explains why a pond left in full sun is harder on its fish than the same pond in shade, and why a fountain or a jet of spray helps them: water thrown into the air takes up oxygen from it again on the way back down.

Solvents Beyond Water, and One Scientist

Water has been the main solvent in Ayurveda, Siddha and other Indian systems of medicine, which also prepare formulations in oils, in ghee and in milk. Asima Chatterjee used solvents and solutions to pull apart medicinal plants and isolate the compounds in them, work that led to drugs against epilepsy and malaria. She was the second Indian woman to earn a Doctorate of Science, the first woman given the Shanti Swarup Bhatnagar Award for work in chemistry, and was honoured with the Padma Bhushan.

What to Carry Forward

For most solids the solubility in water rises with temperature, so a solution saturated at one temperature behaves as unsaturated when warmed. Many gases dissolve in water, oxygen only slightly, and that dissolved oxygen is what aquatic life breathes. The solubility of gases generally falls as temperature rises, so cold water holds more oxygen than warm water.

Scenario:

A school keeps a small ornamental pond with a dozen fish in it. One summer the pond is moved, as part of some building work, from a shaded corner into the middle of an open courtyard. And a pump is added that sprays a thin jet into the air. Within a fortnight several fish are dead. The gardener says the water must have gone bad and empties and refills the pond. A pupil points out that the water is noticeably warmer than it used to be in the shade and asks whether that could matter. Another says warmth should help, since everything dissolves better in warm water and the fish need dissolved oxygen.

Analysis:

The second pupil has the right idea and the wrong rule. It is true that the fish need oxygen dissolved in the water, and true that most SOLIDS dissolve better when water is warmed. But oxygen is a gas, and the solubility of gases in a liquid generally falls as the temperature rises. So the move into full sun warmed the water and the warmed water holds less dissolved oxygen than the shaded water did, leaving the fish with less to breathe. Emptying and refilling the pond does not address that, because the new water will warm up in the same sun. The jet of spray is the one thing working in the fish’s favour, since water thrown into the air takes up oxygen from it. The real repair is shade.

Activity:

Find out whether any pond, tank or aquarium near you has a pump or a fountain, and write down what you think it is for.

Title:

Try it at home: watch the bubbles leave warming water

Safety:

Do not do the heating step yourself and do not lean over the pan. Stop watching well before the water boils.

What You Notice:

Small bubbles gather on the walls of the glass as the water warms. And more of them appear in the pan as it is heated. They are gases that were dissolved in the cold water coming out of it, because the solubility of a gas falls as the temperature rises. The cold tap water held more dissolved gas than the warm water can.

Nothing is added when the undissolved powder vanishes on warming. The same water and the same baking soda are in the beaker; only the limit has moved.

Fishes do not breathe the air above a pond. They breathe the oxygen dissolved in the water itself, which is a very small quantity indeed.

Asima Chatterjee used solvents and solutions to isolate compounds from medicinal plants, work that led to drugs against epilepsy and malaria.

Solids up, gases down — Warm the water and most solids dissolve better while gases dissolve worse. Two rules pointing opposite ways, and the whole topic is remembering which way each goes.

A cold stream is a well-aired stream — Cold water holds more dissolved oxygen than warm water, which is why a cold mountain stream supports fish so well and why warming a river is bad news for them.

Washing the Rice

Rinse a bowl of rice and watch what the water does to it. The grains sink and settle, while bits of husk lift away and ride on the surface. Pour a little oil into water and the oil gathers on top. Drop a stone in and it goes straight down. Some things float and some sink, and the question is what decides which.

The Everyday Answer

The usual reply is that light things float and heavy things sink - lighter than the liquid floats, heavier than the liquid sinks. It is nearly right and it is not quite enough, and the gap is worth pinning down before going on.

A Stick and a Rod

Take an iron rod and a wooden stick of the same size and hold one in each hand. The iron is obviously the heavier, although there is just as much space taken up by each. So "heavier" here cannot mean simply a bigger number on a balance; it means heavier for the same amount of room.

That Property Has a Name

It is called density. Iron is denser than wood, and when we say iron is heavier than wood that is what we mean. Density is the property that compares heaviness fairly, by holding the amount of space fixed.

A Crowded Bus, a Dense Forest

The word is used the same way outside science. A bus packed with people is crowded - high density - and the same bus with a few passengers is low density. A forest whose trees grow close together is called dense, and one with the trees far apart is less dense.

The Definition

Matter is anything that has mass and occupies room, which is volume. Density is the mass packed into one unit of volume of a substance, which is written as a formula: density equals mass divided by volume.

What Density Does Not Depend On

Shape and size. Flatten a lump of clay into a sheet and both its mass and its volume stay what they were, so its density is unchanged. Cut a block of iron in half and each half has the same density as the whole did.

What It Does Depend On

Temperature and pressure. Pressure matters a great deal for gases and hardly at all for solids and liquids, and temperature matters for everything. Those two effects are the subject of the next topic.

The Units Come From the Formula

Since density is a mass divided by a volume, its unit is a mass unit divided by a volume unit. The SI unit of density is the kilogram per cubic metre, since mass is measured in kilograms and volume in cubic metres. For liquids, gram per millilitre and gram per cubic centimetre are often more convenient.

A Number Worth Remembering

The mass of one millilitre of water is close to one gram at room temperature. So ten millilitres of water is about ten grams and a hundred millilitres about a hundred grams, and the density of water comes out at about one gram per cubic centimetre.

Working One Out

An aluminium block has a mass of twenty-seven grams and a volume of ten cubic centimetres. Divide: twenty-seven divided by ten is two point seven, so its density comes out at 2.7 g/cm3. Notice that the unit falls out of the division being chosen.

Comparing With Water

Since water is about 1 g/cm3, aluminium is about 2.7 times as dense as water. That comparison has its own name: aluminium has a relative density of 2.7 as against water. It is a density divided by a density, so it carries no units at all.

Reading a Label

A packet of oil marked one litre and 910 grams is telling you its density. One litre is a thousand cubic centimetres and the mass is 910 grams, so the density is 0.91 g/cm3, which is less than water. That is why oil floats on water.

Why Density Is Not the Whole Story

A ship is made of steel, which is far denser than water, and it floats. So density on its own does not settle whether an object floats or sinks; the way the object is shaped and what it encloses matter too. Density explains part of it, and the book says so plainly.

What to Carry Forward

Density is the mass packed into one unit of volume: mass divided by volume. It does not depend on the shape or size of an object but it does depend on temperature and pressure. The SI unit is kg/m3, and g/cm3 is handy for liquids. Water is about 1 g/cm3. Relative density compares a density with that of water and has no units. Density explains part of floating and sinking, not all of it.

Scenario:

A recycling yard is given three metal bars and has to sort them by material. The bars are of different sizes. The first is long and thick and weighs 2,400 grams. The second is short and thin and weighs 270 grams; the third is middling and weighs 810 grams. A worker lines them up and says the first bar is clearly made of the densest metal, since it is by far the heaviest. His colleague measures the volume of each by lowering it into a tank of water: the first displaces 300 cubic centimetres, the second 100, and the third 300. She then says two of the three bars are the same metal and the heaviest bar is not the densest.

Analysis:

She is right on both counts and the arithmetic shows why. Dividing mass by volume, the first bar is 2,400 divided by 300 which is 8 grams per cubic centimetre. The second is 270 divided by 100, which is 2.7. And the third is 810 divided by 300, which is also 2.7. So the second and third bars have the same density although one weighs three times what the other does, which is exactly what you would expect of two pieces of the same metal in different sizes. And the heaviest bar being the densest was a coincidence of this particular line-up, not a rule. The worker was comparing masses without holding the volume fixed. And density is the mass in a UNIT volume. Taking water at about 1 gram per cubic centimetre, all three bars are denser than water and all three would sink.

Activity:

Weigh three objects at home on a kitchen scale, work out the volume of each, and put them in order of density rather than of weight.

Title:

Try it at home: put four objects in order of density

Safety:

Lower each object in on the thread rather than dropping it, so that no water splashes out and the jug is not cracked.

What You Notice:

Your four densities should all come out above 1 g/cm3, which is why all four objects sank. The order of density will probably not be the same as the order of mass. A light coin of a dense metal can beat a heavier stone. That difference is the whole point of the quantity - it compares the objects at a fixed volume rather than by what the hand reports.

Relative density has no units at all, because it is one density divided by another and the units cancel out.

A packet of oil marked one litre and 910 grams is quietly telling you its density: 0.91 grams per cubic centimetre, which is less than water.

Flattening a lump of modelling clay into a sheet changes neither its mass nor its volume, so its density is exactly what it was.

Same room, different weight — Density answers the question "how heavy for the same amount of room?". Whenever heaviness is being compared, check that the volumes are equal or the comparison means nothing.

The unit falls out of the formula — Density is a mass over a volume, so its unit is a mass unit over a volume unit - kg/m3, or g/cm3. You never have to remember the unit separately; it comes out of the division.

Two Measurements, One Answer

Density is a mass divided by a volume, so finding one means making two measurements and doing a division. Neither measurement is difficult, and both have a way of going quietly wrong, so this topic is mostly about doing them properly.

Weighing on a Digital Balance

Switch the balance on and look at the display: it should read zero. If it does not, press the tare or reset button until it does. Then put a dry, clean watch glass or a piece of butter paper on the pan, note what the display says, and press tare again so that the reading returns to zero with the watch glass still sitting there.

Why Tare Twice

Because the balance is now ignoring the watch glass. Place the stone on the glass and the display shows the mass of the stone alone, say 16.400 grams, with nothing to subtract. For a liquid, replace the watch glass by a beaker and pour the liquid into that.

Mass Is Not Weight

Mass is the quantity of matter in an object, measured in grams and kilograms. Weight is the downward pull that the Earth exerts upon an object, and newtons are its unit. Most balances actually respond to weight but have their scales marked in mass units, so they display grams - which is why the two words get muddled.

Measuring the Volume of a Liquid

A measuring cylinder is the usual instrument: a narrow, transparent, upright tube, closed at the bottom and open at the top, with volume markings up its side. They are made in many sizes - 5, 10, 25, 50, 100, 250 millilitres and more.

How Small a Volume Can It Read?

Look at the gap between two big marks, say between 10 and 20 millilitres, and count the small divisions in that gap. If ten divisions cover ten millilitres, each division is one millilitre, and one millilitre is the smallest volume this cylinder can read. Smaller cylinders read finer: a 10 or 25 millilitre one usually reads to 0.1 millilitre, a 100 millilitre one to 1 millilitre, a 250 to 2 millilitres and a 500 to 5. So accuracy and capacity pull against each other, and choosing the cylinder is part of the measurement.

Choosing the Right One

To measure 70 millilitres, a 50 millilitre cylinder would need two fillings, which is inconvenient and adds error. A 250 or 500 millilitre cylinder does it in one go but reads only to 2 or 5 millilitres. The 100 millilitre cylinder does it in one filling and reads to 1 millilitre, so it is the best choice.

The Meniscus

Pour water in and its surface is not flat: it curves, and that curved surface is called the meniscus. For water and other colourless liquids, read the mark that lines up with the LOWER EDGE of that curve, holding your eye level with it. For a coloured liquid, read the upper edge instead.

Volume of a Regular Solid

If the shape is a cuboid, measure its length, width and height with a scale and multiply the three together. A notebook 25 centimetres long, 18 wide and 2 thick has a volume of 25 times 18 times 2, which is 900 cubic centimetres.

Volume of an Awkward Shape

A stone has no formula. Pour water into a measuring cylinder up to a chosen mark, say 50 millilitres, tie the stone with a thread and lower it in gently. The level rises, to 55 millilitres say. The difference, 5 millilitres, is the volume of the stone, and for a solid that is written as 5 cubic centimetres.

Putting the Two Together

Now the division. The stone had a mass of 16.400 grams and a volume of 5 cubic centimetres, so its density is 16.4 divided by 5, which is 3.28 grams per cubic centimetre - denser than water, which is why it sank.

Why Heating Lowers a Density

Warm a substance and its particles move further apart and spread out. The volume grows while the mass stays exactly what it was, and since density is mass divided by volume, a larger volume with the same mass means a smaller density. That is why hot air rises through cooler air, and it is how a hot air balloon works.

Why Pressure Mostly Matters for Gases

Press on a gas and its particles are pushed closer together, so the volume falls and the density rises. A liquid is nearly incompressible, so the effect on it is small, and the particles of a solid are already so close together that the change in its density is negligible.

The Odd Case of Ice

Water is at its densest at 4 degrees Celsius. Cool it further and, as it freezes at 0 degrees, its particles arrange themselves in a way that takes up MORE room - an expansion. The same mass in a larger volume is less dense, so ice floats. That matters for life: the floating ice forms a lid that keeps the water below it warm enough for fish to survive a hard winter.

What to Carry Forward

Tare the balance with the watch glass on it. Choose a measuring cylinder that takes the whole volume in one filling and still reads finely, and take the reading at the lower edge of the meniscus, eye held level. Multiply length by width by height for a cuboid, and use displacement for an awkward shape. Mass is in grams, weight in newtons. Heating raises volume and so lowers density; pressure raises the density of gases most; and ice floats because freezing expands water.

Scenario:

Three pupils measure the density of the same brass weight and compare answers. The first gets 8.4 grams per cubic centimetre, the second 8.5, and the third 4.2 - almost exactly half. The third pupil has her working written out neatly: mass 84 grams, volume 20 cubic centimetres, and 84 divided by 20 is 4.2. Her mass agrees with the others. Asked how she found the volume, she says she filled a 500 millilitre cylinder to the 100 millilitre mark, lowered the weight in, read 120 at the top of the curve. And took the difference. One of the others says she must have written the mass down wrong, since the arithmetic is plainly correct.

Analysis:

The arithmetic is correct and the mass is correct, so the volume is where the error is, and the 500 millilitre cylinder is the culprit. Such a cylinder reads only to the nearest 5 millilitres. And the true volume of the weight is about 10 cubic centimetres - which is two divisions on that scale. So the measurement had almost no room to be right. A 10 or 25 millilitre cylinder, reading to 0.1 millilitre, would have measured a 10 cubic centimetre object well. Reading the top of the meniscus instead of the bottom added a further error in the same direction, making the volume larger still. And dividing by too large a volume is exactly what makes a density come out too small. The lesson is that the suspect in a wrong answer is the measurement with the coarsest scale, not the division.

Activity:

Measure one small object twice, once in the largest container you have with markings and once in the smallest that will hold it, and compare the two densities you calculate.

Title:

Try it at home: find the density of a stone and of cooking oil

Safety:

Keep oil away from any flame and wipe up spills at once, since oil on a floor is slippery. Lower the stone on the thread rather than dropping it.

What You Notice:

The stone should come out well above 1 g/cm3, which is why it sank. And the oil a little below 1 - around 0.9 - which is why oil floats on water. If your oil comes out above 1, check whether you tared the cup out before weighing: an untared cup adds its own mass and pushes the density up.

Accuracy and capacity pull against each other in a measuring cylinder. A 500 millilitre cylinder holds plenty but reads only to the nearest 5 millilitres.

Most balances actually respond to weight rather than to mass, but their scales are marked in grams and kilograms, which is why the two words are so often muddled.

Water is at its densest at 4 degrees Celsius, not at 0. Cooling it below 4 makes it expand again, which is why ice floats.

Tare twice, then weigh once — Zero the empty balance, put the watch glass on, zero it again. Only then place the object, and the number on the display is the answer with no subtraction to do.

Grams for matter, newtons for pull — Mass is how much matter there is and is measured in grams. Weight is how hard the Earth pulls and is measured in newtons. A balance shows grams although it responds to the pull.