The Amazing World of Solutes, Solvents, and Solutions

What Are Solute, Solvent, and Solution?

The Building Blocks: Solute, Solvent, and Solution

Have you ever made lemonade? You mix sugar, lemon juice, and water. When you stir it well, the sugar seems to disappear, and you get a sweet, tangy drink that looks the same throughout. Now, what if you mixed a spoonful of sand in water? No matter how much you stir, the sand eventually settles at the bottom.

These two examples show us the two main types of mixtures. The lemonade is a uniform mixture, where the components are evenly distributed and you can't see them separately. The sand and water create a non-uniform mixture, where the components remain separate and are not evenly distributed.

In chemistry, we have a special name for uniform mixtures like your lemonade or salt dissolved in water.

{{KEY: concept | title=Uniform vs. Non-Uniform Mixtures | text=In a uniform mixture, the components are evenly spread out, and the mixture looks the same throughout (e.g., salt water). In a non-uniform mixture, the components are not evenly distributed and can often be seen separately (e.g., sand in water).}}

What Exactly is a Solution?

A solution is simply the scientific term for a uniform mixture. When you dissolve salt in water, you create a solution. The salt particles spread out so evenly among the water particles that you can no longer see them. The resulting mixture is perfectly clear and has the same saltiness in every drop.

{{VISUAL: diagram: Two beakers side-by-side. The left beaker, labeled 'Uniform Mixture (Solution)', shows salt completely dissolved in water, appearing clear. The right beaker, labeled 'Non-uniform Mixture', shows sand settled at the bottom of the water.}}

The defining feature of a solution is this complete and even mixing at a microscopic level. It appears as a single substance, even though it's made of two or more different components.

The Key Players: Solute and Solvent

Every solution is made of at least two parts. To understand them, let's go back to our salt water example. We mixed a solid (salt) with a liquid (water).

• The substance that gets dissolved is called the solute. In this case, the salt is the solute.
• The substance that does the dissolving is called the solvent. Here, water is the solvent.

This relationship can be written as a simple equation: Solute + Solvent → Solution

{{KEY: points | title=Components of a Solution | text=- The solute is the substance that dissolves. It is usually present in a smaller amount.

• The solvent is the substance that dissolves the solute. It is usually present in a larger amount.
• Together, they form a solution.}}

Imagine the solvent as a crowd of people, and the solute as a few individuals who spread out and mingle perfectly within that crowd.

{{VISUAL: diagram: A magnified, microscopic view showing individual solute particles (like small blue spheres) evenly distributed among the much more numerous solvent molecules (like larger red spheres). The solute and solvent are clearly labeled.}}

What if Both Components are Liquids?

It's easy when we mix a solid and a liquid. But what happens if you mix two liquids, like a little alcohol in a lot of water? In this case, there's a simple rule:

The substance present in the smaller amount is considered the solute, and the one in the larger amount is the solvent.

So, if you mix 10 mL of alcohol with 100 mL of water, alcohol is the solute and water is the solvent.

Beyond Liquids: Gaseous and Solid Solutions

The world of solutions isn't limited to liquids! Air itself is a perfect example of a gaseous solution.

• Air: A solution where Nitrogen (about 78%) acts as the solvent, and other gases like Oxygen (21%), Argon, and Carbon Dioxide are the solutes.

Even solids can form solutions, which are often called alloys. Brass, for example, is a solid solution of zinc (solute) dissolved in copper (solvent).

{{KEY: exam | title=Identifying Solute and Solvent | text=In exams, you might be asked to identify the solute and solvent in different scenarios. Remember the rules:

1. In solid-liquid solutions, the solid is the solute and the liquid is the solvent.
2. In liquid-liquid or gas-gas solutions, the substance in the smaller quantity is the solute.}}

A Sweet Puzzle: The Case of Sugar Syrup

Indian sweets like Gulab Jamun are soaked in a thick sugar syrup called chashni. To make this, a very large amount of sugar (solid) is dissolved in a relatively small amount of water (liquid).

Based on our rule, sugar is present in a larger amount, so shouldn't it be the solvent? This is a fascinating exception! By convention, in solutions involving water, water is almost always considered the solvent, regardless of its quantity. This is because water is such an excellent and common solvent that it's often called the "universal solvent".

How Much Solute Can a Fixed Amount of Solvent Dissolve?

{{FORMULA: expr=Concentration % = (Mass of Solute / Mass of Solution) × 100 | symbols=Mass of Solute:mass of the substance dissolved (g), Mass of Solution:total mass of solute plus solvent (g)}}

How Much Solute Can a Fixed Amount of Solvent Dissolve?

Have you ever tried making a very sweet glass of lemonade and noticed that after a certain point, no matter how much you stir, the sugar just settles at the bottom? This simple kitchen experiment reveals a fundamental property of solutions: a solvent can only dissolve a limited amount of solute.

Let's explore this limit. Imagine you take a glass half-full of water.

1. You add one teaspoon of salt and stir. It disappears completely, dissolving into the water.
2. You add a second, and then a third teaspoon. Each time, with a bit of stirring, the salt dissolves.
3. But as you add the fourth or fifth spoon, you notice something different. Some salt crystals remain at the bottom of the glass, no matter how vigorously you stir.

This observation tells us that the water has reached its "capacity" to dissolve salt at that particular temperature. This leads us to two very important types of solutions.

Unsaturated vs. Saturated Solutions

When you could still dissolve more salt, the solution was unsaturated. Once the salt stopped dissolving and started to settle, the solution became saturated.

{{KEY: type=definition | title=Unsaturated Solution | text=A solution in which more solute can be dissolved at a given temperature.}}

In our example, the solutions after the first, second, and third spoons of salt were all unsaturated because they still had the capacity to dissolve more salt.

{{KEY: type=definition | title=Saturated Solution | text=A solution in which no more solute can be dissolved at a particular temperature, and any extra solute added will settle at the bottom.}}

When the undissolved salt started collecting at the bottom of your glass, you had created a saturated solution. It was "full" of solute.

{{VISUAL: diagram: Two beakers of water. The left beaker is labeled 'Unsaturated Solution' and shows salt crystals completely dissolved. The right beaker is labeled 'Saturated Solution' and shows excess, undissolved salt crystals at the bottom.}}

Concentration: How "Strong" is the Solution?

The terms we used earlier—a "very sweet" glass of lemonade versus a "less sweet" one—relate to the idea of concentration.

The concentration of a solution is a measure of the amount of solute present in a fixed quantity of the solvent or the solution itself.

Based on concentration, we can describe solutions in relative terms:

• Dilute Solution: A solution that has a relatively small amount of solute dissolved in it. The solution with one spoon of salt was dilute.
• Concentrated Solution: A solution that has a relatively large amount of solute dissolved in it. The solution just before it became saturated was concentrated.

It's important to remember that dilute and concentrated are comparative terms. A solution with two spoons of salt is more concentrated than the one with one spoon, but it's more dilute than the one with three spoons!

Higher Order Thinking Skill (HOTS): Which solution is more concentrated: adding 2 spoons of salt to 100 mL of water, or adding 4 spoons of salt to 50 mL of water?

Answer: The second one! If 50 mL of water has 4 spoons of salt, then 100 mL of water would have 8 spoons (4 × 2). This is much more concentrated than the first solution, which only has 2 spoons in 100 mL.

Solubility: The Ultimate Limit

This brings us to a more precise scientific term. The maximum amount of a solute that can be dissolved in a fixed quantity of a solvent at a specific temperature is called its solubility.

For example, the solubility of common salt (sodium chloride) in water at 20°C is about 36 grams per 100 mL. This means that at 20°C, a maximum of 36 g of salt can dissolve in 100 mL of water. If you add 40 g, 36 g will dissolve and 4 g will remain at the bottom.

But what if we change the conditions? What happens if we heat the water?

How Temperature Affects Solubility

Let's go back to our saturated salt solution with undissolved crystals at the bottom. What do you think would happen if we gently heat the beaker?

You would observe that the undissolved salt crystals begin to disappear! As the temperature of the water increases, its ability to dissolve the salt also increases. The solution that was saturated at a lower temperature becomes unsaturated at a higher temperature, allowing you to dissolve even more salt.

{{VISUAL: photo: Laboratory setup showing a beaker of water with undissolved baking soda on a tripod stand being heated by a spirit lamp, with a thermometer inside the beaker.}}

{{KEY: type=points | title=Solubility and Temperature (for Solids) | text=- For most solid solutes like sugar, salt, and baking soda, solubility increases as the temperature of the solvent increases.

• A saturated solution at a certain temperature becomes an unsaturated solution if the temperature is raised.}}

What About Gases?

Solids aren't the only things that dissolve in liquids. Gases do too! The oxygen that fish and other aquatic animals breathe is dissolved in water.

However, the effect of temperature on the solubility of gases is the opposite of its effect on most solids.

{{KEY: type=exam | title=Common Trap: Solubility of Gases | text=Students often assume that heating increases solubility for everything. Remember this key difference: for gases, solubility DECREASES as temperature increases. This is a very common exam question.}}

More gas can dissolve in cold water than in warm water. This is why aquatic life thrives in colder water bodies, which are richer in dissolved oxygen. When water bodies get warmer due to pollution (thermal pollution), the dissolved oxygen level drops, which can be harmful to fish and other organisms.

{{VISUAL: chart: A simple line graph showing two trend lines. One line, labeled 'Solids (e.g., Sugar)', trends upwards, indicating solubility increases with temperature. The second line, labeled 'Gases (e.g., Oxygen)', trends downwards, indicating solubility decreases with temperature.}}

Solved Numericals

A common way to express concentration is as a mass percentage. It tells us the mass of solute present in 100 grams of the solution.

Hero Formula: Concentration (by mass %) = (Mass of Solute / Mass of Solution) × 100 Note: Mass of Solution = Mass of Solute + Mass of Solvent

Example 1: A solution is prepared by dissolving 40 g of sugar in 160 g of water. Calculate the concentration of this solution.

• GIVEN:

  • Mass of solute (sugar) = 40 g
  • Mass of solvent (water) = 160 g

• FORMULA: First, find the total mass of the solution: Mass of Solution = Mass of Solute + Mass of Solvent Then, use the concentration formula: Concentration % = (Mass of Solute / Mass of Solution) × 100

• SUBSTITUTION: Mass of Solution = 40 g + 160 g = 200 g Concentration % = (40 g / 200 g) × 100

• ANSWER: Concentration = 20%

Example 2: You have 250 g of a salt solution with a concentration of 15%. How much salt is dissolved in this solution?

• GIVEN:

  • Mass of solution = 250 g
  • Concentration = 15%

• FORMULA: We can rearrange the concentration formula to find the mass of the solute: Mass of Solute = (Concentration % / 100) × Mass of Solution

• SUBSTITUTION: Mass of Solute = (15 / 100) × 250 g

• ANSWER: Mass of Solute = 37.5 g

Try It Yourself

1. If 10 g of salt is dissolved in 90 g of water, what is the concentration of the solution?
2. How many grams of sugar are needed to make 500 g of a 10% sugar solution?
3. A beaker contains a saturated solution of salt in water at 30°C. What will you observe if the beaker is placed in a refrigerator for an hour?

Answer Key: 1. 10% | 2. 50 g | 3. Some of the dissolved salt will crystallise and settle at the bottom, as the solubility decreases with the decrease in temperature.

How does temperature affect the solubility of a solute?

How Temperature Changes the Game: Solubility

Have you ever noticed how sugar dissolves much faster in hot tea than in iced tea? It's not just your imagination! Temperature plays a crucial role in how much of a solute can dissolve in a solvent. Let's explore this fascinating relationship.

We know that a saturated solution is one that can't dissolve any more solute at a given temperature. But what if we change that temperature?

The Effect of Heat on Solid Solutes

For most solid substances, like sugar, salt, or baking soda, a little heat can make a big difference. Let's walk through an experiment similar to one a chemist would perform in a lab.

An Experiment with Baking Soda:

1. Start Cold: Imagine taking a beaker with 50 mL of water at room temperature (say, 20°C). You start adding baking soda, spoonful by spoonful, stirring after each addition. Eventually, you reach a point where no more baking soda dissolves, and a little bit settles at the bottom. You have now created a saturated solution at 20°C.

2. Add Some Heat: Now, you gently heat the beaker on a tripod stand, raising the temperature to 50°C. As the water warms up, you'll observe something magical – the undissolved baking soda at the bottom starts to disappear! It has dissolved into the water.

{{VISUAL: photo: A lab setup showing a beaker on a tripod stand over a spirit lamp. A thermometer is in the beaker, and a glass rod is being used to stir the solution.}}

3. Pushing the Limit: At 50°C, the solution is now unsaturated because it can hold more solute. You can add more baking soda, and it will dissolve until the solution becomes saturated again at this new, higher temperature.

4. Go Hotter: If you heat the solution further to 70°C, the same thing happens. The solution can dissolve even more baking soda.

This experiment leads to a very important conclusion.

{{KEY: concept | title=Temperature and Solubility of Solids | text=For most solid solutes, solubility increases as the temperature of the solvent increases. This means that a hot solvent can dissolve more solid solute than a cold solvent. A solution that is saturated at a low temperature will become unsaturated if you heat it up.}}

This principle is used everywhere, from making sugary syrups in the food industry to extracting compounds from plants in medicine.

Do Gases Behave the Same Way?

We know that aquatic animals like fish breathe oxygen that is dissolved in water. But does the temperature of the water affect how much oxygen is available for them?

Interestingly, gases behave in the exact opposite way to most solids.

It has been observed that the solubility of gases generally decreases as the temperature increases.

Think about a bottle of soda. When it's cold, it's full of fizz (dissolved carbon dioxide gas). But if you leave it out in the sun, it quickly goes "flat." The heat causes the dissolved gas to escape from the liquid much faster.

{{KEY: points | title=Solubility and Temperature: Solids vs. Gases | text=- Solids in Liquids: Solubility generally INCREASES with increasing temperature. (e.g., more sugar in hot water).

• Gases in Liquids: Solubility generally DECREASES with increasing temperature. (e.g., less oxygen in warm water).}}

This is why aquatic life thrives in colder water bodies. Cold water can hold more dissolved oxygen, providing a rich environment for fish, plants, and other organisms.

{{VISUAL: chart: A simple line graph showing two trend lines. One line, labeled "Salt (Solid)", goes up as temperature increases. The other line, labeled "Oxygen (Gas)", goes down as temperature increases.}}

Why Do Objects Float or Sink? Enter Density

We've talked about what happens when things dissolve. But what about things that don't, like a piece of wood or an iron nail? They either float or sink. You might say the iron nail is "heavier" than the wood, but what does that really mean, scientifically?

Imagine you have two identical boxes. You fill one with feathers and the other with rocks. Both boxes have the same size (volume), but the box of rocks will have much more material (mass) packed into it. The box of rocks is denser.

What is Density?

In science, we define density as the mass of a substance packed into a certain volume. It's a measure of how "compact" or "crowded" the matter is in an object.

{{KEY: definition | title=Density | text=Density is defined as the mass of a substance per unit of its volume. It tells us how tightly the matter is packed within an object.}}

An object's density is a fundamental property, just like its colour or melting point. A small iron key and a large iron gate have the same density because they are made of the same material.

{{FORMULA: expr=Density = Mass / Volume | symbols=Density:(g/cm³ or kg/m³), Mass:(g or kg), Volume:(cm³ or m³)}}

The formula shows that for the same volume, a substance with more mass will have a higher density. This is why an iron rod feels much heavier than a wooden stick of the exact same size. The iron has more mass packed into the same amount of space.

{{VISUAL: diagram: Two identical cubes side-by-side. The left cube is labeled "Wood, 0.7 g/cm³" and has sparsely distributed dots inside. The right cube is labeled "Iron, 7.8 g/cm³" and is filled with tightly packed dots, illustrating higher density.}}

Solved Numericals

Here, we will practice calculating density using its formula. Remember to always include the correct units in your answer!

Hero Formula: Density = Mass / Volume

Example 1: An aluminum block has a mass of 540 g and a volume of 200 cm³. What is its density?

• GIVEN:
  • Mass (m) = 540 g
  • Volume (V) = 200 cm³
• FORMULA:
  • Density = Mass / Volume
• SUBSTITUTION:
  • Density = 540 g / 200 cm³
• ANSWER:
  • Density = 2.7 g/cm³

Example 2: The density of gold is 19.3 g/cm³. What is the mass of a gold bar with a volume of 100 cm³?

• GIVEN:
  • Density (ρ) = 19.3 g/cm³
  • Volume (V) = 100 cm³
• FORMULA:
  • We need to rearrange the formula to find mass:
  • Mass = Density × Volume
• SUBSTITUTION:
  • Mass = 19.3 g/cm³ × 100 cm³
• ANSWER:
  • Mass = 1930 g (or 1.93 kg)

Try It Yourself

Now, test your understanding with these problems.

1. A piece of rock has a mass of 150 g and a volume of 50 cm³. Calculate the density of the rock.
2. A bottle contains 250 mL of olive oil. If the density of olive oil is 0.92 g/mL, what is the mass of the oil? (Hint: 1 mL = 1 cm³)
3. A wooden toy has a mass of 400 g and a density of 0.8 g/cm³. What is the volume of the toy?

Answer Key: 1. 3 g/cm³ | 2. 230 g | 3. 500 cm³

Solubility of Gases

{{FORMULA: expr=Density = Mass / Volume | symbols=Density:mass per unit volume (kg/m³ or g/cm³), Mass:amount of matter (kg or g), Volume:space occupied (m³ or cm³)}}

The Unseen Guest: Solubility of Gases

We've seen how solids like sugar and salt dissolve in water. But what about gases? Is the air we breathe capable of mixing into liquids? The answer is a resounding yes, and it's a phenomenon that makes life on Earth possible.

Many gases dissolve in water, but one of the most important is oxygen. While oxygen only dissolves to a small extent, this small amount is the lifeline for all aquatic plants and animals. From the smallest algae to the largest fish, every organism living in water depends on this dissolved oxygen for respiration.

When a gas dissolves in a liquid like water, it spreads out evenly. You can't see the individual gas molecules, just as you can't see salt particles in saltwater. This means the mixture of gases in water is a uniform mixture, or a solution.

{{VISUAL: diagram: Cross-section of a pond showing fish and aquatic plants. Arrows indicate fish taking in dissolved oxygen (O₂) from the water and releasing carbon dioxide (CO₂), which is then used by plants for photosynthesis.}}

Temperature's Chilling Effect

Does temperature affect how well gases dissolve? Think about a can of a cold, fizzy drink. When you open it, you hear a "pssshh" and see bubbles. Now, imagine opening a can that's been left out in the sun. It often fizzes over dramatically! This gives us a clue.

It has been observed that the solubility of gases in liquids generally decreases as the temperature increases.

• Cold water can hold more dissolved gas. This is why aquatic life thrives in cooler water bodies, where there is a richer supply of oxygen.
• Warm water can hold less dissolved gas. If a lake or river becomes too warm (for instance, due to industrial discharge, an effect called thermal pollution), the oxygen levels can drop dangerously low, harming or even killing the fish.

{{KEY: concept | title=Temperature and Gas Solubility | text=There is an inverse relationship between the temperature of a liquid and the solubility of a gas in it. As temperature goes up, the amount of gas that can dissolve goes down. Conversely, colder liquids can hold more dissolved gas.}}

Why Do Things Float or Sink?

We've all seen it: a leaf floats on a pond, while a small pebble sinks right to the bottom. In the kitchen, you might notice that rice grains sink in water, but tiny husk particles float. A common guess is that "lighter" things float and "heavier" things sink. This is partly true, but it's not the whole story.

An iron rod and a wooden log of the exact same size are a great example. If you pick them up, the iron rod feels much heavier. When we say iron is heavier than wood, we are comparing a special property that scientists call density.

What is Density?

Imagine two identical rooms. One room is packed with 50 people, and the other has only 5 people. The first room is more "densely" packed. Matter is similar. Some materials have a lot of "stuff" (mass) packed into a small space (volume), while others have less mass in the same amount of space.

Density is the measure of how much mass is contained in a given unit of volume.

{{KEY: definition | title=Density | text=Density is defined as the mass of a substance present per unit volume. It is a measure of how tightly matter is packed together.}}

The relationship can be written as a simple formula:

Density = Mass / Volume

This means if you have two objects of the exact same volume, the one with more mass is denser. If you have two objects of the exact same mass, the one that takes up less space (smaller volume) is denser.

{{VISUAL: diagram: Two identical cubes are on a balance scale. The cube on the left is labelled 'Wood' and is higher up. The cube on the right is labelled 'Iron' and is lower down, showing it is heavier. Inside the wood cube are a few scattered dots. Inside the iron cube are many tightly packed dots, illustrating greater mass in the same volume.}}

Units and Relative Density

Since density is calculated from mass and volume, its units depend on the units used for mass and volume.

• The SI unit for density is kilogram per cubic metre (kg/m³).
• For convenience in the lab and daily life, we often use gram per cubic centimetre (g/cm³) or gram per millilitre (g/mL).

A very useful fact to remember is that the density of pure water is approximately 1 g/cm³. This makes water a great standard for comparison.

This comparison is called relative density. It tells you how many times denser a substance is compared to water.

Relative density = (Density of the substance) / (Density of water)

For example, the density of aluminium is 2.7 g/cm³. Its relative density is (2.7 g/cm³) / (1 g/cm³) = 2.7. Notice that the units cancel out. Relative density is a pure number and has no units.

{{KEY: points | title=Key Facts about Density | text=- Density is an intrinsic property of a substance; it doesn't depend on the object's size or shape.

• The SI unit is kg/m³.
• A more common unit is g/cm³ (or g/mL).
• The density of water is approximately 1 g/cm³.
• Relative density is a unitless ratio comparing a substance's density to water's density.}}

Solved Numericals

Let's put the concept of density into practice with some calculations.

Hero Formula: Density = Mass / Volume

Example 1: Finding the Density of a Wooden Block

A rectangular block of wood has a mass of 300 g. Its dimensions are 10 cm in length, 5 cm in width, and 4 cm in height. Calculate the density of the wood.

• GIVEN:

  • Mass (m) = 300 g
  • Length (l) = 10 cm
  • Width (w) = 5 cm
  • Height (h) = 4 cm

• FORMULA:

  1. First, find the volume: Volume (V) = l × w × h
  2. Then, find the density: Density = Mass / Volume

• SUBSTITUTION:

  1. Volume = 10 cm × 5 cm × 4 cm = 200 cm³
  2. Density = 300 g / 200 cm³

• ANSWER: The density of the wood is 1.5 g/cm³.

Example 2: Finding the Mass of Oil

A can is filled with 500 mL of cooking oil. If the density of the oil is 0.92 g/mL, what is the mass of the oil in the can? (Remember: 1 mL = 1 cm³)

• GIVEN:

  • Volume (V) = 500 mL
  • Density = 0.92 g/mL

• FORMULA: We need to rearrange the density formula to solve for mass: Mass = Density × Volume

• SUBSTITUTION:

  • Mass = 0.92 g/mL × 500 mL

• ANSWER: The mass of the oil is 460 g.

{{KEY: exam | title=Check Your Units! | text=A common mistake in exams is mixing units. If mass is in grams (g), volume should be in cm³ or mL. If mass is in kilograms (kg), volume should be in m³. Always convert your units to be consistent before calculating!}}

Try It Yourself

1. An iron ball has a mass of 156 g and a volume of 20 cm³. What is its density?
2. Mercury is a very dense liquid with a density of 13.6 g/cm³. What is the mass of 10 cm³ of mercury?
3. The relative density of silver is 10.8. What is its density in g/cm³? Will a piece of silver float or sink in water?

Answer Key:

1. 7.8 g/cm³
2. 136 g
3. Density is 10.8 g/cm³. It will sink in water because its density is greater than water's density (1 g/cm³).

Why Do Objects Float or Sink in Water?

{{FORMULA: expr=Density = Mass / Volume | symbols=Density:mass per unit volume (kg/m³ or g/cm³), Mass:the amount of matter in an object (kg or g), Volume:the space an object occupies (m³ or cm³)}}

Why Do Objects Float or Sink in Water?

Have you ever wondered why a heavy log of wood floats effortlessly on a river, but a tiny iron nail sinks straight to the bottom? Or when washing rice, why do the light husk particles float while the heavier rice grains sink?

At first glance, you might think, "Heavier things sink and lighter things float". But the log is much heavier than the nail! This simple observation tells us that it's not just about the total mass of an object. There's another property at play, a property that describes how "packed" the matter is inside an object. This property is called density.

What is Density?

Imagine a school bus. If it's packed with students, standing shoulder-to-shoulder, we can say it has a high density of students. If the same bus has only five students scattered around, it has a low density.

Science uses this same idea. Some materials have their particles (atoms and molecules) packed very tightly together, while others have them more spread out.

{{KEY: type=definition | title=Density | text=Density is defined as the mass of a substance present in a unit of its volume. It's a measure of how much "stuff" (mass) is packed into a given amount of space (volume).}}

This means that for the same amount of space (say, a small cube), a denser material like iron will have more mass packed into it than a less dense material like wood. That's why an iron rod feels much heavier than a wooden stick of the exact same size.

{{VISUAL: diagram: Two cubes of identical volume (1 cm³), one labeled 'Wood' and the other 'Iron'. The wood cube shows sparsely packed particles, while the iron cube shows many densely packed particles, illustrating that iron has more mass in the same volume.}}

Calculating Density

Because density is a precise scientific property, we can calculate it using a simple formula.

The Density Formula

The relationship between density, mass, and volume is expressed mathematically as:

Density = Mass / Volume

• Mass: The amount of matter in an object. We usually measure it in grams (g) or kilograms (kg).
• Volume: The amount of space an object takes up. We usually measure it in cubic centimetres (cm³), millilitres (mL), or cubic metres (m³).

The units for density depend on the units you use for mass and volume.

{{KEY: type=points | title=Common Units of Density | text=- The SI (International System) unit is kilograms per cubic metre (kg/m³).

• For solids and liquids in the lab, it's more convenient to use grams per cubic centimetre (g/cm³).
• For liquids, you will also often see grams per millilitre (g/mL). Note that 1 cm³ is exactly equal to 1 mL.}}

For a very important reference, the density of pure water is approximately 1 g/cm³ (or 1 g/mL). This number is the key to understanding why things float or sink in water!

{{KEY: type=exam | title=The Float or Sink Rule | text=When an object is placed in water, compare its density to water's density (1 g/cm³). If the object's density is greater than 1 g/cm³, it will sink. If its density is less than 1 g/cm³, it will float.}}

Think about the cooking oil mentioned in your textbook. A 1-litre (1000 mL) packet might weigh only 910 grams.

• Its density would be 910 g / 1000 mL = 0.91 g/mL.
• Since 0.91 g/mL is less than water's density of 1 g/mL, oil floats on water.

Relative Density

Sometimes, instead of stating the exact density, we compare it to water. This comparison is called relative density.

Relative Density = (Density of a substance) / (Density of water)

For example, your textbook mentions that an aluminium block has a density of 2.7 g/cm³. To find its relative density: Relative Density of Aluminium = 2.7 g/cm³ / 1 g/cm³ = 2.7

Notice that the units (g/cm³) cancel out. Relative density is a pure number with no units. It simply tells you how many times denser a substance is than water.

{{KEY: type=concept | title=Relative Density | text=Relative density is a ratio that compares the density of a substance to the density of a reference substance, which is almost always water. A relative density greater than 1 means the substance will sink in water, while a relative density less than 1 means it will float.}}

How to Measure Density

To find the density of an object, you need to measure two things: its mass and its volume.

1. Measuring Mass: We use a balance to measure mass. A digital weighing balance is very common and easy to use. You simply place the object on the pan and read the display. It's important to first press the 'TARE' or 'ZERO' button (often after placing an empty container like a watch glass) to ensure you are only measuring the mass of the object itself.

   {{VISUAL: photo: A step-by-step sequence showing how to measure the mass of a small stone on a digital balance. Image 1: Balance shows 0.00 g. Image 2: An empty beaker is placed on the pan. Image 3: The 'TARE' button is pressed, and the balance returns to 0.00 g. Image 4: The stone is placed in the beaker, and the final mass is displayed.}}

2. Measuring Volume: For a regularly shaped object like a cube, you can calculate the volume by measuring its dimensions (length × width × height). For an irregularly shaped object like a stone, you would use the water displacement method with a measuring cylinder.

Once you have both mass and volume, you can use the formula to calculate the density.

Solved Numericals

Here are some examples of how to apply the density formula to solve problems.

Hero Formula: Density = Mass / Volume

Example 1

An iron block has a mass of 390 g and a volume of 50 cm³. Calculate its density. Will it sink or float in water?

• GIVEN:

  • Mass (m) = 390 g
  • Volume (V) = 50 cm³

• FORMULA:

  • Density = Mass / Volume

• SUBSTITUTION:

  • Density = 390 g / 50 cm³

• ANSWER:

  • Density = 7.8 g/cm³
  • Since the density of iron (7.8 g/cm³) is greater than the density of water (1 g/cm³), the iron block will sink.

Example 2

A block of cork has a volume of 200 cm³ and a density of 0.25 g/cm³. What is its mass?

• GIVEN:

  • Volume (V) = 200 cm³
  • Density (D) = 0.25 g/cm³

• FORMULA:

  • We need to rearrange the density formula to solve for mass:
  • Mass = Density × Volume

• SUBSTITUTION:

  • Mass = 0.25 g/cm³ × 200 cm³

• ANSWER:

  • Mass = 50 g
  • The mass of the cork block is 50 g.

Try It Yourself

1. A piece of glass has a mass of 65 g and a volume of 25 cm³. What is the density of the glass?
2. The density of gold is 19.3 g/cm³. What is the volume of a gold bar that has a mass of 965 g?
3. You are given three cubes of the same size: one made of ice (density = 0.92 g/cm³), one of glycerine (density = 1.26 g/cm³), and one of oak wood (density = 0.75 g/cm³). Which of these will sink in water?

Answer Key: 1. 2.6 g/cm³ | 2. 50 cm³ | 3. The glycerine cube will sink.