Spaces Between Particles

Introduction

If you mix 50 mL of water with 50 mL of ethanol, you might expect exactly 100 mL of mixture. Measure it carefully and you find only about 96–97 mL. Where did the missing volume go? No liquid has been lost — the mass is exactly the sum of the two masses. The explanation lies in one of the key ideas of the particle theory: there are spaces between particles.

Core explanation

Spaces exist in every state. Particles in solids and liquids are close together, but they are not packed so perfectly that there is no room between them; there are small gaps. In gases the spaces are enormous compared with the particles themselves. These spaces are empty — they contain nothing at all.

The water and ethanol experiment. Water molecules and ethanol molecules have different sizes and shapes. When the liquids are mixed, some of the molecules of one liquid fit into the spaces between molecules of the other, and the two kinds of molecule also attract each other strongly. The mixture therefore packs more tightly than the separate liquids, and the total volume is less than the sum of the two volumes. The mass is unchanged, because all the molecules are still present.

A model with beans and rice. Mix a cup of dried beans with a cup of rice: the rice grains slip into the gaps between the beans, and the mixture fills noticeably less than two cups. This large-scale model shows the same idea.

Dissolving without much volume increase. Dissolving a few grams of sugar or salt in water increases the volume only slightly, because the solute particles occupy some of the spaces between the water molecules and the water packs around them.

Compressibility. Gases can be compressed a lot because their particles have large spaces between them. Liquids and solids are nearly incompressible because their particles are already very close; the small spaces cannot be squeezed much further.

Evidence from gases. When water boils, 1 cm³ of liquid becomes about 1700 cm³ of steam at 100 °C. The number of molecules is the same, so the spaces between them must have become enormously larger.

Step-by-step reasoning

To explain why 50 mL of water + 50 mL of ethanol gives less than 100 mL:

1. Both liquids are made of particles with small spaces between them. 2. The two kinds of particle have different sizes and shapes. 3. On mixing, some particles fit into spaces between the others, and they attract each other strongly. 4. The particles pack more closely in the mixture. 5. So the total volume is less than 100 mL, while the mass is unchanged.

Visual explanation

A three-panel diagram: a jar of large spheres (with obvious gaps), a jar of small spheres, and the two mixed together, where the small spheres fill the gaps and the total height is less than the two heights added. A measuring cylinder beside it reads 96 mL after 50 mL of water and 50 mL of ethanol are combined.

Real-world analogy

Pour a bag of marbles into a jar, then pour sand in on top. The sand trickles into the gaps between the marbles, and the jar holds both without the level rising as much as you would expect. The sand fills space that looked "full" but was not.

Real-world example

Makers of alcoholic drinks and hand sanitisers must account for volume contraction when mixing ethanol and water. To make a solution with a precise alcohol percentage by volume, they cannot simply add volumes; they use tables of measured densities for water–ethanol mixtures or measure the final volume directly.

Why?

Why does the mass stay the same when the volume shrinks? Mass depends on how many particles there are and how heavy they are. Mixing does not add or remove particles; it only changes how closely they are packed. So volume can change while mass is conserved.

Common misconception

"Some of the liquid disappeared or evaporated when mixed." Careful weighing shows the mass of the mixture is exactly equal to the combined masses. Nothing is lost; the particles simply pack more efficiently.

Worked example

Question: 50.0 cm³ of water (mass 50.0 g) is mixed with 50.0 cm³ of ethanol (mass 39.5 g). The final volume is 96.5 cm³. What is the mass of the mixture, and what is its density?

Reasoning: Mass is conserved: 50.0 + 39.5 = 89.5 g. Density = 89.5 ÷ 96.5.

Answer: Mass 89.5 g; density about 0.927 g/cm³.

Quick check

1. What is found in the spaces between particles? Answer: Nothing — the spaces are empty.

Exam focus

Use volume contraction on mixing as evidence for spaces between particles, and always state that the mass is unchanged. Link compressibility to particle spacing: gases are compressible because their particles are far apart; liquids and solids are not because their particles are close together.

Advanced insight

Volume contraction on mixing water and ethanol comes partly from hydrogen bonding between the two kinds of molecule, not only from geometric packing. Chemists describe this using partial molar volumes: the effective volume each substance occupies in a mixture, which can differ from its volume when pure.

Summary

There are empty spaces between particles in all states of matter — small in solids and liquids, very large in gases. Mixing some liquids, such as water and ethanol, gives a total volume less than the sum of their volumes because particles pack more closely, while mass is conserved. The size of the spaces explains why gases are compressible and liquids and solids are not.

Practice questions

1. 100 cm³ of dried peas and 100 cm³ of sand are mixed. Will the total volume be more, less or equal to 200 cm³? Explain. Answer: Less, because sand grains fill the gaps between the peas. 2. Why can gases be compressed but liquids cannot (easily)? Answer: Gas particles have large spaces between them; liquid particles are already close together. 3. 60 g of water is mixed with 40 g of ethanol. What is the mass of the mixture? Answer: 100 g. 4. What does the large volume increase when water boils show about particle spacing? Answer: The particles in steam are much further apart than in liquid water.