A gas is made of tiny particles that are very far apart compared with their own size.

In room-temperature air, the distance between neighboring particles is roughly ten times a particle's width.

So a gas is mostly empty space — the particles themselves take up almost none of the room.

That is why your arm sweeps through air so easily: it mostly moves through empty space.

This picture is the first claim of the 'kinetic molecular theory' — the particle model chemists use to explain everything a gas does.

Gas particles move constantly — they never stop to rest.

They move rapidly: a nitrogen molecule in room-temperature air travels at roughly 500 m/s, about 1,800 km/h.

Each particle moves in a straight line until it collides with another particle or with a wall.

The collision sends it off in a new direction — again in a straight line.

Because collisions send particles every which way, the motion is random: at any moment, particles are moving in every direction at once.

When everyday objects collide, they lose some of their energy of motion — a dropped ball bounces a little lower each time.

Collisions between gas particles are different: the particles lose none of their energy of motion.

A collision in which no energy of motion is lost is called an 'elastic' collision.

In an elastic collision the two particles may trade energy of motion with each other, but none of it disappears.

Collisions with the container walls are elastic too: a gas particle bounces off a wall without slowing down overall.

Because every collision is elastic, the constant motion never runs down.

The kinetic molecular theory treats gas particles as having no attractions to one another.

The reason is spacing: attractions between particles fade quickly as the distance between them grows.

Gas particles are so far apart that the weak attractions between them barely act.

So each particle moves independently — nothing pulls it toward its neighbors.

Neon atoms in a balloon move independently rather than sticking together.

When the temperature of a gas rises, its particles move faster on average.

When the temperature falls, its particles move slower on average.

'On average' matters: at any moment some particles move faster than others, because collisions keep trading energy of motion between them.

A particle's energy of motion is called its 'kinetic energy' — the faster a particle moves, the more kinetic energy it has.

So temperature tracks the particles' average kinetic energy: hotter gas, higher average kinetic energy.

The particles in a sample of air move faster on a 35 °C day than on a 5 °C day.

Gas particles move constantly and rapidly in straight lines, in random directions.

And nothing pulls them back together — the theory treats gas particles as having no attractions.

So particles released in one spot scatter: each travels its own straight lines, in its own random directions.

The particles keep spreading until they reach the container's walls, which bounce them straight back inside.

That is why a gas fills its whole container and takes the container's shape.

Perfume vapor released in one corner of a sealed box ends up spread throughout the box.

A gas is mostly empty space — its far-apart particles take up almost none of the room.

Squeezing a gas does not squash the particles themselves; it pushes the particles closer together.

The empty space between the particles shrinks; the particles do not.

Because there is so much empty space to give up, a gas can be squeezed into a much smaller volume.

The air in a sealed syringe can be pushed down to half its volume — the same particles, closer together.

A liquid cannot be squeezed this way: its particles are already touching, so there is almost no empty space to give up.

In a gas particle diagram, each dot is one particle, and the arrow on a dot shows that particle's motion.

The LENGTH of an arrow shows the particle's speed: a longer arrow means a faster particle.

Faster particles on average mean a higher temperature, so between two same-size boxes, the box with longer arrows shows the hotter gas.

The NUMBER of dots shows the amount of gas: more dots mean more particles.

Read the two features separately: arrow length answers temperature questions, and dot count answers amount questions.

Dot count says nothing about temperature — a box can hold many slow particles or a few fast ones.

A gas pushes outward on the walls of its container.

The push lands on every part of every wall — top, bottom, and sides — not just one spot.

The strength of that outward push, measured as force spread over the wall area, is called 'pressure'.

The air inside an inflated balloon pushes outward on every part of the balloon's inner surface.

More outward push on the same walls means higher pressure; less push means lower pressure.

Gas particles move constantly and rapidly in straight lines until they hit something.

Every time a particle hits a wall, it gives the wall a tiny outward push.

In even a small container, an enormous number of particles hit the walls every second.

The countless tiny pushes blend into one steady outward push — the gas's pressure.

So a sealed, rigid can of air pushes on its inside walls because pressure comes from gas particles colliding with the container walls — more collisions, or harder collisions, mean more pressure.

The push lands on every wall because the particles move in every direction.

The first unit is the 'atmosphere (atm)': 1 atm is the pressure of the air around you at sea level.

The second is the 'kilopascal (kPa)', the metric pressure unit.

The third is 'millimeters of mercury (mmHg)', an older unit still used in medicine and lab work.

The three units describe the same sea-level air pressure with different numbers: 1 atm = 101.3 kPa = 760 mmHg.

Commit the chain to memory — 1 atm, 101.3 kPa, and 760 mmHg are the same pressure, so a gas at 1 atm is at 760 mmHg.

To convert a pressure, use the equivalence that links your two units: 1 atm = 101.3 kPa, or 1 atm = 760 mmHg.

Going FROM atmospheres, multiply: a pressure in atm × 101.3 gives the same pressure in kPa, and × 760 gives it in mmHg.

Going TO atmospheres, divide: a pressure in kPa ÷ 101.3 gives atm, and a pressure in mmHg ÷ 760 gives atm.

For example, 2.00 atm × 101.3 = 202.6, so 2.00 atm is 202.6 kPa.

A sanity check: the atm number is always the smallest of the three — if your converted value moved the wrong way, you multiplied when you should have divided.

Cooling a gas slows its particles, so cooling has a natural end: the temperature at which the particles have the least possible motion.

That temperature is called 'absolute zero' — no lower temperature exists.

Absolute zero sits at −273 °C.

The 'kelvin' temperature scale starts at absolute zero: 0 K is absolute zero.

One kelvin step is the same size as one Celsius degree, so the two scales run in parallel, 273 apart.

K = °C + 273.

So 0 °C equals 273 K, and 100 °C equals 373 K.

To convert a Celsius temperature to kelvin, add 273.

K = °C + 273.

So 25 °C is 25 + 273 = 298 K.

To convert a kelvin temperature to degrees Celsius, make °C the subject: subtract 273 from both sides.

°C = K − 273.

So 298 K is 298 − 273 = 25 °C.

A kelvin temperature is never negative — if a kelvin answer comes out below zero, you subtracted when you should have added.

The zero of the Celsius scale is a human choice: 0 °C is where water freezes, not where particle motion stops.

Because the Celsius zero is arbitrary, doubling a Celsius value means nothing physical.

The kelvin scale starts at absolute zero — the temperature at which particles have the least possible motion.

Because kelvin starts at absolute zero, a kelvin value is a true measure of particle motion.

Doubling the kelvin temperature doubles the particles' average kinetic energy.

Now answer the morning's question: 10 °C is 283 K and 20 °C is 293 K — the kelvin value rose by barely 4%, so the afternoon air is nowhere near twice as hot.

This is why every calculation in this unit that uses a gas's temperature needs that temperature in kelvin: only kelvin values keep the gas's behavior in true proportion.

Take a fixed amount of gas, hold its temperature steady, and change only its volume.

When the volume decreases, the pressure increases.

When the volume increases, the pressure decreases.

Push the plunger of a sealed syringe of air inward, and the pressure inside rises — that is the push-back you feel.

Pull the plunger outward instead, and the pressure inside falls.

Pressure and volume move in opposite directions: squeeze a gas into less space and it pushes back harder; give it more space and it pushes back less.

A gas presses on its container because pressure comes from gas particles colliding with the container walls — more collisions, or harder collisions, mean more pressure.

Now squeeze a fixed amount of gas into half the space, keeping the temperature constant.

The same particles now travel across a smaller container, so each particle reaches a wall sooner.

Each particle therefore hits the walls more often.

The temperature has not changed, so the particles' speed has not changed — each hit is exactly as hard as before.

More collisions each second, each just as hard, means more pressure.

That is why the pressure doubles when a sealed syringe of air is pushed to half its volume: the same particles hit the walls twice as often.

The graph plots pressure (vertical axis) against volume (horizontal axis) for a fixed amount of gas at constant temperature.

The curve falls steeply at first: at small volumes, even a small increase in volume drops the pressure a lot.

Then the curve levels off: at large volumes, the same increase in volume barely changes the pressure.

The curve never touches either axis — the gas always has some pressure and some volume.

To read a paired value, start at the known value on its axis, move straight to the curve, then straight across (or down) to the other axis.

On this graph, to find the volume at which the pressure is 2.0 atm: start at 2.0 atm, move across to the curve, then down — the volume reads 3.0 L.

For a fixed amount of gas at constant temperature, the pressure multiplied by the volume stays the same.

P₁V₁ = P₂V₂.

P₁ and V₁ are the pressure and volume before the change; P₂ and V₂ are the pressure and volume after.

Halve the volume and the pressure exactly doubles; double the volume and the pressure exactly halves.

This exact trade is known as 'Boyle's law'.

Boyle's law holds only when the amount of gas is fixed and the temperature is constant.

A Boyle's law problem gives you three of the four quantities P₁, V₁, P₂, and V₂, and asks for the fourth.

The routine: write down the values, write down P₁V₁ = P₂V₂, make the unknown the subject, substitute, and calculate.

To find P₂, divide both sides by V₂: P₂ = P₁V₁ / V₂.

To find V₂, divide both sides by P₂: V₂ = P₁V₁ / P₂.

Use the same pressure unit on both sides, and the same volume unit on both sides — matching units cancel, so no conversion is needed.

The temperature is constant in every Boyle's law problem, so no kelvin conversion is needed either.

Here is the routine once through: a gas at 2.0 atm in 6.0 L is squeezed to 3.0 L, so P₂ = 2.0 × 6.0 / 3.0 = 4.0 atm.

Check the direction before moving on: the volume went down, so the pressure must come out higher — 4.0 atm passes.

Take a fixed amount of gas, hold its pressure steady, and change only its temperature.

When the temperature rises, the volume increases.

When the temperature falls, the volume decreases.

That is the freezer balloon: the air inside cooled, so its volume shrank — no air escaped.

Bring the balloon back into the warm room, and it swells back to size.

The pressure stays steady the whole time because the balloon's skin flexes: the gas inside always sits at the pressure of the air around it.

Heat the gas, and every wall hit becomes harder and comes sooner, because particles move faster at higher temperature.

A gas presses on its walls because pressure comes from gas particles colliding with the container walls — more collisions, or harder collisions, mean more pressure.

So the faster particles push harder on the walls than the steady outside air pushes back.

The container is flexible, so it gives way: the gas expands.

As the gas spreads into more space, its particles hit each patch of wall less often, so the gas's push weakens.

The expansion stops exactly when the gas's push falls back to match the steady outside pressure.

That is why a partly inflated balloon grows when it sits above a warm radiator: the warmed air pushes harder, the skin gives, and the balloon settles at a new, larger size.

The graph plots volume (vertical axis) against kelvin temperature (horizontal axis) for a fixed amount of gas at constant pressure.

The measured points lie on a straight line.

Extend that line backward, past the measurements, and it points at one special spot: zero volume at 0 K — absolute zero.

The extension is drawn dashed because it is a prediction, not a measurement — every real gas condenses to a liquid before it gets that cold.

To read a paired value, start at the known value on its axis, move straight to the line, then straight across (or down) to the other axis.

On this graph, to find the volume at 300 K: start at 300 K, move up to the line, then across — the volume reads 0.60 L.

For a fixed amount of gas at constant pressure, the volume divided by the kelvin temperature stays the same.

V₁/T₁ = V₂/T₂.

V₁ and T₁ are the volume and kelvin temperature before the change; V₂ and T₂ are the volume and kelvin temperature after.

Double the kelvin temperature and the volume exactly doubles; halve the kelvin temperature and the volume exactly halves.

This exact relationship is known as 'Charles's law'.

The temperatures in Charles's law must be in kelvin — only a kelvin value is a true measure of particle motion.

Charles's law holds only when the amount of gas is fixed and the pressure is constant.

A Charles's law problem gives you three of the four quantities V₁, T₁, V₂, and T₂, and asks for the fourth.

First, convert every temperature to kelvin: K = °C + 273. This step comes before anything else.

Then run the routine: write down the values, write down V₁/T₁ = V₂/T₂, make the unknown the subject, substitute, and calculate.

To find V₂, multiply both sides by T₂: V₂ = V₁T₂ / T₁.

To find T₂, rearrange to T₂ = T₁V₂ / V₁.

Use the same volume unit on both sides — matching units cancel.

Here is the routine once through: 2.0 L of gas at 300 K is heated to 600 K at constant pressure, so V₂ = 2.0 × 600 / 300 = 4.0 L.

Check the direction before moving on: the temperature went up, so the volume must come out larger — 4.0 L passes.

Take a fixed amount of gas, seal it in a rigid container so its volume cannot change, and change only its temperature.

When the temperature rises, the pressure increases.

When the temperature falls, the pressure decreases.

That is the warning on the can: a sealed spray can left in the sun builds pressure inside as it warms.

Cool the can back down, and the pressure inside falls again.

Compare this with the flexing balloon: when the walls can move, warming shows up as a bigger volume; when the walls cannot move, warming shows up as a higher pressure.

Picture a fixed amount of gas sealed inside a rigid metal tank, so neither the number of particles nor the volume can change.

Heating the gas speeds its particles up, because particles move faster at higher temperature.

Faster particles hit the walls harder.

Faster particles also cross the tank more quickly, so they hit the walls more often.

The pressure rises because pressure comes from gas particles colliding with the container walls — more collisions, or harder collisions, mean more pressure.

So heating a sealed, rigid container of gas raises the pressure, even though nothing about the container changes.

Cooling runs the same chain in reverse: slower particles hit the walls more gently and less often, so the pressure falls.

For a fixed amount of gas at constant volume, the pressure divided by the kelvin temperature gives the same number at any two conditions.

Written as an equation: P₁/T₁ = P₂/T₂.

This equation is called 'Gay-Lussac's law'.

The temperatures must be in kelvin.

The law holds only while the amount of gas and the volume stay fixed.

Because the two sides stay equal, doubling the kelvin temperature exactly doubles the pressure.

Write down the values in the question, and convert every temperature to kelvin with K = °C + 273.

Write down the equation: P₁/T₁ = P₂/T₂.

Make the unknown the subject.

Substitute in the values, and calculate — the result carries the unknown's unit.

Check the direction: heating a sealed, rigid container must raise the pressure, and cooling must lower it.

Read the problem and find the quantity that does not change between the two conditions.

If the temperature stays constant, it is a Boyle's law problem: P₁V₁ = P₂V₂.

If the pressure stays constant, it is a Charles's law problem: V₁/T₁ = V₂/T₂.

If the volume stays constant, it is a Gay-Lussac's law problem: P₁/T₁ = P₂/T₂.

The wording signals the constant quantity.

A rigid container keeps the volume constant.

A flexible container, or a piston free to slide, keeps the gas at the steady outside pressure.

A change made slowly at steady room temperature, or in a water bath, keeps the temperature constant.

All three laws also need the amount of gas to stay fixed — a sealed container with no leaks.

One table gathers the three cases.

For a fixed amount of gas, the pressure times the volume, divided by the kelvin temperature, gives the same number at any two conditions.

Written as an equation: P₁V₁/T₁ = P₂V₂/T₂.

This equation is called the 'combined gas law'.

The temperatures must be in kelvin, and the amount of gas must stay fixed.

Each two-variable gas law is the combined gas law with one quantity held constant.

Hold the temperature constant, and T₁ = T₂ cancels from both sides, leaving Boyle's law: P₁V₁ = P₂V₂.

Hold the pressure constant, and P₁ = P₂ cancels, leaving Charles's law: V₁/T₁ = V₂/T₂.

Hold the volume constant, and V₁ = V₂ cancels, leaving Gay-Lussac's law: P₁/T₁ = P₂/T₂.

Remember the combined gas law, and the three two-variable laws come free.

Write down the values in the question, and convert every temperature to kelvin with K = °C + 273.

Label each value as belonging to condition 1 or condition 2 before touching the equation.

Write down the equation: P₁V₁/T₁ = P₂V₂/T₂.

Make the unknown the subject.

Substitute in the values, and calculate — the result carries the unknown's unit.

If the problem holds one quantity constant, enter the same value on both sides — the equation still works.

When more moles of gas are added to a flexible container at constant temperature and pressure, the volume grows in the same proportion.

Double the moles, and the volume doubles; triple the moles, and the volume triples.

This proportionality is called 'Avogadro's law'.

It runs both ways: letting out half the moles halves the volume.

Turned around, the law says that equal volumes of any two gases at the same temperature and pressure contain equal numbers of particles.

The kind of gas makes no difference — one liter of helium and one liter of carbon dioxide at the same temperature and pressure hold the same number of particles.

Picture a flexible container of gas whose walls have settled where the inside push equals the steady outside pressure.

Pumping in more gas adds particles, and the extra particles add collisions with the walls.

Because pressure comes from gas particles colliding with the container walls — more collisions, or harder collisions, mean more pressure — the inside push now beats the outside push.

The stronger inside push forces the walls outward, so the container expands.

As the container grows, the same particles spread through more space, so the collisions on each patch of wall thin out.

The container stops growing when the inside push has fallen back to match the outside pressure.

Chemists compare gases at one agreed reference condition, called 'standard temperature and pressure', or 'STP'.

Standard temperature is 273 K, which is 0 °C.

Standard pressure is 1 atm.

'At STP' means at 273 K and 1 atm — nothing more.

One mole of any gas occupies 22.4 L at STP.

This volume is called the 'molar volume' of a gas.

The kind of gas makes no difference: 1.00 mol of helium, 1.00 mol of oxygen, and 1.00 mol of carbon dioxide each fill 22.4 L at STP.

22.4 L is about the volume of three basketballs.

The 22.4 L figure holds only at STP — at any other temperature or pressure, a mole of gas fills a different volume.

At STP, divide a gas volume in liters by 22.4 L/mol to get the moles.

Written as an equation: n = V ÷ 22.4 L/mol.

The routine works only at STP, because 22.4 L/mol is the molar volume only there.

A volume smaller than 22.4 L must give less than one mole, and a larger volume more than one mole.

At STP, multiply the moles of gas by 22.4 L/mol to get the volume in liters.

Written as an equation: V = n × 22.4 L/mol.

The routine works only at STP, because 22.4 L/mol is the molar volume only there.

More than one mole must give more than 22.4 L, and less than one mole less than 22.4 L.

For any single snapshot of a gas, the pressure times the volume equals the moles times the gas constant times the kelvin temperature.

Written as an equation: PV = nRT.

This equation is called the 'ideal gas law'.

R is the 'universal gas constant', 0.0821 L·atm/(mol·K) — the same number for every gas.

With R in these units, pressure must be in atm, volume in L, amount in mol, and temperature in K.

An 'ideal gas' is a gas that behaves exactly as the kinetic molecular theory assumes.

The law needs no before and after — one condition, four quantities, one equation.

PV = nRT ties together four measurable quantities, so knowing any three lets you calculate the fourth.

R only works with matched units: pressure in atm, volume in L, amount in mol, and temperature in K.

So check the units first: convert a Celsius temperature to kelvin with K = °C + 273, and convert a kPa or mmHg pressure to atm.

Then make the unknown the subject of PV = nRT.

Substitute the values, and calculate — the answer comes out in the matched unit: atm, L, mol, or K.

Watch the routine run on the STP anchor: 1.00 mol of gas at 273 K in 22.4 L.

Make P the subject: P = nRT ÷ V.

P = 1.00 × 0.0821 × 273 ÷ 22.4 = 1.00 atm — one mole in one molar volume at standard temperature exerts exactly standard pressure.