Do I always have to convert temperature to kelvins, even for Boyle's law?

Boyle's law does not contain a temperature term, so there is nothing to convert — you just need to know that the temperature is constant. For Charles's and Gay-Lussac's laws, kelvins are mandatory every single time. The safest habit is to convert any Celsius temperature the moment you write it down, so you never have to remember which law you are about to use.

Do pressure and volume units need to be converted too?

Only if they do not already match. Because these laws are ratios or products of the same variable, the units cancel. If both volumes are in milliliters, leave them in milliliters and your answer comes out in milliliters. But if one pressure is in atm and the other is in kPa, you must convert one so they match. Common conversions are 1\ atm = 760\ torr = 101.3\ kPa.

How do I tell which law a word problem wants?

Find the quantity that is held constant or never mentioned. A rigid or sealed metal container means constant volume, so use Gay-Lussac. A balloon, syringe with a free plunger, or piston at atmospheric pressure means constant pressure, so use Charles. If a problem says the temperature is held constant or the process happens slowly at room temperature, use Boyle. If all three quantities change, you need the combined gas law from the next lesson.

Why does a Charles's law graph point to -273\ ^?

When you plot volume against Celsius temperature for a real gas at constant pressure and extend the straight line backward, it crosses zero volume near -273\ ^ regardless of which gas you used. That common intercept is what defines absolute zero and sets the starting point of the Kelvin scale. No gas actually reaches it — every real gas condenses to a liquid first — so the low end of the line is an extrapolation rather than data.

CHEM-7.3

The Gas Laws: Boyle's, Charles's & Gay-Lussac's

Master Boyle's, Charles's, and Gay-Lussac's laws: how pressure, volume, and Kelvin temperature trade off in a fixed gas sample, with worked calculations.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on The Gas Laws: Boyle's, Charles's & Gay-Lussac's, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start The Gas Laws: Boyle's, Charles's & Gay-Lussac's free

What this lesson covers

Squeeze a plugged syringe and the plunger pushes back. Leave a balloon in a cold car overnight and it sags. Toss an empty aerosol can in a fire and it bursts. All three of these everyday events are the same physics: a fixed amount of gas has three properties that can change — pressure, volume, and temperature — and when you hold one of them steady, the other two are locked into a strict mathematical relationship.

This lesson gives you the three classic two-variable gas laws. Boyle's law connects pressure and volume, Charles's law connects volume and temperature, and Gay-Lussac's law connects pressure and temperature. Each one is a short equation you can solve in under a minute, but each one comes with the same non-negotiable rule: temperature must be in kelvins, never degrees Celsius. Get comfortable with these three now, because the next lesson simply stitches them together into the combined and ideal gas laws.

The Fixed Sample and the Kelvin Rule

Every calculation in this lesson assumes a fixed sample of gas: the number of gas particles does not change, and none leaks out or gets added. Under that condition, three measurable properties can vary — pressure

P

, volume

V

, and absolute temperature

T

. Each of the three laws holds one property constant and describes how the other two must adjust.

The single most important procedural rule is that temperature always goes into these equations in kelvins:

T(\text{K}) = T(^\circ\text{C}) + 273.15

Most problems accept 273. Why does this matter so much? Because Charles's and Gay-Lussac's laws are ratio relationships. If a gas is cooled from 100 degrees Celsius to 50 degrees Celsius, the Celsius number is cut in half, but the volume does not drop by half — it goes from 373 K to 323 K, a decrease of only about 13 percent. Worse, a Celsius temperature can be zero or negative, and a ratio with zero in the denominator is meaningless. Kelvin fixes this because 0 K is absolute zero, the point where particle motion is minimized; a gas at 0 K would extrapolate to zero volume and zero pressure.

A useful habit: before touching a calculator, write

T_1

and

T_2

in kelvins on your paper. Pressure and volume units, by contrast, only have to match each other — liters with liters, atm with atm — because their units cancel in the ratio. You never have to convert liters to milliliters as long as both volumes use the same unit.

Boyle's Law: Pressure and Volume Trade Off

Boyle's law applies at constant temperature and constant amount of gas. It says pressure and volume are inversely proportional: squeeze the gas into less space and the pressure climbs; let it expand and the pressure drops.

P_1V_1 = P_2V_2 \qquad \text{or} \qquad P \propto \frac{1}{V}

The kinetic-molecular picture explains why. Pressure comes from gas particles colliding with the container walls. Halve the volume and each particle has half the distance to travel between walls, so collisions happen twice as often, and the force per unit area doubles. Particle speeds have not changed — temperature is constant — only the collision frequency.

A graph of

P

versus

V

for Boyle's law is a hyperbola that curves toward both axes and never touches them. A graph of

P

versus

\frac{1}{V}

is a straight line through the origin, which is how chemists confirm the relationship experimentally.

Where students go wrong: setting up

\frac{P_1}{V_1} = \frac{P_2}{V_2}

out of habit, because the other two laws are fractions. Boyle's law is the one law that is a product, not a ratio. A quick sanity check catches this instantly. If you compress a gas from 4.0 L to 1.0 L, the volume shrank by a factor of 4, so the pressure must be 4 times larger. If your answer came out smaller, you flipped the relationship. Always predict the direction of the change in words before you compute, then verify that your number agrees.

Charles's Law and Gay-Lussac's Law: The Direct Relationships

Charles's law holds pressure constant and relates volume to absolute temperature. Gay-Lussac's law holds volume constant and relates pressure to absolute temperature. Both are direct proportions, so both are written as equal ratios.

\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad\qquad \frac{P_1}{T_1} = \frac{P_2}{T_2}

Heating a gas makes its particles move faster. If the container can expand — a balloon, a piston free to slide — the gas pushes outward until the internal pressure again matches the outside pressure, so the volume grows: that is Charles's law. If the container is rigid — a steel cylinder, a sealed aerosol can — the volume cannot change, so faster and harder collisions simply raise the pressure: that is Gay-Lussac's law. Deciding between them is really just asking whether the container can change shape.

Law	Held constant	Relationship	Equation
Boyle	temperature	inverse	$P_1V_1 = P_2V_2$
Charles	pressure	direct	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Gay-Lussac	volume	direct	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Graphing either direct law gives a straight line. Extending a Charles's law line backward until volume reaches zero always lands near

-273\ ^\circ\text{C}

, no matter which gas was tested — historically, this extrapolation is how absolute zero was located. Real gases liquefy long before they get there, so the low-temperature end of the line is a projection, not a measurement.

Setting Up and Checking Any Gas Law Problem

A reliable routine turns these into fast problems. First, list what you are given with subscripts 1 and 2, and mark the unknown. Second, identify which quantity is not mentioned or is described as unchanged — that tells you which law to use. Phrases like "rigid container" or "sealed steel tank" mean constant volume (Gay-Lussac); "balloon" or "movable piston" usually means constant pressure (Charles); "at constant temperature" or "isothermal" means Boyle. Third, convert every temperature to kelvins. Fourth, rearrange algebraically and solve.

Rather than memorizing four rearranged forms of each law, solve for the unknown from the base equation. For Charles's law with

V_2

unknown, multiply both sides by

T_2

V_2 = V_1 \times \frac{T_2}{T_1}

Notice the structure: the original value times a ratio of the two temperatures. If the gas is being heated, the ratio must be greater than 1; if cooled, less than 1. This is the fastest self-check in the whole unit.

Common problems in student work include leaving a temperature in Celsius, mixing units within one variable, such as one volume in liters and the other in milliliters, and using Boyle's law when the temperature is actually changing. Another subtle one: adding 273 to a temperature that is already in kelvins. If a problem gives you 350 K, leave it alone. Finally, remember these laws describe a fixed sample only. If a problem says gas is pumped in or leaks out, none of these three equations applies without more information.

Key terms

Absolute zero.: The lowest theoretically possible temperature, $0$ K or about $-273.15\ ^\circ\text{C}$ , at which the volume and pressure of an ideal gas would extrapolate to zero.
Kelvin scale.: An absolute temperature scale with the same degree size as Celsius but starting at absolute zero; required in all gas law ratio calculations. $T(\text{K}) = T(^\circ\text{C}) + 273.15$ .
Boyle's law.: At constant temperature and amount of gas, pressure and volume are inversely proportional: $P_1V_1 = P_2V_2$ .
Charles's law.: At constant pressure and amount of gas, volume is directly proportional to absolute temperature: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ .
Gay-Lussac's law.: At constant volume and amount of gas, pressure is directly proportional to absolute temperature: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ .
Inverse proportion.: A relationship in which the product of two quantities stays constant, so increasing one decreases the other by the same factor.
Direct proportion.: A relationship in which the ratio of two quantities stays constant, so both increase or decrease by the same factor.
Fixed sample.: A gas system in which the number of particles stays the same throughout the change; a required condition for all three of these laws.

Worked example

A sealed rigid aerosol can holds gas at a pressure of 2.50 atm when the room is at 25 degrees Celsius. The can is left near a heater and warms to 200 degrees Celsius. The can is rated to withstand 4.00 atm. Will it fail?

Step 1 — Identify the constant. The can is rigid and sealed, so the volume and the amount of gas cannot change. Pressure and temperature are the variables, which points to Gay-Lussac's law.

Step 2 — List the data.

P_1 = 2.50

atm,

T_1 = 25\ ^\circ\text{C}

T_2 = 200\ ^\circ\text{C}

, and

P_2

is unknown.

Step 3 — Convert to kelvins.

T_1 = 25 + 273 = 298

K and

T_2 = 200 + 273 = 473

K. Skipping this step and using 25 and 200 would predict a pressure of about 20 atm, which is wildly wrong.

Step 4 — Write the law and solve for the unknown.

\frac{P_1}{T_1} = \frac{P_2}{T_2} \quad \Rightarrow \quad P_2 = P_1 \times \frac{T_2}{T_1}

Step 5 — Substitute and compute.

P_2 = 2.50\ \text{atm} \times \frac{473\ \text{K}}{298\ \text{K}} = 2.50 \times 1.587 = 3.97\ \text{atm}

Step 6 — Check the direction and answer the question. The gas was heated, so the pressure should rise, and the temperature ratio

\frac{473}{298}

is greater than 1 — consistent. The result, 3.97 atm, is just under the 4.00 atm rating, so the can barely holds, with almost no margin. Reporting three significant figures matches the precision of the given data.

Practice questions

A 4.0 L sample of nitrogen gas at 1.5 atm is compressed to 1.0 L while the temperature is held constant. What is the new pressure?

0.38 atm
2.5 atm
6.0 atm
0.17 atm

Answer: 6.0 atm

Temperature is constant and the amount of gas is fixed, so this is Boyle's law:

P_1V_1 = P_2V_2

. Substituting,

(1.5)(4.0) = P_2(1.0)

, so

P_2 = 6.0

atm. Check the logic first: the volume shrank to one quarter of its original size, so the pressure must become four times larger, and

1.5 \times 4 = 6.0

. The answer 0.38 atm comes from dividing instead of multiplying, which is what happens when someone treats Boyle's law as a ratio like the other two laws.

A weather balloon has a volume of 2.5 L at 27 degrees Celsius. It rises until the surrounding temperature is -73 degrees Celsius, while the pressure inside stays constant. Find the new volume and explain why converting to kelvins changes the answer.

Answer: The new volume is about 1.7 L.

Pressure is constant, so use Charles's law:

\frac{V_1}{T_1} = \frac{V_2}{T_2}

. Convert first:

T_1 = 27 + 273 = 300

K and

T_2 = -73 + 273 = 200

K. Then

V_2 = V_1 \times \frac{T_2}{T_1} = 2.5 \times \frac{200}{300} = 1.67 \approx 1.7

L. The gas cooled, so the volume shrinks, and the ratio

\frac{200}{300}

is less than 1 — consistent. Using Celsius numbers directly would require dividing by

-73

, giving a negative volume, which is physically impossible. Kelvin is required because these laws are proportions measured from absolute zero, not from the arbitrary freezing point of water.

Two identical sealed containers of gas are heated from 20 degrees Celsius to 40 degrees Celsius. Container A is a rigid steel cylinder; container B is a balloon open to steady atmospheric pressure. Describe what changes in each container and name the law that applies.

Answer: Container A: pressure rises by a factor of $\frac{313}{293}$ , about 6.8 percent, at constant volume (Gay-Lussac's law). Container B: volume rises by the same factor, about 6.8 percent, at constant pressure (Charles's law).

The deciding question is whether the container can change shape. Steel cannot expand meaningfully, so the faster-moving particles hit the walls more frequently and harder, raising the pressure — Gay-Lussac's law. The balloon expands until its internal pressure again matches the outside air, so the pressure stays constant and the volume grows — Charles's law. Both changes use the same temperature ratio,

\frac{313\ \text{K}}{293\ \text{K}} \approx 1.068

. Notice also that doubling the Celsius reading from 20 to 40 does not double anything, which shows why the Celsius scale cannot be used in these ratios.

FAQ

Do I always have to convert temperature to kelvins, even for Boyle's law?: Boyle's law does not contain a temperature term, so there is nothing to convert — you just need to know that the temperature is constant. For Charles's and Gay-Lussac's laws, kelvins are mandatory every single time. The safest habit is to convert any Celsius temperature the moment you write it down, so you never have to remember which law you are about to use.
Do pressure and volume units need to be converted too?: Only if they do not already match. Because these laws are ratios or products of the same variable, the units cancel. If both volumes are in milliliters, leave them in milliliters and your answer comes out in milliliters. But if one pressure is in atm and the other is in kPa, you must convert one so they match. Common conversions are $1\ \text{atm} = 760\ \text{torr} = 101.3\ \text{kPa}$ .
How do I tell which law a word problem wants?: Find the quantity that is held constant or never mentioned. A rigid or sealed metal container means constant volume, so use Gay-Lussac. A balloon, syringe with a free plunger, or piston at atmospheric pressure means constant pressure, so use Charles. If a problem says the temperature is held constant or the process happens slowly at room temperature, use Boyle. If all three quantities change, you need the combined gas law from the next lesson.
Why does a Charles's law graph point to $-273\ ^\circ\text{C}$ ?: When you plot volume against Celsius temperature for a real gas at constant pressure and extend the straight line backward, it crosses zero volume near $-273\ ^\circ\text{C}$ regardless of which gas you used. That common intercept is what defines absolute zero and sets the starting point of the Kelvin scale. No gas actually reaches it — every real gas condenses to a liquid first — so the low end of the line is an extrapolation rather than data.

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