Ideal Gas Laws

Theory — The Gas Laws

Boyle's Law

At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume: squeeze the gas into half the volume and the pressure doubles.

Boyle's Law (constant T, n) P × V = constant → P₁V₁ = P₂V₂

P₂ = P₁V₁ / V₂

Charles's Law

At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute (kelvin) temperature. Temperature must be in kelvin: T(K) = T(°C) + 273.15.

Charles's Law (constant P, n) V / T = constant → V₁ / T₁ = V₂ / T₂

V₂ = V₁ × T₂ / T₁ (T in kelvin)

Gay-Lussac's Law

At constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature.

Gay-Lussac's Law (constant V, n) P / T = constant → P₁ / T₁ = P₂ / T₂

P₂ = P₁ × T₂ / T₁ (T in kelvin)

The Ideal Gas Law

The three laws combine into one equation relating pressure, volume, amount, and temperature of an ideal gas.

Ideal Gas Law P V = n R T, R = 0.08206 L·atm/mol·K (T in kelvin)

P = nRT/V · V = nRT/P · n = PV/RT

Boyle

P and V inversely related at constant T. P–V curve is a hyperbola.

Charles

V and T directly related at constant P. V–T line points to absolute zero.

Gay-Lussac

P and T directly related at constant V. P–T line points to absolute zero.

Law	Held constant	Relationship
Boyle's	T, n	P₁V₁ = P₂V₂
Charles's	P, n	V₁/T₁ = V₂/T₂
Gay-Lussac's	V, n	P₁/T₁ = P₂/T₂
Ideal gas	—	PV = nRT

Apparatus

The equipment a real ideal-gas-law experiment uses. In the simulation these are modelled for you, but the readings correspond to what each instrument would measure.

Gas syringe

Changes and reads the gas volume for Boyle's and Charles's laws.

Pressure gauge

Measures the gas pressure.

Thermometer

Measures the gas temperature in kelvin.

Water bath

Sets the gas temperature for the temperature-dependent laws.

Manometer

Reads pressure differences for the gas sample.

Analytical balance

Finds the moles of gas through its mass.

Instructions — Running the Virtual Experiment

The simulation has four sections, one for each law. In each one, calculate the predicted value yourself first, then run the experiment to check it, and record both values with screenshots. Prepare a short report for each of Boyle's, Charles's, and Gay-Lussac's laws (with a data table and graph).

Part 1 — Boyle's Law (Boyle's Law tab)

Open Simulation → Boyle's Law. Choose a fixed trial (initial P and V, new V at constant T). Calculate the new pressure yourself with P₂ = P₁V₁/V₂, type it in, then run and compare. Record the P–V data and sketch the P vs V graph.

Part 2 — Charles's Law (Charles's Law tab)

Open Charles's Law. Choose a fixed trial (initial V and T, new T at constant P). Calculate the new volume yourself with V₂ = V₁T₂/T₁ (kelvin), type it in, then check. Record the V–T data and graph.

Part 3 — Gay-Lussac's Law (Gay-Lussac's Law tab)

Open Gay-Lussac's Law. Choose a fixed trial (initial P and T, new T at constant V). Calculate the new pressure yourself with P₂ = P₁T₂/T₁ (kelvin), type it in, then check. Record the P–T data and graph.

Part 4 — Ideal Gas Law (Ideal Gas Law tab)

Open Ideal Gas Law. Choose what to solve for (P, V, or n), set the fixed values, calculate it yourself with PV = nRT, type it in, then check.

Simulation — Ideal Gas Laws

Step 1 — choose a fixed trial

Given in this trial

Known values—

Find—

Step 2 — calculate, then check

Your answer

Your answer—

Correct answer—

Run, work out the unknown, type it, then check.

Step 1 — choose a fixed trial

Given in this trial

Known values—

Find—

Step 2 — calculate, then check

Your answer

Your answer—

Correct answer—

Run, work out the unknown, type it, then check.

Step 1 — choose a fixed trial

Given in this trial

Known values—

Find—

Step 2 — calculate, then check

Your answer

Your answer—

Correct answer—

Run, work out the unknown, type it, then check.

P V = n R T

Step 1 — choose what to find

moles n

Temperature T (K)

Volume V (L)

Pressure P (atm)

Step 2 — calculate, then check

Your P (atm)

Your answer—

Correct answer—

Choose the unknown, calculate it, type it, then check.

Team Questions

Question 1. A gas at 1.0 atm occupies 4.0 L. At constant temperature, what is the pressure when the volume is reduced to 2.0 L? (P₁V₁ = P₂V₂; type to 2 decimals)

Question 2. Boyle's Law describes the relationship between which two quantities, and is it direct or inverse? (Answer in a phrase)

Question 3. A gas occupies 2.0 L at 300 K. At constant pressure, what is its volume at 600 K? (V₁/T₁ = V₂/T₂; type to 2 decimals)

Question 4. Why must temperature be in kelvin when using Charles's or Gay-Lussac's law? (Answer in a phrase)

Question 5. A gas at 1.0 atm and 300 K is heated to 450 K at constant volume. What is the new pressure? (P₁/T₁ = P₂/T₂; type to 2 decimals)

Question 6. Using PV = nRT (R = 0.08206), find the pressure of 1.0 mol of gas at 273 K in a 22.41 L container. (Type to 2 decimals, in atm)

Question 7 — Challenge. Using PV = nRT, how many moles are in 24.45 L of gas at 1.0 atm and 298 K? (Type to 2 decimals)

Example Lab Report

Sample report for one of the three laws. Prepare a short report for each of Boyle's, Charles's, and Gay-Lussac's laws, each with a data table and a graph.

Boyle's Law — Pressure vs Volume

Chemistry | Section: [Your Section] | Date: [Date]

Lab Members: [Names of all members present]

Objective

To verify Boyle's Law by showing that, at constant temperature, the product of pressure and volume of a fixed amount of gas is constant.

Variables

Controlled: temperature and amount of gas. Measured: pressure and volume.

Theory

At constant temperature, P and V are inversely proportional, so P₁V₁ = P₂V₂.

P₂ = P₁V₁ / V₂ · P × V = constant

Data and Worked Example

P (atm)	V (L)	P × V
1.00	4.00	4.00
2.00	2.00	4.00
4.00	1.00	4.00

Worked example: P₁ = 1.00 atm, V₁ = 4.00 L; at V₂ = 2.00 L, P₂ = (1.00 × 4.00)/2.00 = 2.00 atm. The product P × V stays at 4.00, confirming Boyle's Law.

Graph

A plot of P versus V gives a curve (hyperbola); a plot of P versus 1/V gives a straight line through the origin, confirming the inverse relationship.

Conclusion

The product of pressure and volume remained constant as the volume changed at fixed temperature, confirming Boyle's Law (P₁V₁ = P₂V₂).

Practice Questions

Show all work. Use P₁V₁ = P₂V₂, V₁/T₁ = V₂/T₂, P₁/T₁ = P₂/T₂ (T in kelvin), and PV = nRT with R = 0.08206.

Question 1

A gas at 2.0 atm occupies 3.0 L. At constant temperature, find the pressure when the volume increases to 6.0 L.

Hint: P₂ = (2.0 × 3.0)/6.0 = 1.0 atm.

Question 2

A gas occupies 3.0 L at 250 K. At constant pressure, find its volume at 500 K.

Hint: V₂ = 3.0 × 500/250 = 6.0 L.

Question 3

A gas at 2.0 atm and 250 K is heated at constant volume to 500 K. Find the new pressure.

Hint: P₂ = 2.0 × 500/250 = 4.0 atm.

Question 4

A sample of 0.50 mol of gas is at 300 K and 1.0 atm. Find its volume using PV = nRT.

Hint: V = nRT/P = (0.50 × 0.08206 × 300)/1.0 = 12.3 L.

Question 5

Convert 25 °C to kelvin, and explain why the kelvin scale is needed for the gas laws.

Hint: 25 + 273.15 = 298.15 K; ratios only work from absolute zero.

Question 6 — Challenge

2.0 mol of an ideal gas occupies 10.0 L at 350 K. Find the pressure, then explain how it would change if the volume were halved at constant temperature.

Hint: P = (2.0 × 0.08206 × 350)/10.0 = 5.74 atm; halving V doubles P (Boyle).

Ideal Gas Laws

Theory — The Gas Laws

Boyle's Law

Charles's Law

Gay-Lussac's Law

The Ideal Gas Law

Boyle

Charles

Gay-Lussac

Apparatus

Instructions — Running the Virtual Experiment

Simulation — Ideal Gas Laws

Step 1 — choose a fixed trial

Step 2 — calculate, then check

Step 1 — choose a fixed trial

Step 2 — calculate, then check

Step 1 — choose a fixed trial

Step 2 — calculate, then check

Step 1 — choose what to find

Step 2 — calculate, then check

Team Questions

Example Lab Report

Boyle's Law — Pressure vs Volume

Objective

Variables

Theory

Data and Worked Example

Graph

Conclusion

Practice Questions

Welcome — one quick step before you start