Combined Gas Law Problems — Practice Problems with Step-by-Step Solutions
12 fully worked combined gas law practice problems — Boyle’s law, Charles’s law, Gay-Lussac’s law, the combined gas law, and the ideal gas law PV = nRT — with every temperature conversion shown in full
What Is an Ideal Gas? — Definition and Assumptions
An ideal gas is a theoretical gas that obeys the gas laws — including the ideal gas law PV = nRT — perfectly under all conditions. The ideal gas definition in chemistry is: a gas whose molecules occupy negligible volume and exert no intermolecular forces on each other. Real gases approximate ideal gas behavior at low pressures and high temperatures, where molecules are far apart and kinetic energy greatly exceeds intermolecular attraction.
The ideal gas model underlies every formula on this combined gas law worksheet. Understanding what makes a gas ideal — and when a real gas stops behaving ideally — is essential for knowing when gas law formulas give accurate results and when corrections (such as the Van der Waals equation) are needed.
The Five Assumptions of an Ideal Gas
The assumptions of an ideal gas define the conditions under which the combined gas law and ideal gas law apply exactly. All five assumptions must hold for a gas to behave ideally:
Negligible Molecular Volume
Gas molecules are treated as point masses — their physical size is negligible compared to the total volume of the container. This assumption of the ideal gas breaks down at very high pressures, where molecules are packed closely and their own volume becomes a significant fraction of the container volume.
No Intermolecular Forces
There are no attractive or repulsive forces between gas molecules. This ideal gas assumption fails for polar molecules (NH₃, H₂O) and molecules with large electron clouds (CO₂) that have significant London dispersion forces. Non-ideal gases deviate most at low temperatures where intermolecular forces dominate.
Perfectly Elastic Collisions
All collisions — between molecules and between molecules and container walls — are perfectly elastic, meaning no kinetic energy is lost. This assumption of the ideal gas ensures total kinetic energy remains constant, consistent with constant temperature at the molecular level.
Constant Random Motion
Molecules move in constant, random motion in all directions with no preferred orientation. This is why gas fills any container uniformly and exerts equal pressure on all walls — a key ideal gas property that makes pressure isotropic and directly calculable from P = F/A.
Kinetic Energy ∝ Temperature (Kelvin)
The average kinetic energy of gas molecules is directly proportional to absolute temperature in Kelvin. This is why temperature must always be in Kelvin in all gas law equations — at 0 K (absolute zero), molecules have zero kinetic energy and zero volume, making Kelvin the only physically meaningful zero for gas calculations.
Ideal Gas Examples and Non-Ideal Gases
Most ideal real gases: Helium (He), Neon (Ne), Hydrogen (H₂), Nitrogen (N₂) at room temperature and low pressure. Noble gases are the most ideal because they are monatomic with minimal intermolecular forces — the definition of ideal gas behavior in practice.
Non-ideal gases: CO₂, water vapor (H₂O), and ammonia (NH₃) deviate significantly from the ideal gas definition because they have strong intermolecular forces. High pressure (molecules close together) and low temperature (near condensation) make any gas non-ideal. The difference between an ideal gas and a non-ideal gas is largest near the gas’s condensation point.
Rule of thumb for gas law problems: Gas law formulas give accurate results when P < 10 atm and T > 200 K for most gases. Beyond these limits, use the Van der Waals equation to correct for non-ideal behavior.
Gas Law Formulas — Which One to Use?
Every combined gas law problem begins with identifying which of the four gas law formulas applies. The choice depends entirely on which variable is held constant. Use this table as your first step in any gas law practice problem:
| Situation | Gas Law Formula | What’s Constant |
|---|---|---|
| Pressure changes, temperature constant | P₁V₁ = P₂V₂ (Boyle’s law) | T, n |
| Volume changes, pressure constant | V₁/T₁ = V₂/T₂ (Charles’s law) | P, n |
| Pressure changes, volume constant | P₁/T₁ = P₂/T₂ (Gay-Lussac’s law) | V, n |
| All three variables change | P₁V₁/T₁ = P₂V₂/T₂ (Combined gas law) | n only |
| Need moles or mass | PV = nRT (Ideal gas law) | — |
The combined gas law contains all three individual laws:
Set T₁ = T₂ in the combined gas law → Boyle’s law (P₁V₁ = P₂V₂) emerges automatically.
Set P₁ = P₂ in the combined gas law → Charles’s law (V₁/T₁ = V₂/T₂) emerges.
Set V₁ = V₂ in the combined gas law → Gay-Lussac’s law (P₁/T₁ = P₂/T₂) emerges.
This is why the combined gas law P₁V₁/T₁ = P₂V₂/T₂ is the master formula — when in doubt, use it and cancel the constant variable. The gas chemical equation PV = nRT (the ideal gas law) is the further generalization that includes the number of moles.
Boyle’s Law Problems — Pressure and Volume at Constant Temperature
Boyle’s law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. When pressure increases, volume decreases proportionally, and vice versa. Boyle’s law problems are the only gas law problems where temperature conversion to Kelvin is not required (temperature doesn’t appear in the formula) — but temperature must still be verified as constant.
Charles’s Law Problems — Volume and Temperature at Constant Pressure
Charles’s law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature: V₁/T₁ = V₂/T₂. Temperature must always be in Kelvin — using Celsius produces answers that can be wrong by a factor of 3 or more, as Problem 3 demonstrates explicitly. This is the most critical rule in all Charles’s law problems.
The Celsius error produces a number (14.1 L) that looks plausible — it has units, it’s positive — but it is 3.5× wrong. There is no calculation error to spot. The only protection is the habit of converting to Kelvin before every single substitution, every single time.
Gay-Lussac’s Law Problems — Pressure and Temperature at Constant Volume
Gay-Lussac’s law states that for a fixed amount of gas in a rigid container (constant volume), pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂. Gay-Lussac’s law applies whenever the problem mentions a “rigid container,” “sealed vessel,” or “constant volume.” Temperature must always be in Kelvin — the same rule applies to Gay-Lussac’s law as to every other gas law formula.
Combined Gas Law Problems — All Three Variables Change
The combined gas law P₁V₁/T₁ = P₂V₂/T₂ applies when pressure, volume, and temperature all change simultaneously, but the amount of gas (n) remains constant. These combined gas law practice problems require careful algebraic rearrangement and temperature must always be in Kelvin for both T₁ and T₂. The combined gas law is the most versatile formula on this worksheet — when in doubt, start here.
Combined Gas Law — Finding Temperature Problems
Some combined gas law practice problems ask you to find the final temperature. The method is the same — rearrange the combined gas law for T₂ — but you must remember to convert your answer back to Celsius if the question asks for °C. Always solve for T₂ in Kelvin first, then convert.
Ideal Gas Law Problems — Using PV = nRT
The ideal gas law PV = nRT is used when you need to find the number of moles (n) or mass of gas. Unlike the combined gas law (which compares two states), the ideal gas law relates all four variables — pressure, volume, moles, and temperature — in a single state. Temperature must be in Kelvin, and the gas constant R must match your pressure units: R = 0.082057 L·atm/(mol·K) when P is in atm; R = 8.31446 L·kPa/(mol·K) when P is in kPa.
Challenge Problem — Multi-Step Gas Law
This challenge combined gas law problem requires applying three different gas law formulas sequentially. It represents the highest level of combined gas law practice problems — multi-step problems where the output of one step becomes the input of the next. Identify each step independently before calculating.
Gas Law Assumptions and When They Break Down
The combined gas law and ideal gas law give accurate results only when the assumptions of an ideal gas approximately hold. Understanding when these gas law assumptions fail — and why — tells you when to distrust your calculated answer and apply corrections.
High pressure (P > 10 atm): Gas molecules are close together. Their actual volume becomes a significant fraction of the container, and intermolecular attractive forces matter. Both ideal gas model assumptions (negligible volume, no intermolecular forces) break down. The Van der Waals equation adds correction terms for both effects.
Low temperature (near condensation point): Kinetic energy decreases, and intermolecular attractive forces become dominant. The gas begins to behave like a liquid, and the ideal gas definition no longer applies. Gas law formulas give increasingly inaccurate results as temperature approaches the condensation point.
Large or polar molecules: CO₂, NH₃, and H₂O vapor deviate significantly from ideal gas behavior because they have strong London dispersion forces (CO₂) or permanent dipoles and hydrogen bonding (NH₃, H₂O). Helium and hydrogen are the most ideal real gases because they are small and nonpolar — closest to the ideal gas definition.
Rule of thumb for gas law practice problems: Combined gas law and ideal gas law formulas give results accurate to within ~1% when P < 10 atm and T > 200 K for most common gases. Beyond these limits, the assumptions of an ideal gas become increasingly unreliable.
How to Identify Which Gas Law to Use — Decision Flowchart
Use this decision tree at the start of every combined gas law problem or gas law practice problem. Correctly identifying which gas law formula to apply before calculating is the single most important skill for combined gas law worksheets.
Common Mistakes in Gas Law Problems
These five mistakes account for the majority of wrong answers on combined gas law worksheets and gas law practice problem sets. Each example shows the wrong approach and the correct approach side by side.
Temperature must always be in Kelvin in every gas law formula except Boyle’s Law. Using Celsius produces a plausible-looking number that is completely wrong.
If temperature is constant, use Boyle’s law directly. If you apply the combined gas law and cancel T₁ = T₂, you get the right answer — but the extra algebra increases the risk of arithmetic errors. Always identify the constant variable first.
The value of R depends on your pressure units. Mixing R values with incompatible units gives answers off by a factor of 101.325.
P₁ and P₂ must be in the same units. V₁ and V₂ must be in the same units. Mixing atm on one side with kPa on the other produces a completely wrong answer without any obvious error to spot.
When rearranging the combined gas law for V₂, T₂ goes in the numerator and T₁ in the denominator. Swapping them gives a wrong answer that is off by the square of the temperature ratio.
Memory aid: the combined gas law formula is P₁V₁/T₁ = P₂V₂/T₂. When you cross-multiply and rearrange for V₂, T₂ moves to the numerator and T₁ moves to the denominator — opposite sides from where they start.
Frequently Asked Questions — Combined Gas Law Problems
What is the combined gas law and when do you use it?
The combined gas law is P₁V₁/T₁ = P₂V₂/T₂, where P is pressure, V is volume, and T is temperature in Kelvin. It applies when a fixed amount of gas (constant n) undergoes a change in which all three variables — pressure, volume, and temperature — change simultaneously. If any one variable is held constant, a simpler formula (Boyle’s law, Charles’s law, or Gay-Lussac’s law) applies instead. The combined gas law contains all three simpler laws as special cases: set T₁ = T₂ to get Boyle’s law, set P₁ = P₂ to get Charles’s law, set V₁ = V₂ to get Gay-Lussac’s law.
When do you use Boyle’s law vs Charles’s law vs Gay-Lussac’s law?
The choice depends on which variable is constant. Use Boyle’s law (P₁V₁ = P₂V₂) when temperature is constant. Use Charles’s law (V₁/T₁ = V₂/T₂) when pressure is constant. Use Gay-Lussac’s law (P₁/T₁ = P₂/T₂) when volume is constant — typically indicated by a “rigid container” or “sealed vessel” in the problem. Use the combined gas law (P₁V₁/T₁ = P₂V₂/T₂) when all three variables change. Use the ideal gas law (PV = nRT) when you need moles or mass. Temperature must be in Kelvin for all laws except Boyle’s law.
What is the ideal gas law PV = nRT?
The ideal gas law PV = nRT relates pressure (P), volume (V), moles (n), the gas constant (R), and temperature (T) for an ideal gas. Unlike the combined gas law (which compares two states), the ideal gas law describes a single state completely. The gas constant R = 0.082057 L·atm/(mol·K) when pressure is in atm and volume in litres; R = 8.31446 L·kPa/(mol·K) when pressure is in kPa. Temperature must always be in Kelvin. The ideal gas law PV = nRT is the most general gas law formula — the combined gas law is derived from it by holding n constant.
Why must temperature always be in Kelvin in gas law formulas?
Temperature must always be in Kelvin because gas laws describe proportional relationships that require an absolute temperature scale. On the Kelvin scale, 0 K (absolute zero) is the point where gas molecules have zero kinetic energy and zero volume — a true physical zero. Celsius zero (0°C = 273.15 K) is arbitrary. Using Celsius produces completely wrong answers: in Charles’s law (V₁/T₁ = V₂/T₂), a gas at 0°C would appear to have infinite volume relative to a gas at 0.001°C. Using Celsius temperatures like 27°C and 54°C gives a temperature ratio of 2.0, implying volume doubles — but the Kelvin ratio (300 K / 327 K = 1.09) correctly shows only a 9% increase. Always convert: K = °C + 273.15.
What is an ideal gas and what are its assumptions?
An ideal gas is a theoretical gas that obeys PV = nRT exactly under all conditions. The five assumptions of an ideal gas are: (1) molecules have negligible volume (treated as point masses); (2) no intermolecular forces between molecules; (3) all collisions are perfectly elastic; (4) molecules move in constant, random motion; (5) average kinetic energy is directly proportional to absolute temperature in Kelvin. The ideal gas definition in chemistry is a gas obeying these assumptions. Real gases approximate ideal behavior at low pressure and high temperature. Noble gases like helium and neon are the best real-world ideal gas examples. Non-ideal gases like CO₂ and NH₃ deviate because of strong intermolecular forces.
What are gas formulas in chemistry and which is most important?
The main gas formulas in chemistry are: Boyle’s law (P₁V₁ = P₂V₂), Charles’s law (V₁/T₁ = V₂/T₂), Gay-Lussac’s law (P₁/T₁ = P₂/T₂), the combined gas law (P₁V₁/T₁ = P₂V₂/T₂), and the ideal gas law (PV = nRT). The most important and general gas formula is the ideal gas law PV = nRT, from which all others can be derived. The combined gas law is the most versatile for combined gas law practice problems because it handles all scenarios involving two states of a gas. For gas law practice problems on exams, mastering the identification of which formula applies is as important as knowing the formulas themselves.
Related Calculators and Gas Law Tools
⚗️ Ideal Gas Law Calculator
Solve PV = nRT and all combined gas law problems instantly. Enter any three variables and get the fourth with full step-by-step working. Covers Boyle’s law, Charles’s law, Gay-Lussac’s law, and the combined gas law.
🔢 Pressure Calculator
Calculate pressure using P = F/A or hydrostatic pressure P = ρgh. Includes pressure unit conversion across Pa, kPa, atm, psi, bar, and mmHg — useful for gas law problems requiring pressure conversion.
🧪 Molarity Calculator
Connect gas law mole calculations to solution chemistry. Find molarity, moles, volume, or mass for solutions. Combines with the ideal gas law PV = nRT for complete stoichiometry problems involving gases and solutions.
⚖️ Stoichiometry Calculator
Practice stoichiometry with gases — combine mole ratios from balanced equations with the ideal gas law to find volumes and masses of gaseous reactants and products.