Combined Gas Law Calculator

Solve for pressure, volume, or temperature using the combined gas law equation.

The Combined Gas Law relates pressure, volume, and temperature of a gas sample. Enter five known values and calculate the unknown variable.

Examples

Click on any example to load it into the calculator.

Basic Pressure Change

Basic Pressure Change

Calculate final pressure when volume and temperature change.

P₁: 1.0 atm

V₁: 2.0 L

T₁: 273 K

V₂: 1.5 L

T₂: 300 K

Volume Expansion

Volume Expansion

Calculate final volume when pressure decreases and temperature increases.

P₁: 2.0 atm

V₁: 1.0 L

T₁: 250 K

P₂: 1.5 atm

T₂: 300 K

Temperature Change

Temperature Change

Calculate final temperature when pressure and volume change.

P₁: 1.5 atm

V₁: 3.0 L

T₁: 280 K

P₂: 2.0 atm

V₂: 2.5 L

Realistic Gas Compression

Realistic Gas Compression

A realistic example of gas compression in a cylinder.

P₁: 101.3 atm

V₁: 5.0 L

T₁: 298 K

P₂: 202.6 atm

T₂: 350 K

Other Titles
Understanding the Combined Gas Law: A Comprehensive Guide
Master the fundamental relationship between pressure, volume, and temperature in gases. This guide covers the mathematical foundation, practical applications, and common misconceptions about gas behavior.

What is the Combined Gas Law?

  • Mathematical Foundation
  • Physical Meaning
  • Historical Development
The Combined Gas Law is a fundamental equation in chemistry and physics that describes the relationship between pressure (P), volume (V), and temperature (T) of a gas sample. It combines three individual gas laws: Boyle's Law (pressure-volume relationship), Charles's Law (volume-temperature relationship), and Gay-Lussac's Law (pressure-temperature relationship). The mathematical expression is P₁V₁/T₁ = P₂V₂/T₂, where the subscripts 1 and 2 represent initial and final states respectively.
The Mathematical Foundation
The Combined Gas Law equation P₁V₁/T₁ = P₂V₂/T₂ represents a constant ratio that must be maintained when a gas undergoes changes in pressure, volume, or temperature. This ratio is proportional to the number of moles of gas present and the gas constant R. The equation assumes that the amount of gas (number of moles) remains constant and that the gas behaves ideally. This means the gas particles have negligible volume and no intermolecular forces.
Physical Interpretation
The Combined Gas Law tells us that when a gas sample changes from one state to another, the product of pressure and volume divided by temperature remains constant. This makes intuitive sense: if you increase the pressure on a gas while keeping temperature constant, the volume decreases (Boyle's Law). If you heat a gas while keeping pressure constant, the volume increases (Charles's Law). The Combined Gas Law allows us to predict what happens when all three variables change simultaneously.
Historical Development
The Combined Gas Law evolved from centuries of experimental work. Robert Boyle (1627-1691) discovered the inverse relationship between pressure and volume. Jacques Charles (1746-1823) found that volume increases linearly with temperature. Joseph Louis Gay-Lussac (1778-1850) established the direct relationship between pressure and temperature. These three laws were later combined into the single equation we use today, which was further developed into the Ideal Gas Law (PV = nRT) by combining it with Avogadro's Law.

Key Concepts in Gas Behavior:

  • Direct Relationship: When two variables increase or decrease together (P and T, V and T)
  • Inverse Relationship: When one variable increases while the other decreases (P and V)
  • Proportionality: The ratio P×V/T remains constant for a given amount of gas
  • Ideal Gas Assumption: Gas particles have no volume and no intermolecular forces

Step-by-Step Guide to Using the Calculator

  • Identifying Known Variables
  • Unit Conversion
  • Solving the Equation
Using the Combined Gas Law Calculator requires careful attention to units and a systematic approach to problem-solving. Follow these steps to ensure accurate results.
1. Identify Your Known Variables
Start by carefully reading the problem and identifying which five variables you know. You need exactly five known values to solve for the sixth unknown. Common scenarios include: calculating final pressure after volume and temperature changes, finding final volume when pressure and temperature change, or determining final temperature when pressure and volume are modified. Make sure you understand whether you're dealing with initial or final conditions.
2. Convert All Units to Consistent System
The most critical step is ensuring all units are consistent. Temperature must always be in Kelvin (K). Convert from Celsius by adding 273.15, from Fahrenheit using the formula (F-32)×5/9+273.15. Pressure can be in atmospheres (atm), kilopascals (kPa), or other units, but all pressure values must use the same unit. Volume can be in liters (L), cubic meters (m³), or other units, but again, consistency is key. The calculator will work with any consistent unit system.
3. Enter Values and Solve
Input your five known values into the calculator, leaving the unknown variable empty. The calculator will automatically detect which variable is missing and solve for it. Double-check your inputs before calculating. Common errors include forgetting to convert temperature to Kelvin, mixing pressure units, or entering values in the wrong fields. The calculator will validate your inputs and provide error messages if needed.
4. Interpret and Verify Results
Once you get your result, verify that it makes physical sense. If you increased pressure and temperature while decreasing volume, the calculated value should reflect these changes appropriately. Check that the units are correct and that the magnitude of the result is reasonable. If the result seems unrealistic, review your input values and unit conversions.

Common Unit Conversions:

  • Temperature: °C to K = °C + 273.15, °F to K = (°F-32)×5/9+273.15
  • Pressure: 1 atm = 101.325 kPa = 760 mmHg = 14.696 psi
  • Volume: 1 L = 0.001 m³ = 1000 cm³ = 61.02 in³
  • Always use Kelvin for temperature calculations in gas laws

Real-World Applications of the Combined Gas Law

  • Industrial Processes
  • Environmental Science
  • Medical Applications
The Combined Gas Law has countless applications in modern science and technology, from industrial processes to medical treatments and environmental monitoring.
Industrial and Engineering Applications
In chemical engineering, the Combined Gas Law is essential for designing reactors, distillation columns, and storage tanks. Engineers use it to predict how gases will behave under different operating conditions. For example, when designing a gas storage system, engineers must account for temperature changes that affect pressure and volume. The law is also crucial in the petroleum industry for understanding gas behavior in pipelines and storage facilities.
Environmental and Atmospheric Science
Meteorologists use gas laws to understand atmospheric pressure changes and predict weather patterns. The Combined Gas Law helps explain why air pressure decreases with altitude and how temperature changes affect atmospheric density. Environmental scientists apply these principles to study air pollution dispersion, greenhouse gas behavior, and climate change modeling. Understanding gas behavior is crucial for predicting how pollutants spread in the atmosphere.
Medical and Biological Applications
In medicine, the Combined Gas Law is fundamental to respiratory physiology. It explains how breathing works: when you inhale, your diaphragm contracts, increasing lung volume and decreasing pressure, allowing air to flow in. The law is also essential in anesthesia, where precise control of gas mixtures and pressures is critical. In scuba diving, understanding gas behavior at different depths (pressures) is vital for safety and decompression planning.

Practical Examples:

  • Scuba diving: Gas volume decreases with depth (increased pressure)
  • Hot air balloons: Air expands when heated, reducing density
  • Automotive engines: Gas compression and expansion in cylinders
  • Respiratory systems: Lung volume changes during breathing

Common Misconceptions and Correct Methods

  • Temperature Units
  • Ideal vs Real Gases
  • Variable Relationships
Many students and practitioners make common errors when applying the Combined Gas Law. Understanding these misconceptions is crucial for accurate calculations.
Misconception: Temperature Can Be in Celsius or Fahrenheit
This is the most common and critical error. The Combined Gas Law requires absolute temperature in Kelvin. Using Celsius or Fahrenheit will give incorrect results because these scales have arbitrary zero points. Kelvin has an absolute zero (0 K = -273.15°C), which is essential for gas law calculations. Always convert temperatures to Kelvin before using the equation. Remember: 0°C = 273.15 K, and 0°F = 255.37 K.
Misconception: The Law Works for All Gases Under All Conditions
The Combined Gas Law assumes ideal gas behavior, which is a good approximation for most gases at moderate temperatures and pressures. However, real gases deviate from ideal behavior at high pressures or low temperatures. Under these conditions, intermolecular forces and particle volume become significant. For very accurate calculations with real gases, more complex equations like the van der Waals equation are needed.
Misconception: All Variables Must Change
The Combined Gas Law applies even when only one or two variables change. For example, if temperature remains constant, you're essentially using Boyle's Law (P₁V₁ = P₂V₂). If pressure is constant, you're using Charles's Law (V₁/T₁ = V₂/T₂). The Combined Gas Law is more general and includes these special cases. You can hold any variable constant and still use the equation.

Error Prevention Tips:

  • Always convert temperature to Kelvin before calculation
  • Use consistent units for pressure and volume
  • Verify that exactly one variable is unknown
  • Check that results make physical sense

Mathematical Derivation and Examples

  • Derivation from Individual Laws
  • Problem-Solving Strategies
  • Advanced Applications
Understanding the mathematical foundation of the Combined Gas Law helps develop intuition for gas behavior and enables solving complex problems.
Derivation from Individual Gas Laws
The Combined Gas Law can be derived by combining Boyle's Law (P₁V₁ = P₂V₂ at constant T), Charles's Law (V₁/T₁ = V₂/T₂ at constant P), and Gay-Lussac's Law (P₁/T₁ = P₂/T₂ at constant V). When we allow all three variables to change, we can combine these relationships. Starting with Boyle's Law and then applying Charles's Law to both sides, we arrive at P₁V₁/T₁ = P₂V₂/T₂. This derivation shows how the individual laws are special cases of the more general Combined Gas Law.
Problem-Solving Strategies
Effective problem-solving with the Combined Gas Law involves several strategies. First, always draw a clear diagram showing initial and final states. Label all known and unknown variables. Second, convert all units to a consistent system, especially ensuring temperature is in Kelvin. Third, identify which variable is unknown and rearrange the equation if necessary. Fourth, substitute values and solve step-by-step. Finally, verify your answer by checking units and ensuring the result makes physical sense.
Advanced Applications and Extensions
The Combined Gas Law can be extended to include changes in the amount of gas (moles) by incorporating Avogadro's Law, leading to the Ideal Gas Law: PV = nRT. This more general equation allows calculations involving chemical reactions and gas mixtures. For real gases, the van der Waals equation (P + a(n/V)²)(V - nb) = nRT provides better accuracy by accounting for intermolecular forces and particle volume. These extensions build upon the foundation provided by the Combined Gas Law.

Sample Calculations:

  • A gas at 1.0 atm, 2.0 L, 273 K changes to 2.0 atm, 1.5 L. Find final temperature.
  • A balloon at 1.5 atm, 3.0 L, 280 K changes to 2.0 atm, 2.5 L. Find final temperature.
  • A gas cylinder at 101.3 kPa, 5.0 L, 298 K is compressed to 202.6 kPa at 350 K. Find final volume.