Science, Tech, Math › Science What Is the Ideal Gas Law? Ideal Gas Law and Equations of State Share Flipboard Email Print Most of the time, the Ideal Gas Law can be used to make calculations for real gases. Ben Edwards, Getty Images Science Chemistry Chemical Laws Basics Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry In Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate By Anne Marie Helmenstine, Ph.D. Chemistry Expert Ph.D., Biomedical Sciences, University of Tennessee at Knoxville B.A., Physics and Mathematics, Hastings College Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. She has taught science courses at the high school, college, and graduate levels. our editorial process Facebook Facebook Twitter Twitter Anne Marie Helmenstine, Ph.D. Updated April 03, 2019 The Ideal Gas Law is one of the Equations of State. Although the law describes the behavior of an ideal gas, the equation is applicable to real gases under many conditions, so it is a useful equation to learn to use. The Ideal Gas Law may be expressed as: PV = NkT where:P = absolute pressure in atmospheresV = volume (usually in liters)n = number of particles of gask = Boltzmann's constant (1.38·10−23 J·K−1)T = temperature in Kelvin The Ideal Gas Law may be expressed in SI units where pressure is in pascals, volume is in cubic meters, N becomes n and is expressed as moles, and k is replaced by R, the Gas Constant (8.314 J·K−1·mol−1): PV = nRT Ideal Gases Versus Real Gases The Ideal Gas Law applies to ideal gases. An ideal gas contains molecules of a negligible size that have an average molar kinetic energy that depends only on temperature. Intermolecular forces and molecular size are not considered by the Ideal Gas Law. The Ideal Gas Law applies best to monoatomic gases at low pressure and high temperature. Lower pressure is best because then the average distance between molecules is much greater than the molecular size. Increasing the temperature helps because of the kinetic energy of the molecules increases, making the effect of intermolecular attraction less significant. Derivation of the Ideal Gas Law There are a couple of different ways to derive the Ideal as Law. A simple way to understand the law is to view it as a combination of Avogadro's Law and the Combined Gas Law. The Combined Gas Law may be expressed as: PV / T = C where C is a constant that is directly proportional to the quantity of the gas or number of moles of gas, n. This is Avogadro's Law: C = nR where R is the universal gas constant or proportionality factor. Combining the laws: PV / T = nRMultiplying both sides by T yields:PV = nRT Ideal Gas Law - Worked Example Problems Ideal vs Non-Ideal Gas ProblemsIdeal Gas Law - Constant VolumeIdeal Gas Law - Partial PressureIdeal Gas Law - Calculating MolesIdeal Gas Law - Solving for PressureIdeal Gas Law - Solving for Temperature Ideal Gas Equation for Thermodynamic Processes Process(Constant) KnownRatio P2 V2 T2 Isobaric(P) V2/V1T2/T1 P2=P1P2=P1 V2=V1(V2/V1)V2=V1(T2/T1) T2=T1(V2/V1)T2=T1(T2/T1) Isochoric(V) P2/P1T2/T1 P2=P1(P2/P1)P2=P1(T2/T1) V2=V1V2=V1 T2=T1(P2/P1)T2=T1(T2/T1) Isothermal(T) P2/P1V2/V1 P2=P1(P2/P1)P2=P1/(V2/V1) V2=V1/(P2/P1)V2=V1(V2/V1) T2=T1T2=T1 isoentropicreversibleadiabatic(entropy) P2/P1V2/V1T2/T1 P2=P1(P2/P1)P2=P1(V2/V1)−γP2=P1(T2/T1)γ/(γ − 1) V2=V1(P2/P1)(−1/γ)V2=V1(V2/V1)V2=V1(T2/T1)1/(1 − γ) T2=T1(P2/P1)(1 − 1/γ)T2=T1(V2/V1)(1 − γ)T2=T1(T2/T1) polytropic(PVn) P2/P1V2/V1T2/T1 P2=P1(P2/P1)P2=P1(V2/V1)−nP2=P1(T2/T1)n/(n − 1) V2=V1(P2/P1)(-1/n)V2=V1(V2/V1)V2=V1(T2/T1)1/(1 − n) T2=T1(P2/P1)(1 - 1/n)T2=T1(V2/V1)(1−n)T2=T1(T2/T1) Calculate Pressure of a Gas Using Van Der Waal's Equation How to Calculate the Density of a Gas What Is Avogadro's Law? Ideal Gas Law Test Questions Review the Ideal Gas Law With These Worked Chemistry Sample Problems The Major Laws of Chemistry What Is the Ideal Gas Law Definition and Equation? Review Gay-Lussac's Gas Law Know the Density of Air at STP 3 Ways To Increase the Pressure of a Gas Specific Volume: What It Means And How to Calculate It How to Solve a Charles' Gas Law Problem Your Chemistry Study Guide for Gases What Is the Most Ideal Gas? Here's How to Use the Boyle's Law Formula for Ideal Gases What Is an Ideal or Perfect Gas?