# Kinetic Molecular Theory (KMT) of Gases KMT is a model to explain the behavior of gaseous particles and is based on extensive observations of the behavior.

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Kinetic Molecular Theory (KMT) of Gases KMT is a model to explain the behavior of gaseous particles and is based on extensive observations of the behavior of gases. If a gas follows all the postulates of the the KMT it is said to be an ideal gas.

Postulates of the KMT Particles are in constant, random, straight line motion. Collisions with walls of their container generate pressure. The actual volume of gas particles is negligible. Particles are far apart. The volume of a gas is effectively the volume the particles occupy, not their particle volume.

Postulates of the KMT Gas particles do not attract or repel. The average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of the gas.

Ideal vs Real Gases How do gas volumes respond under a range of conditions (such as changing pressures and temperatures)? If a gas is ideal, the graph of PV/RT vs P for one mole of gas will have a slope of 1. http://intro.chem.okstate.edu/1314F97/Chap ter10/RealGas.htmlhttp://intro.chem.okstate.edu/1314F97/Chap ter10/RealGas.html

Deviations from Ideality For an ideal gas: PV = nRT or V = nRT/P When you actually measure gas volume at high pressures and low temperatures, the V experimental often does not match V theoretical

Deviations from Ideality Why doesn’t V exp = V theor ? If V exp > V theor :  Some gas particles do repel each other so volume is greater than predicted.  Gas particles do have a volume so volume cannot be reduced beyond a certain point.

Deviations from Ideality Why doesn’t V exp = V theor ? If V exp < V theor :  Some gas particles do attract each other so volume is reduced more than expected.

Corrections for Deviations from Ideality Johannes van der Waals modified the ideal gas law to account for deviations. P x V = nRT [P exp + a(n/V) 2 ] x (V-nb) = nRT  [P exp + a(n/V) 2 ] corrects for attractive or repulsive forces (“a” depends on the particle)  V-nb corrects for particle volume (“b” is a measure of particle volume)

GasFormulaa [(L 2 · atm)/mole 2 ]b [L/mole] HeliumHe0.034120.02370 HydrogenH2H2 0.24440.02661 NitrogenN2N2 1.3900.03913 OxygenO2O2 1.3600.03183 Carbon dioxideCO 2 3.5920.04267 AcetyleneC2H2C2H2 4.3900.05136 ChlorineCl 2 6.4930.05622 n - ButaneC 4 H 10 14.470.1226 n - OctaneC 8 H 18 37.320.2368 Selected Values for a and b for the van der Waals Equation

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