Kinetic Molecular Theory of Gases A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. Gas molecules exert neither attractive nor repulsive forces on one another. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy KE = 1 2 𝑚 𝑢 2

Use the data to sketch a plot of Pressure versus Volume Pressure (mmHg) 724 869 951 998 1230 1893 2250 Volume (Liters) 1.5 1.33 1.22 1.18 0.94 0.61 0.58 Does your sketch reflect a linear relationship between pressure and volume?

Pressure (mmHg) 724 869 951 998 1230 1893 2250 Volume (Liters) 1.5 What happens to pressure as the volume decreases? What is this kind of relationship called? Calculate 1/V for each pressure. Sketch a plot of P vs 1/V Pressure (mmHg) 724 869 951 998 1230 1893 2250 Volume (Liters) 1.5 1.33 1.22 1.18 0.94 0.61 0.58

Boyle’s Law 𝑃∝ 1 𝑉 Constant temperature 𝑃×𝑉=constant Constant amount of gas 𝑃×𝑉=constant 𝑃 1 × 𝑉 1 = 𝑃 2 × 𝑉 2

Variation of Gas Volume with Temperature at Constant Pressure Charles’ & Gay-Lussac’s Law 𝑉∝𝑇 Temperature must be in Kelvin 𝑉=constant×𝑇 𝑉 1 𝑇 1 = 𝑉 2 𝑇 2 𝑇 K =𝑡 °C +2.73.15

Avogadro’s Law 𝑉∝number of moles 𝑛 𝑉=constant×𝑛 𝑉 1 𝑛 1 = 𝑉 2 𝑛 2 Constant temperature Constant pressure 𝑉∝number of moles 𝑛 𝑉=constant×𝑛 𝑉 1 𝑛 1 = 𝑉 2 𝑛 2

Summary of Gas Laws Boyle’s Law

Charles’s Law Copyright © McGrew-Hill Education. Permission required for reproduction or display.

Avogadro’s Law (1) Copyright © McGrew-Hill Education. Permission required for reproduction or display.

Ideal Gas Equation Boyle’s law: 𝑃∝ 1 𝑉 (at constant n and T) Charles’s law: 𝑉∝𝑇 (at constant n and P) Avogadro’s law: 𝑉∝𝑛 (at constant P and T) 𝑉∝ 𝑛𝑇 𝑃 𝑉=constant× 𝑛𝑇 𝑃 =𝑅 𝑛𝑇 𝑃 R is the gas constant 𝑃𝑉=𝑛𝑅𝑇

Standard Temperature and Pressure The conditions 0 °C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. 𝑃𝑉=𝑛𝑅𝑇 𝑅= 𝑃𝑉 𝑛𝑇 = 1 atm 22.414L 1 mol 273.15 K 𝑅=0.082057 L∙atm mol∙K