Gas Laws

The Gas Laws are mathematical The gas laws will describe HOW gases behave. Gas behavior can be predicted by the theory. The amount of change can be calculated with mathematical equations. You need to know both of these: the theory, and the math

Variables for Gas Laws P=pressure V=volume T=temperature n=number of moles R=gas constant

Units for Gas Laws P=pressure (mmHg, atm, torr, kPa) V=volume (Liters or L) T=temperature (Kelvin or K) n=number of moles (mol) R=gas constant (atm x L/mol x K)

Robert Boyle (1627-1691)

#1. Boyle’s Law - 1662 Gas pressure is inversely proportional to the volume, when temperature is held constant. Pressure x Volume = a constant Equation: P1V1 = P2V2 (T = constant)

Graph of Boyle’s Law Boyle’s Law says the pressure is inverse to the volume. Note that when the volume goes up, the pressure goes down

Jacques Charles (1746-1823)

#2. Charles’s Law - 1787 The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant. This extrapolates to zero volume at a temperature of zero Kelvin.

Graph of Charles’ Law Charles’ Law says the volume is proportional to the temperature. Note that when the volume goes up, the temp goes up

Converting Celsius to Kelvin Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.) Kelvin = C + 273 °C = Kelvin - 273 and

Converting pressure 1 atm = 760 mmHg 1 atm = 760 torr 1 atm = 101.3 kPa

Converting grams to moles 1 mole = molar mass in grams

Joseph Louis Gay-Lussac (1778 – 1850)

#3. Gay-Lussac’s Law - 1802 The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. How does a pressure cooker affect the time needed to cook food?

Graph of Gay-Lussac’s Law Gay-Lussac’s Law says the pressure is proportional to the temperature. Note that when the pressure goes up, the temp goes up

#4. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

The combined gas law contains all the other gas laws! If the temperature remains constant... P1 x V1 P2 x V2 = T1 T2 Boyle’s Law

P1 x V1 P2 x V2 = T1 T2 Charles’s Law The combined gas law contains all the other gas laws! If the pressure remains constant... P1 x V1 P2 x V2 = T1 T2 Charles’s Law

P1 x V1 P2 x V2 = T1 T2 Gay-Lussac’s Law The combined gas law contains all the other gas laws! If the volume remains constant... P1 x V1 P2 x V2 = T1 T2 Gay-Lussac’s Law

5. The Ideal Gas Law #1 R = 0.0802 (L x atm) / (mol x K) Equation: PV = nRT Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the Temperature in Kelvin. R = 0.0802 (L x atm) / (mol x K)

The Ideal Gas Law We now have a new way to count moles (the amount of matter), by measuring T, P, and V. P x V R x T n =

Ideal Gases We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure An ideal gas does not really exist, but it makes the math easier and is a close approximation. Particles have no volume? Wrong! No attractive forces? Wrong!

Ideal Gases There are no gases for which this is true (acting “ideal”); however, Real gases behave this way at a) high temperature, and b) low pressure. Because at these conditions, a gas will stay a gas!