The Behavior of Gases Chapter 5

Kinetic Theory Review The following five tenets are the basis for ideal gases Gases consist of hard spherical particles Particles have insignificant volume There are large distances between particles There are NO attractive or repulsive forces between particles Particles are in constant, random motion with elastic collisions

Variables and Equations 4 variables are pressure (P) in kilopascals, temperature (T) in kelvins, volume (V) in liters, and number of moles (n). Help to understand everyday applications such as airbags, scuba-diving equipment, and hot-air balloons.

Compressibility Why are gases compressed more easily than liquids or solids? How does the overall volume of the particles in a gas compare to the overall volume of the gas How does an airbag work?

Amount of a Gas What happens to the pressure if you double the amount of particles in a rigid container? How does an aerosol can work?

Volume If you double the volume of a rigid container, what can be said about the pressure? What about if you halve the volume?

Temperature When you increase the temperature of gas molecules in a container, what happens to the pressure? The molecules gain more KE, move faster, and thus create more pressure. If you leave a bag of potato chips in the sun, it will bulge at the seams

Gas Laws Boyle’s Law Charles’ Law Gay-Lussac’s Law Combined Gas Law Ideal Gas Law Dalton’s Law Graham’s Law

Boyle’s Law As volume increases, pressure _________. Therefore, volume and pressure are inversely related We can show this by P 1 V 1 = P 2 V 2

Charles’ Law As temperature increases, volume _________. Therefore temperature and volume are directly related. We can show this by

Gay-Lussac’s Law As the pressure of an enclosed gas increases, the temperature __________. Therefore temperature and pressure are directly related. We can show this by

The Combined Gas Law We can combine the previous three laws into one law that involves P, T and V. The combined gas law is written as

The Ideal Gas Law To calculate the number of moles of a contained gas, we use the variable ‘n’ The ideal gas law is PV = nRT R is known as the ideal gas constant R = 8.31 (if pressure is in kPa) R = (if pressure is in atm)

Ideal Gas Law PV = nRT What are the units on R? Can we derive the value for R? Remember that at STP, T = 273 K, P = kPa, n = 1 mol, V = 22.4 L

Ideal vs. Real Real gases differ most from an ideal gas at low temperatures and high pressures Remember, in reality, there are attractive forces between molecules

Dalton’s Law Also known as the law of partial pressures: In a mixture of gases, the total pressure is the sum of the partial pressures of the gases Simply, P total = P 1 + P 2 + P 3 + … Why would a climber at the top of Mt. Everest care about Dalton’s Law?

Graham’s Law Gases with a lower molar mass will diffuse faster than gases with a larger mass It makes sense that a lighter object will have to move faster to have the same energy as a larger object moving slowly We can show this law as

How to Solve Problems Here is a sample problem: 5 moles of gas is heated to 400K in a 2.5 L container. What is the pressure of the gas? Identify and write down variables. n = 5, T = 400K, V = 3.5 L N – 5, T = 5, 400