Gas Laws Chapter 12

Boyle’s Law: The Pressure-Volume Relationship The Anglo-Irish chemist, Robert Boyle ( ), was the first person to do systematic studies of pressure and volume concerning gases. In 1662 he proposed a law to describe this relationship. If pressure increases, volume decreases. If pressure decreases, volume increases. This is assuming that the number of molecules and the temperature remain constant. P 1 V 1 = P 2 V 2

This relationship is an inverse relationship. Pressure is inversely proportional to volume. With an inverse proportion, the product will always be equal to a constant.

A proof for an inverse proportion… In the pressure-volume lab, an inverse proportion graph was generated. By making the x-axis the reciprocal of the volume (1/V), a new graph can be generated that will be a direct proportion and linear.

Boyle’s Law Practice Problem A high altitude balloon contains 30.0 L of helium gas at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kPa? (assume temperature remains constant) 124 L

Charles’ Law: Temperature-Volume Relationship In 1787, French physicist (and balloonist) Jacque Charles investigated the effect of temperature on the volume of a gas at constant pressure. Charles’ Law: the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. V 1 V 2 T 1 T 2

A proof for a direct proportion… Graphing a direct proportionality will give a linear graph. For Charles’ Law, as the temperature of a gas increases, the volume will increase.

Charles’ Law Practice Problem A balloon inflated at 24°C has a volume of 4.00 L. The balloon is then heated to a temperature of 58°C. What is the new volume if the pressure remains constant? 4.46 L

Guy-Lussac’s Law: The Temperature-Pressure Relationship Joseph Guy-Lussac ( ) a French chemist discovered in 1802 ( at 24 years old ) that temperature and pressure are directly proportional. G-L Law: the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant

Guy-Lussac’s Formula P 1 P 2 T 1 T 2

G-L Practice Problem A gas has a pressure of 6.58 kPa at 539 K. What will be the pressure at 211 K if the volume does not change? 2.58 kPa

The Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 Problems using the combined gas law typically take advantage of the knowledge of conditions at STP to save space…

Combined Gas Law practice problem: The volume of a gas-filled balloon is 30.0 L at 40.0°C and 153 kPa pressure. What volume will the balloon have at standard temperature and pressure (STP=0°C and 101.3kPa)? 39.5 L

The Ideal Gas Law P 1 V 1 P 2 V 2 T 1 n 1 T 2 n 2 R Using standard conditions for all variables, a value for “R” can be calculated. R = 8.31 (kPa*L)/(K*mol)

Ideal Gas Law rewritten… Rearrange the variables and “R” so that there are no numbers in the denominator: PV=nRT

Ideal Gas Law Worksheet…

Gas Molecules: Mixtures and Movements Section 12.5

Avogadro’s Hypothesis Compare chlorine gas to hydrogen gas. Look at structure and molar mass. Cl 2 and H 2 ; 70.9 g/mol and 2 g/mol, respectively. If you have a collection of equal numbers of molecules of both chlorine and hydrogen at the same temperature, will they take up the same volume or will one take up more and the other less?

A.H. continued… Avogadro’s Hypothesis stated that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. This is possible because gas particles are incredibly small and very far apart. Therefore the spaces between particles is so great, the size difference between gas molecules is insignificant at normal pressures.

Calculations… What is the volume occupied by mol of a gas at STP? 5.60 L What volume is occupied by 4.02 x molecules of helium gas at STP? 1.50 L He

Dalton’s Law Gas mixtures (with nonreacting gases) at the same temperature have the same average kinetic energy. Pressure is determined by the number of gas particles… each particle makes the same contribution. If you know the pressure exerted by each gas in a mixture, you add the individual pressures to get the total pressure.

Dalton’s Law P total = P 1 + P 2 + P 3 … Dalton’s Law of Partial Pressures: At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases.

Dalton’s Law Problem Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium if the partial pressures of the gases are as follows: P O 2 = 20.0 kPa, P N 2 = 46.7 kPa, and P He = 26.7 kPa? 93.4 kPa

Graham’s Law Terms Diffusion: the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout. Effusion: the process in which a gas escapes through a tiny hole in its container.

Graham’s Law Thomas Graham ( )a Scottish chemist who noticed that gases of lower molar mass effuse faster than gases of higher molar mass. Graham’s Law: the rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. (This is also true for a gas’s rate of diffusion) Rate =. 1. molar mass