The Behavior of Gases AW Chapter 10, section 1 and Chapter 12

Gas Pressure –Changing altitude Atmospheric Pressure

Measuring Gas Pressure A barometer measures atmospheric pressure. The barometer was invented by Evangelista Torricelli in 1643

Measuring Gas Pressure A manometer measures the pressure of a gas in a container.

Units of Gas Pressure 1 standard atmosphere = atm = mm Hg = torr = kPa

Partial Pressure Partial pressure is the contribution each gas in a mixture makes to the total pressure.

Dalton’s Law of Partial Pressures For a mixtures of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. P total = P 1 + P 2 + P 3

Dalton’s Law of Partial Pressures The pressure is independent of the nature of the particles. The pressure of the gas is affected by the number of particles.

Collecting a gas over water Dalton’s Law of Partial Pressures Total pressure is the pressure of the gas + the vapor pressure of the water.

Collecting a gas over water Dalton’s Law of Partial Pressures How can we find the pressure of the gas collected alone?

Robert Boyle’s experiment Pressure and Volume: Boyle’s Law

Graphing Boyle’s results: This graph has the shape of half of a hyperbola with an equation PV = k Pressure and Volume: Boyle’s Law

Boyle’s Law For a given mass of gas at constant temperature, the volume of a gas varies inversely with pressure. –If one increases the other decreases.

Boyle’s Law Another way of stating Boyle’s Law is P 1 V 1 = P 2 V 2

Graphing data for several gases Volume and Temperature: Charles’s Law

It is easier to write an equation for the relationship if the lines intersect the origin of the graph. Charles’s Law –Use absolute zero for the temperature

Charles’s 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 (where T is in kelvins) –If one increases the other increases.

Pressure and Temperature: Gay Lussac’s Law The pressure of a fixed mass of gas is directly proportional to its Kelvin temperature if the volume is held constant. P 1 = P 2 T 1 T 2

Pressure, Volume, and Temperature: Combined Gas Law The three laws, Boyle’s, Charles’s, and Gay Lussac’s laws, can be combined into a single expression called the combined gas law: P 1 V 1 = P 2 V 2 T 1 T 2

Volume and Moles of Gas: Avogadro’s Principle The volume of a fixed mass of gas is directly proportional to the number of moles of gas if the pressure and temperature are kept constant. V 1 = V 2 n 1 n 2 ( n = moles of gas)

Avogadro’s Principle: If one increases the other increases.

Pressure, Volume, Temperature and Moles of Gas: General Gas Law Combining Boyle’s, Charles’s, Gay Lussac’s laws and Avogadro’s principle gives the general gas law: P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2

Solve the General Gas Law, using data for any gas at standard conditions (STP) P = 1 atm, V = 22.4 L, n = 1 mole of gas, T = 0 o C (or 273 K) P 1 V 1 = (1 atm)(22.4 L) = L·atm n 1 T 1 (1 mol)(273 K)K·mol L·atmis the Ideal Gas Constant (R) K·mol

The Ideal Gas Law P 1 V 1 = R = L atm n 1 T 1 mol K Rearranging the equation gives the ideal gas law PV = nRT

Explaining the Ideal Gas Law Increasing the temperature of a gas increases the number of collisions with the container and the force of the collisions, so the pressure increases

Explaining the Ideal Gas Law Increasing the concentration of a gas increases the number of collisions with the container, so the pressure Increases (concentration does not affect the force of the collisions)

Explaining the Ideal Gas Law Decreasing the volume of a gas increases the number of collisions with the container, so the pressure Increases (volume changes do not affect the force of the collisions)

Ideal Behavior of Gases: The Kinetic Molecular Theory

Implications of the Kinetic Molecular Theory Meaning of temperature – Kelvin temperature is directly proportional to the average kinetic energy of the gas particles Relationship between Pressure and Temperature – gas pressure increases as the temperature increases because the particles speed up Relationship between Volume and Temperature – volume of a gas increases with temperature because the particles speed up

Gases do not behave ideally under conditions of high pressure and low temperature. Why? Real Gases

At high pressure the volume is decreased –Molecule volumes become important –Attractions become important Real Gases

Diffusion and Effusion of a Gas Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout. Effusion is the process in which a gas escapes through a tiny hole in its container

Diffusion and Effusion of a Gas Graham’s Law The rate of diffusion or effusion of a gas is inversely proportional to the square root of the gas’s molar mass.

Graham’s Law: Question… If a cotton ball with NH 3 is placed into one end of a long glass tube, and a cotton ball with HCl is placed into the other end, a ring of solid NH 4 Cl will form where the vapors meet inside the tube. NH 3(g) + HCl (g)  NH 4 Cl(solid) NH 3 HCl a)b) c) Where will the white ring of NH 4 Cl form in the tube? Location a, b or c?

Since the HCl is so large in mass, it moves more slowly through the tube.