Chapter 10 “Gases” A Gas 4 Uniformly fills any container. 4 Mixes completely with any other gas 4 Exerts pressure on its surroundings. 4 (show demo with another beaker)

Measuring Pressure The atmospheric pressure can be measured by using “ Barometer”. Manometer is used to measure the pressure of a gas in a closed container. Units of pressure: Pascal, mm Hg, atm, torr STP: Standard Temperature and Pressure, 1 atm and 0°C. RTP: Room temp and pressure 25 ° C, 1 atm

A Torricellian Barometer P= h.d.g, where, p= pressure h= height of the mercury column d= density of the liquid g= acceleration due to gravity= 9.8 m/s^2 Would a mercury barometer or a water barometer be taller? Why? Density of Mercury: 13.6 g/cm^3 Density of Water: 1.0 g/cm^3

Barometer

Open Tube Manometer Manometer: is used to measure the gas pressure. Manometers have a U tube connected on one side to the gas flask and is either open or closed on other side. The U-tube is filled with Mercury and the pressure is calculated using the formula p=h.d.g, where h is the difference in the height of two arms in U tube.

Manometer

Pressure 4 is equal to force/unit area 4 SI units = Newton/meter 2 = 1 Pascal (Pa) 4 1 standard atmosphere = 101,325 Pa = kPa 4 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

Boyle’s Law There is an inverse relationship between the pressure and volume of a gas at constant temperature. P = k. 1/V PV = k ( constant) P 1 V 1 = P 2 V 2

Boyle’s Law (at Constant T)

Charles’ Law Volume of a fixed mass of gas at constant pressure varies directly with the kelvin temperature. V= k. T V/T= k V 1 /T 1 = V 2 /T 2 Absolute Zero: ^0 C or 0 Kelvin

Gas Volume v. Temperature Graphs: Charles’ Law

Charles’ Law (at Constant P)

Gay Lusaac’s Law The pressure of a fixed mass of gas at constant volume varies directly with the kelvin temperature. P=k. T P/T = k P 1 /T 1 =P 2 /T 2

Gay Lusaac’s Law(at constant V)

The Combined Gas Law By combining all the gas laws, the combined gas law is achieved. PV/T = k P 1 V 1 /T 1 = P 2 V 2 /T 2

Dalton’s Law of Partial Pressures Total pressure of a mixture of gases is equal to the sum of the partial pressures of component gases. P Total = p 1 +p 2 +p 3 ….. If a gas is collected by water displacement method, then the pressure in the bottle is equal to atmospheric pressure, which is given by: P atm= p gas+ p water.

Gas collected over water

Kinetic Molecular Theory (KMT) Gases consist of large number of tiny particles that are far apart relative to their size. The volume occupied by these gas particles as compared to total gas volume is negligible. Since the distance between molecules (or atoms) is so large, intermolecular forces can be ignored. The gas particles are in constant motion and move in straight lines until they collide with each other or the walls of their container. It is the collisions with the walls of the container that causes pressure. These collisions are elastic.

Path followed by a gas particle

Temperature Temperature of a gas is directly to the average kinetic energy of molecules in a sample of gas. (hence, the average velocity of gas molecules) As the temperature of a gas is increased, the speeds of the particles increase. (Kinetic energy increases.) Average kinetic energy is given by the equation: k= ½ mv 2, where, k=kinetic energy, m=mass of particle, v= average velocity of particles Do all gas molecules have same velocity at a given temperature? Will the molecules of hydrogen and nitrogen have same average velocity at the same temperature? How about average kinetic energy?

Applications of KMT Explanation of nature of gases based on KMT Expansion Fluidity Low density Compressibility Diffusion and effusion

Real Gases Real behavior of gases All gases deviate from ideality at conditions of high pressures and low temperatures In a real gas, especially at high pressures and low temperatures, intermolecular forces can not be completely ignored. These forces do become important any time two molecules move close together. The assumption that the volume of gas particles is negligible as compared to overall volume of gas, does not hold good at low temp or high pressures, when the total volume of gas in itself is very small.