Gases

Review KMT (kinetic molecular theory)

Molecules have vibrational motion Molecules vibrate, rotate and translate Molecules vibrate and rotate

Kinetic Molecular Theory Gases consist of tiny particles. (atoms or molecules) These particles are so small, compared to the distances between them, that the volume (size) of the individual particles can be assume to be negligible.(zero) The particles are in constant motion, colliding with the walls of the container. These collisions with the wall cause the pressure exerted by the gas. The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas.

Properties of Real Gases can be compressed exert pressure on whatever surrounds them expand into whatever volume is available easily diffuse into one another can be described in terms of temperature, pressure, volume and amount

Pressure gases exert a pressure on the walls of their container. pressure is defined as force per unit area:

Atmospheric Pressure The atmospheric pressure can be measured using a barometer.

Standard atmospheric pressure supports a column of mercury about 760 mm high. 760 mm Hg = 1 atm= 101.325 kPa

Pressure Conversion If the barometer reads 753.3 mm Hg, what is the atmospheric pressure in atm and kPa? 1 atm 753.3 mm Hg = 0.9912 atm 760 mm Hg 101.325 kPa 753.3 mm Hg = 100.4 kPa 760 mm Hg

Standard Temperature and Pressure In order to compare two gases, we choose a standard temperature and pressure: STP: standard temperature and pressure → 0.00 oC and 101.325 kPa (1.00 atm.) → one mole of gas has a volume of 22.4 L SATP: standard ambient temperature and pressure → 25.0 oC and 100.0 KPa → one mole of gas has a volume of 24.8 L

Gas Laws

Carry out the CBL lab to determine the relationship between pressure and volume for a sample of gas.

Graph the following information Pressure (KPa) Volume (L) 100 5.00 110 4.55 120 4.16 130 3.85 140 3.57 K (VP) 500 500.5 499.2 499.8 Is there a relationship between pressure and volume? volume pressure P1V1 = K = P2V2

Boyle’s Law For a given mass of gas at constant temperature, the volume of a gas varies inversely with pressure. P1V1 = P2V2

Graph the following data Temperature (K) Volume (L) 298 5.00 323 5.42 348 5.84 373 6.26 398 6.68 K (V/T) 0.0167 0.0168 temperature volume Is there a relationship between pressure and volume? V1/T1 = K = V2/T2

Kelvin Scale Lord Kelvin proposed an absolute temperature scale defined by: T(K) = T(C) + 273.15

Examples Convert the following temperatures into Kelvin or celcius: 45 oC → 318.15 K 207 oC → 480.15 K -48 oC → 225.15 K 100 K → -173.15 oC

Charles’ Law Charles discovered that volume is directly proportional to its Kelvin temperature if a fixed mass remains under constant pressure. V1 V2 T1 T2 =

V versus T for different gases

Lussac Law P1 P2 = T1 T2 The pressure of a gas is directly proportional to the Kelvin temperature, providing the volume and mass remain constant. Joseph Louis Gay-Lussac and Jean-Baptistse Biot in their balloon on 24 August 1804

Combined Gas Law P1V1 = P2V2 T1 T2

Avogadro’s Law In 1811, Avogadro proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. It follows that the volume of a gas at constant temperature and pressure is proportional to number of moles. V1 V2 n1 n2 =

The relationship between volume V and number of moles n.

The Ideal Gas Equation Combining the gas laws gives: PV = nRT where R is called the Gas constant: kPa R L mol K = × 8.314

Standard Temperature and Pressure In order to compare two gases, we choose a standard temperature and pressure: STP: 0°C and 1 atm What is the volume of a mole of gas at STP? 1 mol 8.314 kPa L /mol K × 273.15 K = 101.325 kPa = 22.4 L

Gas Stoichiometry

Examples If 6.45 grams of water are decomposed, how many liters of oxygen will be produced at STP? 2 H2O(g) ® 2 H2(g) + O2(g) 1 mol H2O 1 mol O2 22.4 L O2 6.45 g H2O 18.02 g H2O 2 mol H2O 1 mol O2

CH4(g) + 2 O2(g) ® CO2(g) + 2 H2O(g) Examples How many liters of CH4 at STP are required to completely react with 17.5 L of O2 ? CH4(g) + 2 O2(g) ® CO2(g) + 2 H2O(g) 22.4 L O2 1 mol O2 1 mol CH4 22.4 L CH4 1 mol O2 1 mol CH4 22.4 L CH4 17.5 L O2 22.4 L O2 2 mol O2 1 mol CH4 = 8.75 L CH4

Avagadro Equal volumes of gas, at the same temperature and pressure contain the same number of particles. Moles are numbers of particles You can treat reactions as if they happen liters at a time, as long as you keep the temperature and pressure the same.

CH4(g) + 2 O2(g) ® CO2(g) + 2 H2O(g) Examples How many liters of H2O at STP are produced by completely burning 17.5 L of CH4 ? CH4(g) + 2 O2(g) ® CO2(g) + 2 H2O(g) 2 mol H2O 17.5 L CH4 = 35.0 L H2O 1 mol CH4

Air Bag Chemistry

Air Bag Chemistry 2 NaN3(s) 2Na (s) + 3N2(g) Secondary reaction: 10 Na + 2 KNO3 K2O + 5 Na2O + N2(g)

Mg(s) + 2 HCl(aq) ® MgCl2(aq) + H2(g) Measuring Gases To measure the amount of gas produced in a reaction, it is often collected over water. Reaction of magnesium with HCl: Mg(s) + 2 HCl(aq) ® MgCl2(aq) + H2(g) O H gas 2 P + = = Patm