Ch. 11: Molecular Composition of Gases Volume-Mass Relationships of Gases

Pressure P : force per unit area on a surface Newton – SI unit for force (1 kg*m/s2) why would shoes with smaller diameter heel not be allowed on gym floor? As surface area decreases, pressure increases Pressure exerted by a gas depends on volume temperature number of molecules

Measuring Pressure barometer instrument used to measure atmospheric pressure first one created by Torricelli in early 1600s glass tube filled with mercury is inverted in a dish mercury flows out of the tube until pressure of the Hg inside the tube is equal to the atmospheric pressure on the Hg in the dish

Measuring Pressure manometer: measures pressure of gas in a container gas has less pressure than atmosphere if the Hg is closer to chamber gas has more pressure than atmosphere if the Hg is further from chamber

Units of Pressure millimeters of mercury (mmHg) torr (torr) from mercury barometer torr (torr) from Toricelli inventing barometer atmosphere of pressure (atm) Pascal (Pa) = 1N/m2 (SI unit) named after French scientist 1 atm = 760 mmHg = 760 torr = 101.325 kPa

Practice Conversions Convert 0.927 atm to mmHg torr kPa

Practice Conversions Convert 148.6 kPa to atm mmHg torr

The pressure of a gas is measured as 49 torr The pressure of a gas is measured as 49 torr. Convert this pressure to atmospheres, kiloPascals, and mmHg.

Boyle’s Law: P and V as one increases, the other decreases inversely proportional pressure is caused by moving molecules hitting container walls If V is decreased and the # of molecules stays constant, there will be more molecules hitting the walls per unit

Boyle’s Law: P and V Boyle’s Law: the V of fixed mass of gas varies inversely with P at a constant T. PV = k k is a constant for a certain sample of gas that depends on the mass of gas and T What kind of graph is V vs. P? If we have a set of new conditions for the same sample of gas, they will have same k so:

Boyle’s Law

Boyle’s Law: P and V Discovered by Irish chemist, Robert Boyle Used a J-shaped tube to experiment with varying pressures in multistory home and effects on volume of enclosed gas

Example: Boyle’s Law Consider a 1.53-L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 104 Pa at constant temperature, what will be the new volume of the gas?

Charles’ Law: V and T if P is constant, gases expand when heated when T increases, gas molecules move faster and collide with the walls more often and with greater force to keep the P constant, the V must increase

Charles’ Law: V and T Problem: if we use Celsius, we could end up with negative values from calculations in gas laws for volumes we need a T system with no negative values: Kelvin Temperature Scale starts at -273.15 ° C = absolute zero = 0 K lowest possible temperature balloon going into liquid nitrogen

Charles’ Law: V and T Charles’ Law: the V of fixed mass of gas at constant P varies directly with Kelvin T. V = kT k is a constant for a certain sample of gas that depends on the mass of gas and P What kind of graph is V vs. T? If we have a set of new conditions for the same sample of gas, they will have same k so:

Charles’ Law discovered by French physicist, Jacques Charles in 1787 first person to fill balloon with hydrogen gas and make solo balloon flight

Example: Charles’ Law & Temp. A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm?

A weather balloon is released at a pressure of 744 mmHg with a volume of 12 L. What will the volume be at a pressure of 704 torr?

Gay-Lussac’s Law of Combining Volumes of Gases at constant T and P, coefficients in balanced equation represent ratio of volumes of gaseous reactants too 2H2(g) + O2(g)  2H2O(g) 2 L 1 L 2 L

Gay-Lussac’s Law: P and T Gay-Lussac’s Law: the P of fixed mass of gas at constant V varies directly with Kelvin T. P = kT k is a constant for a certain sample of gas that depends on the mass of gas and V What kind of graph is P vs. T? If we have a set of new conditions for the same sample of gas, they will have same k so:

Example: Gay-Lussac’s Law The gas in an aerosol can is at a pressure of 3.00 atm at 25°C. Directions on the can warn the user not to keep the can in a place where temperature exceeds 52°C. What would the gas pressure be in the can at 52°C?

Example 3O2(g)  2O3(g) How many liters of O3 can be made from 12 L of O2? How many moles of O2 are needed to make 24 moles of O3? How many molecules of O3 can be made from 18 molecules of O2?

Avogadro’s Law equal volumes of gases at the same T and P contain equal numbers of molecules at same T and P, volumes varies directly with number of moles (n) V = kn

Molar Volume of Gases like molar mass but with volume mass of one mole of substance but with volume volume of one mole of substance because of Avogadro’s law, one mole of any gas has the same volume as any other gas at the same T and P

Molar Volume of Gases Standard Molar Volume of Gas volume of one mole of gas at 1 atm and 0°C is 22.4 22.4 L of any gas has one mole of particles but has different masses Standard Temperature and Pressure STP 1 atm and 0°C

Molar Volume of Gases

Example A chemical reaction produces 0.0680 mol of oxygen gas. What volume in liters is occupied by this gas sample at STP? 1 mol : 22.4 L

Example 2 A chemical reaction produced 98.0 mL of sulfur dioxide gas at STP. What was the mass of gas made? convert mL to L convert L to moles using molar volume convert moles to grams using molar mass

Example 3 A chemical reaction produced 3.1 g of CO2 gas. What volume will it have in mL at STP? convert grams to moles convert moles to liters convert liters to milliliters

Example 4 How many moles of gas are in a container with a volume of 2.46 L at STP?

Combined Gas Law a gas often changes in T, P, and V all at once the other gas laws can be combined into one law Combined Gas Law- relationship between P, V, and T of a fixed amount of gas

Example: Combined Gas Law A Helium-filled balloon has volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.°C?

Example A balloon containing 5.5 L of air at 25C and 755 torr is put at the bottom of the ocean. The new temperature is 4 C and the new volume is 230 mL. What is the new pressure?

Dalton’s Law of Partial Pressure John Dalton responsible for atomic theory also studied gas mixtures the P of gas mixture is the sum of the individual pressures of each gas alone the P that each gas exerts in the mixture is independent of the P that are exerted by other gases

Dalton’s Law of Partial Pressure the total P of a mixture of gases is equal to the sum of partial P of component gases, no matter how many different gases PT = P1 + P2 + P3 + … Partial Pressure- P of each gas in mixture

Why? the particles of each gas in a mixture have an equal chance to hit the walls so each gas exerts P independent of that exerted by other gases total P is result of the total # of collisions per unit of wall area

Water Displacement gas produced is less dense than water so it replaces the water in the bottle gas collected is not pure because it contains vapor from the water PT = Pgas + Pwater set for a certain T equal to atmospheric pressure

Example Oxygen gas from decomposition of KClO3 was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0°C respectively. If the partial pressure of water vapor is 17.5 torr at 20.0°C. What was the partial pressure of oxygen collected? PT = PO2 + PH2O 731.0 torr = PO2 + 17.5 PO2 = 713.5 torr

Example Find the partial pressure by 2 gases (A and B) mixed if the overall pressure is 790 mmHg. The percent by volume is A: 20% and B: 80%. PT = PA + PB = 790 mmHg A: 0.20 x 790 = 158 mmHg B: 0.80 x 790 = 632 mmHg

Ch. 11: Molecular Composition of Gases Ideal Gas Law

Ideal Gas Law relationship among P, V, T, and number of moles of gas (n) combination of all the laws we learned helps us approximate “real” gas behavior where R: ideal gas constant 0.08206 L atm/mol K (use most often) 8.314 J/mol K (only for when P is in Pascals) check units before using equation

Example What is the P in atm exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K?

Example What is the volume in liters of 0.250 mol of oxygen gas at 20.0°C and 0.974 atm?

Example What mass of chlorine gas is in a 10.0 L tank at 27°C and 3.50 atm?

Finding Molar Mass mass of one mole of substance units : g/mol represented by M

Finding Molar Mass At 28°C and 0.974 atm, 1.00 L of gas has a mass of 5.16g. What is the molar mass?

Finding Density

Finding Molar Mass The density of dry air at sea level (with pressure of exactly 1 atm) is 1.225 g/L at 15°C. What is the molar mass of air?

Finding Density What is the density of carbon monoxide gas at STP?

Finding Density A sample of gas has a mass of 50.0 g and volume of 26.0 L at 25C and 1.2 atm. What is the molar mass of the gas?

Ch. 11: Molecular Composition of Gases Stoichiometry of Gases

Stoichiometry of Gases Remember that coefficients give you ratio of moles ratio of molecules ratio of volumes even if the gases have different conditions only when gases are all at same T and P

Calculations Review getting moles from grams? molar mass (periodic table) getting volume from moles for gas? at STP only Molar Volume (22.4 L = 1 mol) any conditions Ideal Gas Law (PV = nRT, solve for V) getting from one type gas to new gas mole ratio (coefficients in equation)

CaCO3(s)  CaO(s) + CO2(g) Example 1 Calcium carbonate can be heated to make calcium oxide according to the following equation: CaCO3(s)  CaO(s) + CO2(g) How many grams of CaCO3 must be decomposed to make 5.00 L of CO2 at STP? volume of CO2  moles CO2 (molar volume) moles CO2  moles CaCO3 (mole ratio) moles CaCO3  grams CaCO3 (molar mass)

Example 1 find moles of CO2 convert mol CO2 to mol CaCO3 convert mol CaCO3 to grams

WO3(s) + 3H2(g)  W(s) + 3H2O(l) Example 2 Tungsten is made industrially by: WO3(s) + 3H2(g)  W(s) + 3H2O(l) How many liters of hydrogen gas at 35°C and 0.980 atm are needed to react completely with 875 g WO3? grams of WO3  moles WO3 (molar mass) moles WO3  moles H2 (mole ratio) moles H2  volume H2 (PV = nRT)

Example 2 find moles of WO3 find moles of H2 find volume of H2

CH4(g) + 2O2(g)  CO2(g) + 2H2O(g) Example 3 Combustion of methane gas produces carbon dioxide gas and water vapor. CH4(g) + 2O2(g)  CO2(g) + 2H2O(g) If the reaction produces 213 L of CO2 at STP, what volume of O2 must have been used at 23C and 0.89 atm? volume of CO2  moles CO2 (molar volume) moles CO2  moles O2 (mole ratio) moles O2  volume O2 (PV = nRT)

Example 3 find moles of CO2 convert mol CO2 to mol O2 Find volume of O2