Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.
Chapter 2 The Behaviour of Gases 2.1 Pressure 2.2 Describing Gases 2.3 Gas Mixtures 2.4 Gas Stoichiometry 2.5 Molecular View of Gases 2.6 Additional Gas Properties 2.7 Non-Ideal (Real) Gases 2.8 Chemistry of the Earth’s Atmosphere Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.1 Pressure Pressure (p) – in a gas it is caused by molecular collisions with a container. The air around us is a huge reservoir of gas that exerts pressure on the Earth’s Surface The atmospheric pressure can be measured with a mercury barometer. Why does pressure have units of mm Hg? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

How Do We Measure the Pressure of a Gas in a Closed Container?
We use a manometer. In the U-shaped manometer, the difference between the two mercury levels gives the pressure (in mm Hg) of the gas. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Units of Pressure Because the pressure at sea level is 760 mm Hg we define another unit called the atmosphere. 1 atm = 760 mm Hg Another common pressure unit is Torr 1 atm = 760 Torr The official SI unit is the pascal (Pa) 1 atm = Pa Another SI unit is the bar (1 bar = 100,000 Pa) 1 atm = bar Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 1 Measuring Pressure
A scientist collected an atmospheric gas sample. A manometer attached to the gas sample gave the reading shown in the figure, and the barometric pressure in the laboratory was 752 mmHg. Calculate the pressure of the sample in atmospheres and in bars. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.2 Describing Gases Molecules in a gas move freely throughout the entire volume of a container, changing direction whenever they collide with other molecules or with a wall. The line traces a possible path of a single molecule. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Variations in Gas Volume
Boyle investigated gases in a J-tube and determined that volume was inversely proportional to pressure. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Charles reported studies of gas volume as a function of temperature. He determined that the volume of gas is directly proportional to its temperature. The volume of gas also changes when the amount changes. Gas volume is directly proportional to the amount of gas. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

The Ideal Gas Equation All four variables (p, T, V, and n) can be related through the Ideal Gas Equation: pV = nRT Units: n (mol), p (bar or kPa), V (L) and T (K) Units of the ideal gas constant, R: R = L bar mol-1 K-1 R = L kPa mol-1 K-1 Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 2 Calculation of Gas Pressure
A 10 m3 steel storage tank contains 8.85 kg of methane (CH4). If the temperature is 25 °C, what is the pressure inside the tank? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 3 Calculation of Gas Amount
A pressure gauge on a tank of molecular oxygen reads 5.67 bar. If the tank holds 75.0 L and the temperature in the lab is 27.6 °C, how many grams of molecular oxygen are in the tank? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 4 Using the Molar Volume of Gas
A cement factory produces large volumes of CO2 gas by the reaction CaCO3 (s) → CaO (s) + CO2 (g). If the factory processes 10.0 tonnes of CaCO3 (s) per hour, what volume of CO2 (g) per hour is produced at 25.0 oC and kPa? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 5 Pressure-Volume Variations
A sample of helium gas is held at constant temperature inside a cylinder whose volume is 0.80 L when a piston exerts a pressure of 1.5 bar. If the external pressure on the piston is increased to 2.1 bar, what will be the new volume? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Variations on the Gas Equation
During transformations, any of the four variables in the ideal gas equation may change, and any of them remain constant. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 6 Changing Gas Conditions
A sample of carbon dioxide in a 10.0-L gas cylinder at 25°C and 1.00 bar pressure is compressed and heated. The final temperature and volume are 55 °C and 5.00 L. Compute the final pressure Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 7 Gas Calculations
Two natural gas storage tanks, with volumes of 1.5 x 104 and 2.2 x 104 L, are at the same temperature. The tanks are connected by pipes that equalize their pressures. What fraction of the stored natural gas is in the larger tank? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Dalton’s Law of Partial Pressures
In a mixture of gases, each gas contributes to the total pressure the amount that it would exert if the gas were present in the container by itself. ptotal = p1 + p2 + p3 + p4 + … and ntotal = n1 + n2 + n3 + n4 + … Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Mole Fraction and Partial Pressures
Mole fraction, X – the number of moles of a particular substance in a mixture divided by the total moles and consequently pA = XA ptotal Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 8 Gas Mixtures The amount of gas introduced into a diving tank can be determined by weighing the tank before and after charging the tank with gas. A diving shop placed 80.0 g of O2 and 20.0 g of He in a 5.00 L tank at 298 K. Determine the total pressure of the mixture and find the partial pressures and mole fractions of the two gases. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

ppm and ppb When we are talking about mixtures (gas or liquid) that have a very small amount of solute, we may use parts per million (ppm) as a unit for concentration. Parts per million measures how many molecules of a substance are present in one million molecules of a sample. 1 ppm = 1 molecule out of every 106 molecules Another common unit for concentration is parts per billion (ppb). 1 ppb = 1 molecule out of every 109 molecules Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 9 Working with Concentrations in ppm
The exhaust gas from an average automobile contains 206 ppm of the pollutant nitrogen oxide, NO. If an automobile emits 125 L of exhaust gas at 100 kPa and 350 K, what mass of NO has been added to the atmosphere? Assume the atmospheric pressure is 100 kPa. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.4 Gas Stoichiometry Stoichiometry applies to solids, liquids and gases. Notice that the ideal gas law contains moles. Remember that in order to use stoichiometry, you must be using units of moles. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 10 Gas Stoichiometry
This example describes the synthesis of acetylene (C2H2) from calcium carbide (CaC2). Modern industrial production of acetylene is based on a reaction of methane (CH4) under carefully controlled conditions. At temperatures greater than 1600 K, two methane molecules rearrange to give three molecules of hydrogen and one molecule of acetylene: A 50.0 L steel vessel, filled with CH4 to a pressure of 10.0 bar at 298 K, is heated to 1600 K to convert CH4 into C2H2. What mass of C2H2 can be produced? What pressure does the reactor reach at 1600 K? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 11 Limiting Reagents in a Gas Mixture
Margarine can be made from natural oils, such as coconut oil, by hydrogenation: An industrial hydrogenator with a volume of 2.50 x 102 L is charged with 12.0 kg of oil and 7.09 bar (= 709 kPa) of hydrogen (H2) at 473 K (200 °C), and the reaction goes to completion. What is the final pressure of H2 and how many kilograms of margarine will be produced? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 12 General Stoichiometry
The reaction of a metal with an acid generates hydrogen gas and an aqueous solution of ions. Suppose that 3.50 g of magnesium metal is dropped into L of 6.00 M HCl in a 5.00-L cylinder with an initial gas pressure of 1.00 bar at 25.0 °C, and the cylinder is immediately sealed. Find the final partial pressure of hydrogen, the total pressure in the container, and the concentrations of all ions in solution. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.5 Molecular View of Gases
Learning Objective: Explain the basic concepts of kinetic molecular theory: molecular speed, energy, and the effects of temperature and volume on gas pressure Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.5 Molecular View of Gases
How do gases behave at a molecular level? Let’s examine Molecular Speed. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 13 A Molecular Beam Experiment
The figures below represent mixtures of neon atom and hydrogen molecules. One of the gas mixtures was used in a pulsed molecular beam experiment. The result of the experiment is shown below. Which of the two gas samples, A or B, was used for this experiment? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Speed and Energy How would we calculate the kinetic energy of a molecule of hydrogen if a molecule has a most probable speed of 1.57 x 103 m/s at 300 K? (You will need to calculate the mass of a molecule of H2 ) How about for methane, CH4 at 300 K? (v = 5.57 x 102 m/s) What conclusion can be drawn from these calculations? At a given temperature, all gases have the same molecular kinetic energy distribution. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Average Kinetic Energy
The average kinetic energy of gas molecules depends on the temperature of the gas. R = J mol-1 K-1 Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

What is an Ideal Gas? An ideal gas has the following two characteristics: The volume occupied by the molecules of an ideal gas is negligible compared with the volume of its container. The energies generated by forces among ideal gas molecules are negligible compared with molecular kinetic energies. (Small gas molecules are not attracted to one another) Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.6 Additional Gas Properties
Learning Objective: Calculate gas densities and molar masses from pressure-volume-temperature data Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.6 Additional Gas Properties
Determination of molar mass using pV=nRT Gas density Rates of gas movement Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Molar Mass and the Ideal Gas Law
Easy to manipulate the ideal gas law to include the molar mass: Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example Calcium Carbide (CaC2) is a hard, gray-black solid that has a melting point of 2000 °C. This compound reacts strongly with water to produce a gas and a solution containing OH- ions. A 12.8 g sample of CaC2 was treated with excess water. The resulting gas was collected in an evacuated 5.00 L glass bulb with a mass of g. The filled bulb had a mass of g and a pressure of 98.8 kPa atm when its temperature was 26.8 °C. Calculate the molar mass and determine the formula of the gas. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Density and the Ideal Gas Law
Easy to manipulate ideal gas law to determine the density. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example A hot-air balloon will rise when the density of its air is 15% lower than that of the atmospheric air. Calculate the density of air at 295 K, 100 kPa (assume that dry air is 78% N2 and 22% O2) and determine the minimum temperature of air that will cause a balloon to rise. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Rates of gas movement Effusion – movement of gas through a tiny opening into a vacuum Diffusion – mixing of two gases due to their molecular motion Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Rates of Gas Movement When you are driving, do you follow a semitrailer up a mountain or do you pass it? Similarly, the heavier the gas molecule, the slower it will diffuse or effuse. It just moves slower. We can relate the mass of a molecule to speed using the root-mean-squared speed, . Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 17 Graham’s Law: Relative Rates of Diffusion
Refer to Figure 2-17, and calculate how far from the HCl end of the tube the NH4Cl (s) forms. Assume the distance between the HCl and NH3 is initially 60 cm. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example 2 – 18 Graham’s Law: Measuring Molecular Weights
A sample of krypton gas (Kr) escapes through a small hole in 64.4 s. The same amount of a gas whose identity is unknown escapes through the hole in 31.6 s, under identical conditions. Calculate the molecular weight of the unknown gas. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.7 Non-Ideal (Real) Gases
Learning Objective: Calculate the pressure of a gas under non-ideal conditions, and explain the deviations from ideality Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

2.7 Non-Ideal (Real) Gases
Intermolecular forces: forces of attraction between molecules which result in liquids and solids. At STP, only 11 elements are gases. Intermolecular forces are important in all elements, except for those which are gases. Intermolecular forces become important in gases at high pressure and/or low temperature Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

van der Waals Equation During conditions of high pressure and/or low temperature and when forces exist between molecules, the ideal gas equation does not work At high pressure, molecular volume is important At low temperature, the attractive potential energies may be larger than the kinetic energies The van der Waals Equation corrects for these problems Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

Example 2 – 19 Real Gas Pressures
Gases such as methane are supplied in steel cylinders. A 15.0 L cylinder contains 62.0 mol CH4 when full, and mol CH4 after prolonged use. Compare the ideal and real (van der Waals) pressures before and after use if the cylinder is at 27 °C. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.8 Chemistry of the Earth’s Atmosphere
Learning Objective: Do calculations involving water vapour pressure and relative humidity and describe some of the basic chemistry of the troposphere Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

2.8 Chemistry of the Earth’s Atmosphere
Our atmosphere behaves as an ideal gas, where gravity determines its volume Pressure varies with atmospheric conditions: Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Troposphere Layer of the atmosphere closest to the earth. 99% (N2 and O2) H2O, Ar and CO2 are the only other gases present in amounts greater than 0.01% H2O concentration can vary depending on the atmospheric conditions. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Vapour Pressure In a closed container, a gas will evaporate until it reaches a dynamic equilibrium. At dynamic equilibrium, the pressure of the gas in the closed container is called the vapour pressure, pvap. So what about for water in the earth’s atmosphere? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Relative Humidity Most of the time, the atmosphere contains less water vapour than the maximum amount it can hold. The amount of water in the earth’s atmosphere is called relative humidity: where pvap,H2O is the partial pressure of water present in the atmosphere Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Dew Point The formation of dew and fog are the result of relative humidity. Warm air with a high relative humidity may cool. When the air temperature falls below a certain temperature, some water must condense from the atmosphere. This temperature is called the dew point. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Example Fog forms when humid warm air from above a body of water moves inland and cools. What is the highest temperature at which fog could form from air that is at 65% relative humidity when its temperature is 27.5 °C? Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Chemistry in the Troposphere
The majority of the pollution in the earth’s atmosphere is due to fossil fuels. Some important reactions involve: Oxides of nitrogen and Oxides of sulphur Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Oxides of Nitrogen Normally, N2 is very stable. However, under extreme conditions (like in a car engine), it reacts with oxygen to form NO: NO can then react in the atmosphere with O2 to form nitrogen dioxide. NO2 is a red-brown gas that can be seen over many large cities where the concentration can reach 0.9 ppm. (intolerable > 5 ppm) Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Formation of Ozone Nitrogen dioxide absorbs energy from the sunlight and decomposes to NO and O atoms O atoms are very reactive and will react with O2 to form ozone, O3 (highly toxic and reactive) Both O2 and O3 react with hydrocarbons to produce harmful pollutants sometimes referred to as photochemical smog. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Oxides of Sulphur SO2 is generated from burning sulphur-containing fuels: S (organic) + O2 (g) → SO2 (g) or from metal refining operations: NiS (s) O2 (g) → NiO (s) + SO2 (g) and in the presence of dust particles or UV light, SO2will react with oxygen to form SO3: Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Oxides of Sulphur In humans, prolonged exposure to SO2 diminishes lung capacity and aggravates respiratory problems. At 0.15 ppm, people with existing problems will be incapacitated. At 5 ppm, everyone will experience breathing difficulties. Also, SO2 and SO3 can react with water to produce acid rain. SO2 (g) + H2O (g) → H2SO3(aq) SO3 (g) + H2O (g) → H2SO4 (aq) SO2 can be scrubbed from flu gases before it reaches the atmosphere: SO2(g) + CaO (s) → CaSO3 (s) Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5

Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd.

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