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Gases Chapter 10

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Characteristics of Gases 1. The particles in gases are far apart, therefore they are very compressible. 2. Gases expand to fill the volume of their container (V cont. = V gas ) 3. Their motion is constant, random, and very fast. 4. Average Kinetic NRG of gas is determined by Temperature

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5. The volume and mass of gas particles is negligable. 6. For gas particles, the energy remains constant within a system. 7. During collisions between gas particles, the collision is perfectly ellastic. 8. When gas particles collide with the walls of their container, they exert a pressure.

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Pressure Gases exert a pressure on the walls of their container. Gases exert a pressure on the walls of their container. Pressure is defined as force per unit area: P = SI unit: 1 N/m 2 = 1 Pascal (Pa) F A

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Atmospheric Pressure The result of ALL the gas molecules of the atmosphere from sea level to the top of the exosphere. The result of ALL the gas molecules of the atmosphere from sea level to the top of the exosphere. Gravity pulls all of them down toward the center of the earth. Gravity pulls all of them down toward the center of the earth. A Large Force! A Large Force! 1 m 2 column air = 10,000 kg at sea level 1 m 2 column air = 10,000 kg at sea level Air pressure changes slightly from day to day, but changes dramatically with altitude. Air pressure changes slightly from day to day, but changes dramatically with altitude.

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Where is there higher pressure: up in the mountains or down at the beach? Where is there higher pressure: up in the mountains or down at the beach? Why? Why? What does that mean for us? What does that mean for us?

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A Barometer measures atmospheric pressure The pressure of the atmosphere at sea level at 25 o C will hold a column of mercury 760 mm. The pressure of the atmosphere at sea level at 25 o C will hold a column of mercury 760 mm. 1 atm = 760 mm Hg 1 atm = 760 mm Hg 1 atm = 760 torr 1 atm = 760 torr 1 atm = kPa 1 atm = kPa 1 atm = 29.9 inches Hg 1 atm = 29.9 inches Hg “Standard Atmospheric Pressure” “Standard Atmospheric Pressure” 1 atm Pressure 760 mm Hg Vacuum

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A Manometer measures the pressure of gas in a container Gas h Column of mercury measures pressure. Column of mercury measures pressure. h is how much lower the pressure is than outside. h is how much lower the pressure is than outside. SUBTRACT h from the room pressure. SUBTRACT h from the room pressure.

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Manometer h is how much higher the gas pressure is than the atmosphere. h is how much higher the gas pressure is than the atmosphere. ADD the difference in the height to the room pressure ADD the difference in the height to the room pressure h Gas

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Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,325 Pascals = kPa Use dimensional analysis to convert Use dimensional analysis to convert 1. What is 724 mm Hg in kPa? 1. What is 724 mm Hg in kPa? 2. in torr? 2. in torr? 3. in atm? 3. in atm? 96.5 kPa 724 torr atm

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The Gas Laws Boyle’s Law: Boyle’s Law: Pressure and volume are inversely related at constant temperature. Pressure and volume are inversely related at constant temperature. PV= k PV= k As one goes up, the other goes down. As one goes up, the other goes down. P 1 V 1 = P 2 V 2 P 1 V 1 = P 2 V 2 Graphically... Graphically...

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P V (at constant T) Boyle’s Law

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P 1/V (at constant T) Slope = k

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Charles’ Law Volume of a gas varies directly with the absolute temperature at constant pressure. Volume of a gas varies directly with the absolute temperature at constant pressure. V = kT (if T is in Kelvin) V = kT (if T is in Kelvin) V 1 V 2 T 1 T 2 V 1 V 2 T 1 T 2 Graphically... =

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V (L) T (ºC) ºC

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Gay- Lussac Law At constant volume, pressure and absolute temperature are directly related. At constant volume, pressure and absolute temperature are directly related. P = k T P = k T P 1 P 2 T 1 T 2 P 1 P 2 T 1 T 2 Graphically... =

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Temperature K P Slope = k

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Avogadro's Law At constant temperature and pressure, the volume of gas is directly related to the number of moles. At constant temperature and pressure, the volume of gas is directly related to the number of moles. V = k n (n is the number of moles) V = k n (n is the number of moles) V 1 V 2 n 1 n 2 V 1 V 2 n 1 n 2 =

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Combined Gas Law If the moles of gas remains constant, use this formula and cancel out the other things that don’t change. If the moles of gas remains constant, use this formula and cancel out the other things that don’t change. P 1 V 1 = P 2 V 2 T 1 T 2 P 1 V 1 = P 2 V 2 T 1 T 2

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Examples A spray can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the pressure be if the can was heated to 100.ºC? A spray can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the pressure be if the can was heated to 100.ºC? What volume of gas could the can release at 22ºC and 743 torr? What volume of gas could the can release at 22ºC and 743 torr?

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Ideal Gas Law PV = nRT PV = nRT V = L at 1 atm, 0ºC, n = 1 mole, what is R? V = L at 1 atm, 0ºC, n = 1 mole, what is R? R is the ideal gas constant. R is the ideal gas constant. R = L atm/ mol K R = L atm/ mol K How do you get R for different units of P? How do you get R for different units of P? Tells you about a gas NOW. Tells you about a gas NOW. The other laws tell you about a gas when it changes. The other laws tell you about a gas when it changes.

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Ideal Gas Law An equation of state. (a state function) An equation of state. (a state function) Independent of how you end up where you are at. Does not depend on the path. Independent of how you end up where you are at. Does not depend on the path. Given 3 you can determine the fourth. Given 3 you can determine the fourth. An Empirical Equation - based on experimental evidence. An Empirical Equation - based on experimental evidence.

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Ideal Gas Law A hypothetical substance - the ideal gas A hypothetical substance - the ideal gas Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Use the laws anyway, unless told to do otherwise. Use the laws anyway, unless told to do otherwise. They give good estimates. They give good estimates.

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Examples A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature? A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature? Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr? Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr? A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr? A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr?

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Gas Stoichiometry D = m/V D = m/V Let M stand for molar mass Let M stand for molar mass M = m/n M = m/n n= PV/RT n= PV/RT M = m PV/RT M = m PV/RT M = mRT = m RT = DRT PV V P P M = mRT = m RT = DRT PV V P P May be easier to convert to moles, then use stoich. May be easier to convert to moles, then use stoich.

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Examples What is the density of ammonia at 23ºC and 735 torr? What is the density of ammonia at 23ºC and 735 torr? A compound has the empirical formula CHCl. A 256 mL flask at 100.ºC and 750 torr contains.80 g of the gaseous compound. What is the molecular formula? A compound has the empirical formula CHCl. A 256 mL flask at 100.ºC and 750 torr contains.80 g of the gaseous compound. What is the molecular formula?

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The molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan’s atmosphere. The molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan’s atmosphere. 5.9 g/L 5.9 g/L

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2NaN 3 (s) 2Na (s) + 3 N 2 (g) The safety air bags in automobiles are inflated by nitrogen gas (see the equation above). If an air bag has a volume of 36 L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0 o C, how many grams of NaN 3 must be decomposed? The safety air bags in automobiles are inflated by nitrogen gas (see the equation above). If an air bag has a volume of 36 L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0 o C, how many grams of NaN 3 must be decomposed? 72 g NaN 3 72 g NaN 3

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Gases and Stoichiometry Reactions happen in moles Reactions happen in moles At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occuppies L. At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occuppies L. If not at STP, use the ideal gas law to calculate moles of reactant or volume of product. If not at STP, use the ideal gas law to calculate moles of reactant or volume of product.

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Examples Mercury can be achieved by the following reaction above. What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP? Mercury can be achieved by the following reaction above. What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP? At 400.ºC and 740 torr? At 400.ºC and 740 torr?

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Examples Using the following reaction Using the following reaction calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm. calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm. If 27 L of gas are produced at 26ºC and 745 torr when 2.6 L of HCl are added what is the concentration of HCl? If 27 L of gas are produced at 26ºC and 745 torr when 2.6 L of HCl are added what is the concentration of HCl?

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Examples Consider the following reaction What volume of NO at 1.0 atm and 1000ºC can be produced from 10.0 L of NH 3 and excess O 2 at the same temperature and pressure? Consider the following reaction What volume of NO at 1.0 atm and 1000ºC can be produced from 10.0 L of NH 3 and excess O 2 at the same temperature and pressure? What volume of O 2 measured at STP will be consumed when 10.0 kg NH 3 is reacted? What volume of O 2 measured at STP will be consumed when 10.0 kg NH 3 is reacted?

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The Same reaction What mass of H 2 O will be produced from 65.0 L of O 2 and 75.0 L of NH 3 both measured at STP? What mass of H 2 O will be produced from 65.0 L of O 2 and 75.0 L of NH 3 both measured at STP? What volume Of NO would be produced? What volume Of NO would be produced? What mass of NO is produced from 500. L of NH3 at 250.0ºC and 3.00 atm? What mass of NO is produced from 500. L of NH3 at 250.0ºC and 3.00 atm?

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Dalton’s Law of Partial Pressures The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. The total pressure is the sum of the partial pressures. The total pressure is the sum of the partial pressures. P Total = P 1 + P 2 + P 3 + P 4 + P 5... P Total = P 1 + P 2 + P 3 + P 4 + P 5... For each P = nRT/V For each P = nRT/V

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Dalton's Law P Total = n 1 RT + n 2 RT + n 3 RT +... V V V P Total = n 1 RT + n 2 RT + n 3 RT +... V V V In the same container R, T and V are the same. In the same container R, T and V are the same. P Total = (n 1 + n 2 + n )RT V P Total = (n 1 + n 2 + n )RT V P Total = (n Total )RT V P Total = (n Total )RT V

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The mole fraction Ratio of moles of the substance to the total moles. Ratio of moles of the substance to the total moles. symbol is Greek letter chi symbol is Greek letter chi = n 1 = P 1 n Total P Total

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Examples The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm? What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm? atm

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Examples 3.50 L O L N atm When these valves are opened, what is each partial pressure and the total pressure? When these valves are opened, what is each partial pressure and the total pressure? 4.00 L CH atm atm

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When valve is opened, the gases mix and fill the total volume of all vessels: When valve is opened, the gases mix and fill the total volume of all vessels: 4.0 L L L = 9.0 L 4.0 L L L = 9.0 L Since the #moles and temp. is constant, this is a simple Boyle’s Law problem: Since the #moles and temp. is constant, this is a simple Boyle’s Law problem: 4.0 L 4.0 L P CH4 = 2.7 atm = 1.2 atm 9.0 L 9.0 L 1.5 L 1.5 L P N2 = 4.58 atm = 0.76 atm 9.0 L 9.0 L 3.5 L 3.5 L P O2 =.752 atm = 0.29 atm 9.0 L 9.0 L So, the total pressure of all the gases is = 2.25 atm

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Kinetic Molecular Theory (KMT) Theory tells why the things happen. Theory tells why the things happen. Explains why ideal gases behave the way they do. Explains why ideal gases behave the way they do. Assumptions that simplify the theory, but don’t work in real gases. Assumptions that simplify the theory, but don’t work in real gases.

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Kinetic Molecular Theory… 1. The particles are so small we can ignore their volume. 2. The particles are in constant motion and their collisions cause pressure. 3. The particles do not exert forces on each either (attractive or repulsive) 4. The average Kinetic NRG is proportional to the Kelvin temperature (KE = 1/2 mv 2 )

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What it tells us (KE) avg = 3/2 RT (KE) avg = 3/2 RT This the meaning of temperature. This the meaning of temperature. Molecules move about at a random average KE. It is not a true average, but the root-mean- square speed (RMS speed). RMS is the square root of the average squared speeds. It is close to the average.

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Combine these two equations (KE) avg = N A (1/2 mu 2 ) (KE) avg = N A (1/2 mu 2 ) (KE) avg = 3/2 RT (KE) avg = 3/2 RT

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Combine these two equations (KE) avg = N A (1/2 mu 2 ) (KE) avg = N A (1/2 mu 2 ) (KE) avg = 3/2 RT Where M is the molar mass in kg/mole, and R has the units J/Kmol. (KE) avg = 3/2 RT Where M is the molar mass in kg/mole, and R has the units J/Kmol. The velocity will be in m/s The velocity will be in m/s

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Range of velocities The average distance a molecule travels before colliding with another is called the mean free path and is small (near ) The average distance a molecule travels before colliding with another is called the mean free path and is small (near ) Temperature is an average. There are molecules of many speeds in the average. Temperature is an average. There are molecules of many speeds in the average. Shown on a graph called a velocity distribution Shown on a graph called a velocity distribution

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number of particles Molecular Velocity 273 K

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number of particles Molecular Velocity 273 K 1273 K

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number of particles Molecular Velocity 273 K 1273 K 2273 K

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Velocity Average increases as temperature increases. Average increases as temperature increases. Spread increases as temperature increases. Spread increases as temperature increases.

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Molecular Effusion and Diffusion Effusion: Effusion: Movement of gas through a small opening into an evacuated container (vacuum) The effusion rate measures how fast this happens. The effusion rate measures how fast this happens. Graham’s Law -the rate of effusion is inversely proportional to the square root of the mass of its particles. Graham’s Law -the rate of effusion is inversely proportional to the square root of the mass of its particles.

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Graham’s Law

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Examples A compound effuses through a porous cylinder 3.20 times faster than helium. What is it’s molar mass? A compound effuses through a porous cylinder 3.20 times faster than helium. What is it’s molar mass? If mol of NH 3 effuse through a hole in 2.47 min, how much HCl would effuse in the same time? If mol of NH 3 effuse through a hole in 2.47 min, how much HCl would effuse in the same time? A sample of N 2 effuses through a hole in 38 seconds. what must be the molecular weight of gas that effuses in 55 seconds under identical conditions? A sample of N 2 effuses through a hole in 38 seconds. what must be the molecular weight of gas that effuses in 55 seconds under identical conditions?

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Diffusion The mixing of gases (the spreading of gas through a room) The mixing of gases (the spreading of gas through a room) Slow considering that gases move at 100’s of meters per second Slow considering that gases move at 100’s of meters per second Why is it so slow? Why is it so slow? Collisions with other molecules slow it down. Collisions with other molecules slow it down. Best estimate is Graham’s Law Best estimate is Graham’s Law

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Real Gases Real molecules do take up space and they do interact with each other (especially polar molecules). Real molecules do take up space and they do interact with each other (especially polar molecules). Need to add correction factors to the ideal gas law to account for these. Need to add correction factors to the ideal gas law to account for these.

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Volume Correction The actual volume free to move in is less because of particle size. The actual volume free to move in is less because of particle size. More molecules will have more effect. More molecules will have more effect. Corrected volume V’ = V - nb Corrected volume V’ = V - nb b is a constant that differs for each gas. b is a constant that differs for each gas. P’ = nRT (V-nb) P’ = nRT (V-nb)

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Pressure correction Because the molecules are attracted to each other, the pressure on the container will be less than ideal Because the molecules are attracted to each other, the pressure on the container will be less than ideal depends on the number of molecules per liter. depends on the number of molecules per liter. since two molecules interact, the effect must be squared. since two molecules interact, the effect must be squared.

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Pressure correction n Because the molecules are attracted to each other, the pressure on the container will be less than ideal n depends on the number of molecules per liter. n since two molecules interact, the effect must be squared. P observed = P’ - a 2 () V n

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Altogether P obs = nRT - a n 2 V-nb V P obs = nRT - a n 2 V-nb V Called the Van der Waal’s equation if rearranged Called the Van der Waal’s equation if rearranged Corrected Corrected Pressure Volume ()

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Where does it come from a and b are determined by experiment. a and b are determined by experiment. Different for each gas. Different for each gas. Bigger molecules have larger b. Bigger molecules have larger b. a depends on both size and polarity. a depends on both size and polarity. once given, plug and chug. once given, plug and chug.

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Example Calculate the pressure exerted by mol Cl 2 in a L container at 25.0ºC Calculate the pressure exerted by mol Cl 2 in a L container at 25.0ºC Using the ideal gas law. Using the ideal gas law. Van der Waal’s equation Van der Waal’s equation a = 6.49 atm L 2 /mol 2 b = L/mol

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