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How Do Gases Behave?

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What is a solid, liquid or gas? Help Marvin the Martian understand what a solid, liquid and gas are! Help Marvin the Martian understand what a solid, liquid and gas are! Draw what solids, liquids, gases look like Draw what solids, liquids, gases look like Describe physical/chemical properties Describe physical/chemical properties What would happen if we changed pressure? What would happen if we changed pressure? What would happen if we changed temperature? What would happen if we changed temperature?

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What is Pressure? Pressure = Force/Area Pressure = Force/Area 1 atmosphere (atm) 1 atmosphere (atm) 760 Torr 760 Torr 760 mmHg 760 mmHg 1.01 Bar 1.01 Bar 101,327 Pascal 101,327 Pascal Kpa Kpa 14.7 lbs/in lbs/in 2 Measured with Measured with a barometer

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MANOMETER Column of mercury to measure pressure. Column of mercury to measure pressure. h is how much lower or higher the pressure is than outside. h is how much lower or higher the pressure is than outside. P gas = P atm - h P gas = P atm - h P gas = P atm + h P gas = P atm + h h h

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What is Temperature? Average Kinetic Energy (1/2 mv 2 ) of an atom or molecule Average Kinetic Energy (1/2 mv 2 ) of an atom or molecule Measured in Fahrenheit, Celsius or Kelvin (SI) Measured in Fahrenheit, Celsius or Kelvin (SI) F = (C x 1.8) + 32 F = (C x 1.8) + 32 K = C K = C Kelvin: absolute zero (atom stops moving completely) 0 Kelvin: absolute zero (atom stops moving completely) Is there a maximum temperature in the universe? Is there a maximum temperature in the universe?

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Kinetic Molecular Theory Theory explains why ideal gases behave the way they do. Theory explains why ideal gases behave the way they do. Assumptions that simplify the theory, but dont work in real gases. Assumptions that simplify the theory, but dont work in real gases. 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 affect each other, neither attracting or repelling. 4. The average kinetic energy is proportional to the Kelvin temperature. 5. The molecules move in straight path and all collisions are elastic

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What is an Ideal Gas? An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of: An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of: Negligible volume Negligible volume With no intermolecular forces With no intermolecular forces Atoms or molecules undergo perfectly elastic collisions with the walls of the container Atoms or molecules undergo perfectly elastic collisions with the walls of the container Ideal gas law calculations are favored at low pressures and high temperatures. Ideal gas law calculations are favored at low pressures and high temperatures. Real gases existing in reality do not exhibit these exact properties, although the approximation is often good enough to describe real gases. Real gases existing in reality do not exhibit these exact properties, although the approximation is often good enough to describe real gases.

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What is Boyles Law? Boyles In the mid 1600's, Robert Boyle studied the relationship between the pressure P and the volume V of a confined gas held at a constant temperature. In the mid 1600's, Robert Boyle studied the relationship between the pressure P and the volume V of a confined gas held at a constant temperature. Boyle observed that the product of the pressure and volume are observed to be nearly constant. Boyle observed that the product of the pressure and volume are observed to be nearly constant. The product of pressure and volume is exactly a constant for an ideal gas. The product of pressure and volume is exactly a constant for an ideal gas. P * V = constant P * V = constant This relationship between pressure and volume is called Boyle's Law in his honor. This relationship between pressure and volume is called Boyle's Law in his honor.

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V P (at constant T) BOYLES LAW

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

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PV P (at constant T) CO 2 O2O L atm

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20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? P 1 V 1 =P 2 V 2 (0.98 atm)(20.5 L) = (9.8 atm)(V 2 ) atm*L/9.8 atm= V L = V mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa? 30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa? (30.6mL)(740Torr)=(750 mL)(P 2 ) 22,644 mL*Torr/750 mL= P Torr =P 2 (30.2 Torr) (1 atm/760 Torr) (101.3 kPa/1 atm)= kPa/760= 4.03 kPa

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What is Charles Law? Charles The relationship between temperature and volume, at a constant number of moles and pressure, is called Charles and Gay-Lussac's Law in honor of the two French scientists who first investigated this relationship. The relationship between temperature and volume, at a constant number of moles and pressure, is called Charles and Gay-Lussac's Law in honor of the two French scientists who first investigated this relationship. Charles did the original work, which was verified by Gay-Lussac. They observed that if the pressure is held constant, the volume V is equal to a constant times the temperature T, or: Charles did the original work, which was verified by Gay-Lussac. They observed that if the pressure is held constant, the volume V is equal to a constant times the temperature T, or: V / T= constant V / T= constant

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V (L) T (ºC) He H2OH2O CH 4 H2H ºC CHARLES LAW

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What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC, if the pressure is held constant? What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC, if the pressure is held constant? 247 ml/295 K = X ml/371 K 91,637 mL * K = 295 X * K 91,637 mL * K/295 K= X 310 mL = X If the volume of oxygen at 21 °C is 785 L, at what temperature would oxygen occupy 804 L? If the volume of oxygen at 21 °C is 785 L, at what temperature would oxygen occupy 804 L? 785 L/294 K = 804 L/X K 785 X = 236,376 X = 236,376/785 X= 301 K = 28 °C

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Combined Gas Law Combining Charless Law and Boyles Law in a single statement: Combining Charless Law and Boyles Law in a single statement: P 1 V 1 /T 1 = P 2 V 2 /T 2 P 1 V 1 /T 1 = P 2 V 2 /T mg of caffeine gives 10.1 mL of nitrogen gas at 23°C and 746 mmHg. What is the volume of nitrogen at 0°C and 760 mmHg? 39.8 mg of caffeine gives 10.1 mL of nitrogen gas at 23°C and 746 mmHg. What is the volume of nitrogen at 0°C and 760 mmHg? First change temperature to Kelvin First change temperature to Kelvin V 1 = 10.1mL P 1 = 746 mmHg K 1 = 296 K V 1 = 10.1mL P 1 = 746 mmHg K 1 = 296 K V 2 = ? P 2 = 760 mmHg K 2 = 273 K V 2 = ? P 2 = 760 mmHg K 2 = 273 K 10.1 * 746/296 = V 2 * 760/273 V 2 = 9.14 mL

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Other Gas Laws Gay-Lussac Law Gay-Lussac Law At constant volume, pressure and absolute temperature are directly related. At constant volume, pressure and absolute temperature are directly related. P/T = k (constant) P/T = k (constant) Avogadros Law Avogadros 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 /n= k (n is the number of moles) V /n= k (n is the number of moles)

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Gas Law Summary LawStatementEquationConstant Boyles P inversely proportional to V PV = k 1 T, n Charles V directly proportional to T V/T = k 2 P, n Gay-Lussac P directly proportional to T P/T = k 3 V, n Avogadros V directly proportional to n V/n = k 4 P, T What equation would we get if we combined them all?

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What is the Ideal Gas Law? Ideal Combining Boyles Law, Charles law & Avogadros Law we derive the Ideal Gas Law: Combining Boyles Law, Charles law & Avogadros Law we derive the Ideal Gas Law: P V = n R T P V = n R T P = Pressure (atm) P = Pressure (atm) V = Volume (L) V = Volume (L) n = # moles (mol) n = # moles (mol) R = Gas Constant ( L atm /mol K) R = Gas Constant ( L atm /mol K) T = Temperature (K) T = Temperature (K) Ideal gas law calculations are favored at low pressures and high temperatures Ideal gas law calculations are favored at low pressures and high temperatures 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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Let Try It! Example: Example: If we had 1.0 mol of gas at 1.0 atm of pressure at 0°C (STP), what would be the volume? If we had 1.0 mol of gas at 1.0 atm of pressure at 0°C (STP), what would be the volume? PV = nRT PV = nRT V = nRT/P V = nRT/P V = (1.0 mol)( L atm/mol K)(273 K)/(1.0 atm) V = (1.0 mol)( L atm/mol K)(273 K)/(1.0 atm) V = L V = L 1 mole of ANY gas at STP will occupy 22.4 Liters of volume 1 mole of ANY gas at STP will occupy 22.4 Liters of volume

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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 = m/M n = m/M PV = nRT PV = nRT PV = (m/M) RT PV = (m/M) RT P = mRT/VM = (m/V)(RT/M) P = mRT/VM = (m/V)(RT/M) P = d RT/M P = d RT/M PM/RT = d (density) PM/RT = d (density) Gas Density and Molar Mass

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What is the density of ammonia at 23ºC and 735 torr? What is the density of ammonia at 23ºC and 735 torr? Units must be: atm, K Units must be: atm, K 735 torr(1 atm/760 torr) = atm 735 torr(1 atm/760 torr) = atm = 296 K = 296 K Molar mass of NH 3 = 17.0 g Molar mass of NH 3 = 17.0 g d = * 17.0 g ( L* atm/mol * K)(296 K) ( L* atm/mol * K)(296 K) d = g / L Examples

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Reactions happen in moles Reactions happen in moles At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occupies L. At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occupies 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. Gases and Stoichiometry

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Consider the following reaction: Consider the following reaction: Suppose you heat mol of potassium chlorate, KClO 3, in a test tube. How many liters of oxygen can you produce at 298 K and 1.02 atm? Suppose you heat mol of potassium chlorate, KClO 3, in a test tube. How many liters of oxygen can you produce at 298 K and 1.02 atm? Break it into 2 problems, one involving stoichiometry and the other using the ideal gas law Break it into 2 problems, one involving stoichiometry and the other using the ideal gas law Examples

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mol KClO 3 X 3 mol O 2 /2 mol KClO 3 = mol O 2 Now that you have the moles of oxygen use the ideal gas law to calculate the volume: V = nRT/P mol x L * atm (K * mol) x 298 K 1.02 atm V = L

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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. n = PV/RT = (2.00 atm)(2.87 L) ( L*atm/K*mol)(298 K) ( L*atm/K*mol)(298 K) n= mol CO mol CO 2 (1 mol NaHCO 3 ) ( 84.0 g) (1 mol CO 2 ) (1 mol NaHCO 3 ) (1 mol CO 2 ) (1 mol NaHCO 3 ) 19.7 g NaHCO 3

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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 Daltons Law

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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 Dalton's Law

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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 Because pressure of a gas is proportional to moles, for fixed volume and temperature then, Because pressure of a gas is proportional to moles, for fixed volume and temperature then, = n 1 = P 1 n Total P Total = n 1 = P 1 n Total P Total The Mole Fraction

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Calculating the Partial Pressure and Mole Fraction of a Gas Mixture A 1.00 L sample of dry air at 25°C and 786 mmHg contains g N 2, plus other gases including oxygen, argon and carbon dioxide. A 1.00 L sample of dry air at 25°C and 786 mmHg contains g N 2, plus other gases including oxygen, argon and carbon dioxide. What is the partial pressure (in mmHg) of N 2 in the air sample? What is the partial pressure (in mmHg) of N 2 in the air sample? What is the mole fraction and mole percent of N 2 in the mixture? What is the mole fraction and mole percent of N 2 in the mixture?

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Convert grams into moles Convert grams into moles g N 2 x (1 mol N 2 /28.0g N 2 ) = mol N 2 Substitute into ideal gas law Substitute into ideal gas law P N2 = n N2 RT/V =0.0330mol x L*atm/K*mol x L =0.807 atm = 613 mmHg

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The mole fraction of N 2 in the air is The mole fraction of N 2 in the air is = P N2 /P = 613 mmHg/786 mmHg =0.780 Mole percent equals mole fraction x 100 Mole percent equals mole fraction x 100 =0.780 x 100 = 78% Air contains 78.0 mole percent of N 2 Air contains 78.0 mole percent of N 2

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Water evaporates! Water evaporates! When that water evaporates, the vapor has a pressure. When that water evaporates, the vapor has a pressure. Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure. Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure. Vapor pressure varies by temperature and must be given in the problem or in a table. Vapor pressure varies by temperature and must be given in the problem or in a table. Vapor Pressure

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Hydrogen gas is produced by the reaction of hydrochloric acid, HCl, on zinc metal: Hydrogen gas is produced by the reaction of hydrochloric acid, HCl, on zinc metal: 2HCl (aq) + Zn (s) > ZnCl 2 (aq) + H 2 (g) The gas is collected over water. If 156 mL of gas is collected at 19°C and 769 mmHg total pressure, what is the mass of hydrogen collected? The gas is collected over water. If 156 mL of gas is collected at 19°C and 769 mmHg total pressure, what is the mass of hydrogen collected?

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First find the Partial Pressure. The vapor pressure of water at 19°C is 16.5 mmHg First find the Partial Pressure. The vapor pressure of water at 19°C is 16.5 mmHg P = P H2 + P H2O P H2 = P - P H2O P H2 =769 – 16.5 = 752 mmHg Use the ideal gas law to find the moles of hydrogen collected. Use the ideal gas law to find the moles of hydrogen collected. P: 752 mmHg x (1 atm/760 mmHg) = atm V: 156 mL x (1 L/1000 mL) = L T: = 292 K R: L*atm/K*mol n: ?

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Solve for moles: Solve for moles: n = PV/RT = x 0.156/ x 292 = mol H 2 Convert moles to grams: Convert moles to grams: mol H 2 x (2.02g/1 mol H 2 ) = g H 2

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Whats Diffusion and Effusion? Only a few physical properties of gases depends on the identity of the gas. Only a few physical properties of gases depends on the identity of the gas. Diffusion - The rate at which two gases mix. Diffusion - The rate at which two gases mix. Effusion - The rate at which a gas escapes through a pinhole into a vacuum. Effusion - The rate at which a gas escapes through a pinhole into a vacuum.

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What is Grahams Law? Grahams We know that Kinetic energy = 1/2 mv 2 We know that Kinetic energy = 1/2 mv 2 If two bodies of unequal mass have the same kinetic energy, which moves faster? If two bodies of unequal mass have the same kinetic energy, which moves faster? The lighter one! The lighter one! Thus, for two gases at the same temperature, the one with lower molecular mass will diffuse/effuse faster. Thus, for two gases at the same temperature, the one with lower molecular mass will diffuse/effuse faster. The rate of effusion/diffusion of a gas is inversely proportional to the square root of its mass. The rate of effusion/diffusion of a gas is inversely proportional to the square root of its mass.

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Calculate the ratio of effusion rates of molecules of carbon dioxide and sulfur dioxide from the same container and at the same temperature and pressure: Calculate the ratio of effusion rates of molecules of carbon dioxide and sulfur dioxide from the same container and at the same temperature and pressure: Rate of effusion of CO 2 = M m SO 2 Rate of effusion of SO 2 M m CO 2 = 64.1/44.0 = 1.21 In other words, carbon dioxide effuses 1.21 times faster than sulfur dioxide. In other words, carbon dioxide effuses 1.21 times faster than sulfur dioxide.

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