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You can predict how pressure, volume, temperature, and number of gas particles are related to each other based on the molecular model of a gas.

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The Kinetic Molecular Theory 1.) Gas particles are in constant motion and move in a straight line until they hit another gas particle or the side of the container. 2.) There are not attractive or repulsive forces between the gas particles. 3.) The volume of the actual gas particle is assumed to be zero, since it is insignificant to the volume of the whole sample of gas.

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The Kinetic Molecular Theory (cont.) 4.) The temperature is an indirect measure the average kinetic energy of all the gas particles in the sample. Kinetic Energy = ½ (mass) x (velocity) 2 5.) There is no exchange of energy when 2 gas particles collide, the collision is totally elastic. (Just like when two billiard balls collide.)

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Pressure Pressure = Force Applied / Area (P = F / A) When the gas molecules collide with the inside wall of the container, it exerts a force over an area. Therefore there is always an internal pressure on a gas.

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Measuring Pressure Pressure can be measured using a device called a manometer.

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Measuring Pressure Atmospheric Pressure can be measured using a device called a barometer.

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Units for Measuring Pressure Pascal (Pa) – Metric System unit for pressure Atmosphere (atm) Pounds per square inch (psi) Torricelli (torr) Millimeter of Mercury (mm Hg) 1 atm = 101,300 Pa = 101.3 kPa = 14.7 psi = 760 torr = 760 mm Hg

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Pressure Conversions 1 atm = 101,300 Pa = 101.3 kPa = 14.7 psi = 760 torr = 760 mm Hg Convert 0.75 atm into mm Hg. Convert 32.0 psi into kPa.

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Robert Boyle (1627 – 1691) An English scientist whose work revolved around trying to discover the relationship between the pressure and volume of a gas.

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Boyles Law If the pressure exerted on a gas increases, the volume of the gas will proportionally decrease. What is the relationship between the pressure exerted on a gas and its volume?

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Boyles Law The product of the pressure and volume of a gas must always be a constant as long as the temperature and # of moles of gas remain constant. Pressure x Volume = constant Pressure (initial) x Volume (initial) = Pressure (final) x Volume (final) P 1 V 1 = P 2 V 2

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Boyles Law Initially, a 3.0 L expandable tank of gas is under a pressure of 13 atm. What would be the volume of the tank if the pressure inside the tank is reduced to 5.0 atm. The temperature and # of moles of gas remain constant.

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Jacques Charles (1746 – 1823) A French scientist, inventor, and avid balloonist. He was interested in discovering the affect that the temperature had on the volume of a gas.

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Charles Law The volume of a gas divided by its Kelvin temperature must remain constant. As long as the pressure and # moles of gas does not change. Volume = constant Temperature Volume (initial) = Volume (final) Temperature (initial) Temperature (final) V 1 = V 2 T 1 T 2 Temperature must be in Kelvins!

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Charles Law This is how absolute zero was determined. Is it possible?

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Charles Law Problem A balloon has a volume of 1.0 L at 23.0°C. What is the volume of the balloon if the temperature decreases to -10.0°C? Assume that the pressure and # of moles of gas particles remains constant.

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Combined Gas Law (Boyles and Charles Law) P 1.V 1 = P 2.V 2 T 1 T 2 The number of moles of gas must remain constant.

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Combined Gas Law (Boyles and Charles Law) A 2.0 L balloon initially at Standard Temperature and Pressure (STP) is heated to 100.0 °C and pressurized to 1.5 atmospheres. Calculate the new volume of the balloon.

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Joseph Louis Gay-Lussac (1778 – 1850) French Chemist and Physicist who discovered th relationship between the pressure and the temperature of a gas.

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Joseph Louis Gay-Lussac (1778 – 1850) Gay-Lussacs Law P 1 = P 2 T 1 T 2 The volume and number of moles of gas must remain constant.

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Gay-Lussacs Law Initially, a sample of gas has a temperature of 10.0°C. It is then pressurized from 740. mm Hg to 800. mm Hg. What will be the new temperature of the gas if the volume and number of moles of gas remain constant?

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The Ideal Gas Law The only gas law that incorporates moles into it. PV = nRT P = Pressure (atm or kPa) V = Volume (L) n = # of moles of gas particles R = The Gas Law Constant (0.0821 L.atm) mol.K T = Temperature (K)

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The Ideal Gas Law What volume would 44.01 grams of CO 2 occupy at 0.00°C and 1.00 atmosphere?

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The Ideal Gas Law What is pressure of 10.0 grams of NH 3 in a 5.0 L tank at 50.0°C?

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Using the Ideal Gas Law to Relate Molar Mass and Density of Gas; We can rearrange the Ideal Gas Law to get the following equation - P.V = nRT ==== n = P V RT

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Using the Ideal Gas Law to Relate Molar Mass and Density of Gas; If we multiply both sides of the Ideal Gas Law by molar mass, we have the following – (molar mass) n = P (molar mass) V RT Mass = P (molar mass) Volume RT

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Using the Ideal Gas Law to Relate Molar Mass and Density of Gas; Mass = P (molar mass) Volume RT Density = P (molar mass) RT

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Using the Ideal Gas Law to Relate Molar Mass and Density of Gas; Density = P (molar mass) RT Calculate the density of nitrogen gas at a pressure of 1.5 atm and a temperature of -10.0°C.

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Using the Ideal Gas Law to Relate Molar Mass and Density of Gas; Density = P (molar mass) RT Calculate the molar mass of a gas that has a density of 0.029 g / L when it is at a pressure of 800. kPa and 25.0°C.

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Using the Ideal Gas Law with Gas Stoichiometry; How many grams of hydrogen gas is needed to fill a 100.0 L vessel with ammonia gas at 1.2 atm at a temperature of -25.0°C? N 2(g) + 3H 2(g) 2NH 3(g)

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Using the Ideal Gas Law with Gas Stoichiometry; Automobile airbags are inflated with nitrogen gas using the following chemical reaction; 2NaN 3(s) 2Na (s) + 3N 2(g) How many grams of NaN 3 must decompose in order to fill a 40.0 L airbag with nitrogen gas at 30.0°C and 1.0 atm?

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John Dalton (1766-1844) What did he not do?

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Daltons Law of Partial Pressures The partial pressure (p gas X ) of a gas is the pressure that the gas exerts when it is part of a mixture of gases. Right now, the room that we are sitting in contains nitrogen gas, oxygen gas, water vapor, and trace amount of other gases. 0.21 atm O 2 + 0.78 atm N 2 + 0.05 atm CO 2 + 0.05atm trace gases = 1.0 atm (atmospheric pressure)

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Daltons Law of Partial Pressures The total pressure of a mixture of gases is equal to the sum of all of the partial pressures of the gases that make up the gas mixture. p gas 1 + p gas 2 + p gas 3 + ……… = P total

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Grahams Law of Effusion Grahams Law Describes the relative speed (velocity) at which gas particles will move, or diffuse.

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Grahams Law of Effusion Effusion – The movement of a gas molecule through a small hole so its velocity may be measured. Diffusion – The movement of gas particles from an area of high concentration to an area of low concentration.

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Grahams Law of Effusion What is diffusion?

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Grahams Law of Effusion A heavier gas particle will travel slower than a lighter gas particle. KE = ½ mass x velocity 2 If the kinetic energy is the same for a heavy and a light gas particle, then the velocity of the heavier one will be less than the velocity of the lighter one.

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Grahams Law of Effusion Ammonia and hydrogen chloride gas will form the white precipitate ammonium chloride; NH 3(g) + HCl (g) NH 4 Cl (s)

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Grahams Law of Effusion Ammonia and hydrogen chloride gas will form the white precipitate ammonium chloride; NH 3(g) + HCl (g) NH 4 Cl (s) Which end contains the ammonia?

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Grahams Law of Effusion Which molecule will diffuse faster, H 2 or O 2 ? How many times faster will the faster molecule diffuse compared to the slower one?

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