cm2 - The Gas Laws Describe HOW gases behave. x Can be...

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Unformatted text preview: The Gas Laws Describe HOW gases behave. x Can be predicted by the theory. • The Kinetic Theory x Amount of change can be calculated with mathematical equations. x The effect of adding gas. When we blow up a balloon we are adding gas molecules. x Doubling the number of gas particles doubles the pressure (of the same volume at the same temperature). x 4 things x In order to completely describe a gas you need to measure 4 things 1. Pressure 2. Temperature 3. Volume 4. Number of particles 4 Pressure and the number of molecules are directly related More molecules means more collisions x Fewer molecules means fewer collisions. x x If you double the number of molecules 1 atm If you double the number of molecules x You double the pressure. x 2 atm 4 atm x As you remove molecules from a container 2 atm x As you remove molecules from a container the pressure decreases 1 atm As you remove molecules from a container the pressure decreases x Until the pressure inside equals the pressure outside x Molecules naturally move from high to low pressure x Changing the size of the container In a smaller container molecules have less room to move x Hit the sides of the container more often x As volume decreases pressure increases. x 1 atm x As the pressure on a gas increases 4 Liters 2 atm 2 Liters As the pressure on a gas increases the volume decreases x Pressure and volume are inversely related x Temperature Raising the temperature of a gas increases the pressure if the volume is held constant. x The molecules hit the walls harder. x The only way to increase the temperature at constant pressure is to increase the volume. x 300 K If you start with 1 liter of gas at 1 atm pressure and 300 K x and heat it to 600 K one of 2 things happens x 600 K 300 K x Either the volume will increase to 2 liters at 1 atm 300 K 600 K •Or the pressure will increase to 2 atm. •Or someplace in between Ideal Gases In this chapter we are going to assume the gases behave ideally x Does not really exist • makes the math easier • close approximation. x Assume particles have no volume x Assume no attractive forces between molecules x Ideal Gases There are no gases for which this is true. x Real gases behave this way at high temperature and low pressure. x Boyle’s Law At a constant temperature pressure and volume are inversely related x As one goes up the other goes down xPxV=K (K is some constant) x x Easier to use P1 x V1= P2 x V2 Graph P V Example x A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm what is the new volume? Example x A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to volume to 43 L? Charles’ Law The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. x V = K x T (K is some constant) x V =K T x V1 = V2 Graph T1 T2 x V T x What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure. Example x What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC? Example Gay Lussac’s Law The temperature and the pressure of a gas are directly related at constant volume. x P = K x T (K is some constant) x P =K T x P1 = P2 T1 T2 x P T Examples What is the pressure inside a 0.250 L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? x At what temperature will the can above have a pressure of 2.2 atm? x Animation Putting the pieces together The Combined Gas Law Deals with the situation where only the number of molecules stays constant. x P1 x V1 = P2 x V2 T1 T2 x x Lets us figure out one thing when two of the others change. The combined gas law contains all the other gas laws! x If the temperature remains constant. x P1x V1 T1 Boyle’s Law = P2x V2 T2 The combined gas law contains all the other gas laws! x If the pressure remains constant. x P1x V1 T1 = P2x V2 T2 Charles’ Law The combined gas law contains all the other gas laws! x If the volume remains constant. x P1x V1 T1 = P2x V2 T2 Gay-Lussac’s Law Examples x A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 17 atm. What is the new volume? Examples x If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas? The Fourth Part Avagadro’s Hypothesis x V is proportional to number of molecules at constant T and P. x V is proportional to moles. x V = K n ( n is the number of moles. x Gets put into the combined gas law x P1 x V1 = P2 x V2 =K R n1 x T1 n1 x T2 x The Ideal Gas Law PxV=nxRxT x Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. x This time R does not depend on anything, it is really constant x The Ideal Gas Constant R = 0.0821 (L atm) (mol K) x R = 62.4 (L mm Hg) (K mol) x R = 8.31 (L kPa) (K mol) x The Ideal Gas Law PV = nRT x We now have a new way to count moles of a gas. By measuring T, P, and V. x We aren’t restricted to STP. x n = PV/RT x Nothing is required to change, • No 1’s and 2’s x x How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg? Example Example x What is the pressure exerted by 1.8 g of H2 gas exert in a 4.3 L balloon at 27ºC? Density The Molar mass of a gas can be determined by the density of the gas. x D= mass = m Volume V x Molar mass = mass = m Moles n x n = PV RT x m (PV/RT) x Molar mass = m RT VP x Molar mass = DRT P x Molar Mass = At STP At STP determining the amount of gas required or produced is easy. x 22.4 L = 1 mole x Not At STP Chemical reactions happen in MOLES. x If you know how much gas - change it to moles x Use the Ideal Gas Law n = PV/RT x If you want to find how much gas - use moles to figure out volume V = nRT/P x Use the equation in place of 22.4 L x Example HCl(g) can be formed by the following reaction x 2NaCl(aq) + H2SO4 (aq) → 2HCl(g) + Na2SO4(aq) x x What mass of NaCl is needed to produce 340 mL of HCl at 1.51 atm at 20ºC? Example x 2NaCl(aq) + H2SO4 (aq) → 2HCl(g) + Na2SO4 (aq) What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10.2 g of NaCl react? x Ideal Gases don’t exist Molecules do take up space • All matter has volume x There are attractive forces • otherwise there would be no liquids x Real Gases behave like Ideal Gases When the molecules are far apart x They take a smaller percentage of the space x Ignoring their volume is reasonable x This is at low pressure x Real Gases behave like Ideal gases when When molecules are moving fast. x Molecules are not next to each other very long x Attractive forces can’t play a role. x At high temp. x Far above boiling point. x Effect of Pressure Molecule size because they are close together Intermolecular forces stick molecules together 54 Effect of Temperature 55 2 n x V - nb = nRT ) Pobs + a ( V Corrected Corrected Van der Waal’s equation Pressure x Volume a is a number that depends on how much the molecules stick to each other x b is a number that determined by how big the molecules are 56 Dalton’s Law of Partial Pressures The total pressure inside a container is equal to the sum of the partial pressure due to each gas. x The partial pressure of a gas is the contribution by that gas hitting the wall. x x PTotal = P1 + P2 + P3 + … x For example We can find out the pressure in the fourth container x By adding up the pressure in the first 3 x 2 atm 1 atm 3 atm 6 atm Dalton’s Law This means that we can treat gases in the same container as if they don’t affect each other. x Figure out their pressures separately x Add them to get total x 59 Examples x What is the total pressure in a balloon filled with air if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg? Examples In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg? There are two containers connected by a valve. One holds 4.0 L of N2 at 2.0 atm the other holds 2.0 L of O2 at 8.0 atm. x The valve is opened. What is • The pressure of N2 ? x • The pressure of O2 ? • The total pressure? 62 2.0 L O2 at 8.0 atm 4.0 L N2 at 2.0 atm 63 2.0 L 4.0 L 64 Diffusion Molecules moving from areas of high concentration to low concentration. x Perfume molecules spreading across the room. x Effusion - Gas escaping through a tiny hole in a container. x From high to low concentration x Both depend on the speed of the molecules x Graham’s Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. x Kinetic energy = 1/2 mv2 x m is the mass v is the velocity x Chem Express Graham’s Law bigger molecules move slower at the same temp. (by Square root) x Bigger molecules effuse and diffuse slower x Helium effuses and diffuses faster than air -escapes from balloon. x Grahams Law effusion rate 1 = effusion rate 2 Velocity 1 = Velocity 2 Time 2 = Time 1 M2 M1 M2 M1 M2 M1 Example x In a test He effused at 3.5 moles/minute. How fast would N2 effuse in the same conditions? 69 Example x H2 effused 2.82 times faster than an unknown gas. What was the molar mass of the unknown gas. 70 Example x It took an unknown gas 89.3 seconds to effuse through a hole. Oxygen effused through the same hole in 60 seconds. What is the molar mass of the gas? 71 ...
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cm2 - The Gas Laws Describe HOW gases behave. x Can be...

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