# The Gas Laws. The effect of adding gas. 4 things. Pressure and the number of molecules are directly related. Page 1

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1 The Gas Laws Describe HOW gases behave. Can be predicted by the theory. The Kinetic Theory Amount of change can be calculated with mathematical equations. The effect of adding gas. When we blow up a balloon we are adding gas molecules. Doubling the number of gas particles doubles the pressure (of the same volume at the same temperature). 4 things 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 Fewer molecules means fewer collisions. If you double the number of molecules 1 atm Page 1 1

2 If you double the number of molecules You double the pressure. 2 atm 4 atm As you remove molecules from a container 2 atm As you remove molecules from a container the pressure decreases 1 atm As you remove molecules from a container the pressure decreases Until the pressure inside equals the pressure outside Molecules naturally move from high to low pressure Changing the size of the container In a smaller container molecules have less room to move 1 atm As the pressure on a gas increases Hit the sides of the container more often As volume decreases pressure increases. 4 Liters Page 2 2

3 2 atm 2 Liters As the pressure on a gas increases the volume decreases Pressure and volume are inversely related Temperature Raising the temperature of a gas increases the pressure if the volume is held constant. The molecules hit the walls harder. The only way to increase the temperature at constant pressure is to increase the volume. 300 K 600 K 300 K If you start with 1 liter of gas at 1 atm pressure and 300 K and heat it to 600 K one of 2 things happens 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 Does not really exist makes the math easier close approximation. Assume particles have no volume Assume no attractive forces between molecules Page 3 3

4 Ideal Gases There are no gases for which this is true. Real gases behave this way at high temperature and low pressure. Boyle s Law At a constant temperature pressure and volume are inversely related As one goes up the other goes down P x V = K (K is some constant) Easier to use P 1 x V 1 = P 2 x V 2 Graph P 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? V 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. V = K x T (K is some constant) V = K T V 1 = V 2 T 1 T 2 Graph Page 4 4

5 V What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure. T What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC? Gay Lussac s Law The temperature and the pressure of a gas are directly related at constant volume. P = K x T (K is some constant) P = K T P 1 = P 2 T 1 T 2 P s What is the pressure inside a L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? At what temperature will the can above have a pressure of 2.2 atm? T Animation Page 5 5

6 Putting the pieces together The Combined Gas Law Deals with the situation where only the number of molecules stays constant. P 1 x V 1 = P 2 x V 2 T 1 T 2 Lets us figure out one thing when two of the others change. The combined gas law contains all the other gas laws! If the temperature remains constant. P 1 x V 1 P 2 x V = 2 Boyle s Law T 1 T 2 The combined gas law contains all the other gas laws! If the pressure remains constant. The combined gas law contains all the other gas laws! If the volume remains constant. P 1 x V 1 = P 2 x V 2 P 1 x V 1 = P 2 x V 2 T 1 T 2 T 1 T 2 Charles Law Gay-Lussac s Law s 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? s 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? Page 6 6

7 The Fourth Part Avagadro s Hypothesis V is proportional to number of molecules at constant T and P. V is proportional to moles. V = K n ( n is the number of moles. Gets put into the combined gas law P 1 x V 1 = P 2 x V 2 = KR n 1 x T 1 n 1 x T 2 The Ideal Gas Law P x V = n x R x T Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. This time R does not depend on anything, it is really constant The Ideal Gas Constant R = (L atm) (mol K) R = 62.4 (L mm Hg) (K mol) R = 8.31 (L kpa) (K mol) PV = nrt We now have a new way to count moles of a gas. By measuring T, P, and V. We aren t restricted to STP. n = PV/RT The Ideal Gas Law Nothing is required to change, No 1 s and 2 s How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg? What is the pressure exerted by 1.8 g of H 2 gas exert in a 4.3 L balloon at 27ºC? Page 7 7

8 Density The Molar mass of a gas can be determined by the density of the gas. D= mass = m Volume V Molar mass = mass = m Moles n n = PV RT Molar Mass = m (PV/RT) Molar mass = m RT V P Molar mass = DRT P At STP At STP determining the amount of gas required or produced is easy L = 1 mole Not At STP Chemical reactions happen in MOLES. If you know how much gas - change it to moles Use the Ideal Gas Law n = PV/RT If you want to find how much gas - use moles to figure out volume V = nrt/p Use the equation in place of 22.4 L HCl(g) can be formed by the following reaction 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) What mass of NaCl is needed to produce 340 ml of HCl at 1.51 atm at 20ºC? Page 8 8

9 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10.2 g of NaCl react? Ideal Gases don t exist Molecules do take up space All matter has volume There are attractive forces otherwise there would be no liquids Real Gases behave like Ideal Gases When the molecules are far apart They take a smaller percentage of the space Ignoring their volume is reasonable This is at low pressure Real Gases behave like Ideal gases when When molecules are moving fast. Molecules are not next to each other very long Attractive forces can t play a role. At high temp. Far above boiling point. Effect of Pressure Molecule size because they are close together Intermolecular forces stick molecules together 54 Page 9 9

10 Effect of Temperature Van der Waal s equation P + a n 2 obs x ( V- nb ) nrt V = Corrected Pressure Corrected Volume a is a number that depends on how much the molecules stick to each other b is a number that determined by how big the molecules are 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. The partial pressure of a gas is the contribution by that gas hitting the wall. P Total = P 1 + P 2 + P 3 + For example We can find out the pressure in the fourth container By adding up the pressure in the first 3 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. Figure out their pressures separately Add them to get total s 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? 59 Page 10 10

11 s 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 N 2 at 2.0 atm the other holds 2.0 L of O 2 at 8.0 atm. The valve is opened. What is The pressure of N 2? The pressure of O 2? The total pressure? L O 2 at 8.0 atm 2.0 L 4.0 L N 2 at 2.0 atm 4.0 L Diffusion Molecules moving from areas of high concentration to low concentration. Perfume molecules spreading across the room. Effusion - Gas escaping through a tiny hole in a container. From high to low concentration Both depend on the speed of the molecules Graham s Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Kinetic energy = 1/2 mv 2 m is the mass v is the velocity Chem Express Page 11 11

12 Graham s Law bigger molecules move slower at the same temp. (by Square root) Bigger molecules effuse and diffuse slower Helium effuses and diffuses faster than air - escapes from balloon. Grahams Law effusion rate 1 = effusion rate 2 Velocity 1 = Velocity 2 Time 2 = Time 1 M M M M 2 1 M M In a test He effused at 3.5 moles/minute. How fast would N 2 effuse in the same conditions? H 2 effused 2.82 times faster than an unknown gas. What was the molar mass of the unknown gas 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 Page 12 12

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