Gas Laws

1. Gas Laws

2. Gases-Review Remember: - according to the kinetic theory, all matter is composed of particles in constant motion, and pressure is caused by the force of gas particles striking the walls of their container. - the more often gas particles collide with the walls of their container, the greater the pressure. - the pressure is directly proportional to the number of particles. - at higher temperatures, the particles in a gas have greater kinetic energy, causing them to collide with the walls of the container more often and with greater force, so the pressure rises. - standard atmosphere(atm) is defined as the pressure that supports a 760-mm column of mercury. - the SI unit for measuring pressure is the pascal(Pa), named after the French physicist Blaise Pascal (1623-1662).

3. Kinetic-Molecular Theory Review The gas laws apply to ideal gases, which are described by the kinetic theory in the following five statements. -Gas particles do not attract or repel each other. -Gas particles are much smaller than the spaces between them. -Gas particles are in constant, random motion. -No kinetic energy is lost when gas particles collide with each other or with the walls of their container. -All gases have the same kinetic energy at a given temperature.

4. Boyle’s Law-Pressure & Volume Robert Boyle (1627-1691), an English scientist, used a simple apparatus to compress gases at constant temperatures, he had four findings: 1. If the pressure of a gas increases, its volume decreases proportionately. 2. If the pressure of a gas decreases, its volume increases proportionately. 3. If the volume of a gas increases, its pressure decreases proportionately. 4. If the volume of a gas decreases, its pressure increases proportionately.

5. Boyle’s Law By using inverse proportions, all four findings can be included in one statement called Boyle’s law. -At constant temperature, the pressure exerted by a gas depends on the frequency of collisions between gas particles and the container. -If the same number of particles is squeezed into a smaller space, the frequency of collisions increases, thereby increasing the pressure. -Thus, Boyle’s law states that at constant temperature, the pressure and volume of a gas are inversely related.

6. Applying Boyle’s Law A sample of compressed methane has a volume of 648 mL at a pressure of 503 kPa. To what pressure would the methane have to be compressed in order to have a volume of 216 mL? Step 1: Examine the Boyle’s law equation. -You need to find P2, the new pressure, so solve the equation for P2. Step 2: Substitute known values and solve.

7. Boyle’s Law Practice (p 422 #1-4) • The volume of a gas at 99.0kPa is 300.0mL. If the pressure is increased to 188kPa, what will the new volume be? • The pressure of a sample of helium in an 1.00L container is 0.988atm. What is the new pressure of the sample is placed in a 2.00L container? • Air trapped in a cylinder fitted with a piston occupies 145.7mL at 1.08atm pressure. What is the new volume of air when the pressure is increased to 1.43atm by applying force to the piston? • If it takes 0.0500L of oxygen gas kept in a cylinder under pressure to fill an evacuated 4.00L reaction vessel in which the pressure is 0.980atm, what was the initial pressure of the gas?

8. Charles’s Law • When the temperature of a sample of gas is increased and the volume is free to change, the pressure of the gas does not increase. Instead, the volume of the gas increases in proportion to the increase in Kelvin temperature. This observation is Charles’s law, which can be stated mathematically as follows.

9. Applying Charles’s Law A weather balloon contains 5.30 kL of helium gas when the temperature is 12°C. At what temperature will the balloon’s volume have increased to 6.00 kL? Step 1: convert the given temperature to Kelvin. Step 2: solve the Charles’s law equation for the new temperature, T2.

10. Applying Charles’s Law A weather balloon contains 5.30 kL of helium gas when the temperature is 12°C. At what temperature will the balloon’s volume have increased to 6.00 kL? Step 3: substitute the known values and compute the result Step 4: convert the Kelvin temperature back to Celsius. New Temperature = 323 – 273 = 50oC

11. Charles’s Law Practice (p 425 #6-8) • A gas at 89⁰C occupies a volume of 0.67L. At what Celsius temperature will the volume increase to 1.12L? • The Celsius temperature of a 3.00L sample of gas is lowered from 80.0⁰C to 30.0⁰C. What will the resulting volume be? • What is the volume of the air in a balloon that occupies 0.620L at 25.0⁰C if the temperature is lowered to 0.00⁰C?

12. Gay-Lussac’s Law Boyle’s Law relates pressure and volume of a gas. Charles’s Law relates a gas’s temperature and volume. Gay-Lussac’s Law relates a gas’s temperature and pressure. Gay-Lussac’s Law states that the pressure of a given mass of gas varies directly with the Kelvin temperature when the volume remains constant. P1 = P2 T1 T2

13. Applying Gay-Lussac’s Law The pressure of a gas in a tank is 3.20atm at 22.0⁰C. If the temperature rises to 60.0⁰C, what will the be gas pressure in the tank? Step 1: obtain the temperatures in Kelvin TK = 273 + TC = 273 + 22.0 = 295K TK = 273 + TC = 273 + 60.0 = 333K Step 2: solve the Charles’s law equation for the new pressure, P2. P2 = P1 T2 T1 P1 = P2 T1 T2

14. Applying Gay-Lussac’s Law The pressure of a gas in a tank is 3.20atm at 22.0⁰C. If the temperature rises to 60.0⁰C, what will the be gas pressure in the tank? Step 3: substitute the known values into the equations and solve P2 = P1 T2 = (3.20atm)(333K) T1 295K = 3.61atm

15. Gay-Lussac’s Law Practice (p 427 #9-12) 9. A gas in a sealed container has a pressure of 125kPa at a temperature of 30.0⁰C. If the pressure in the container is increased to 201kPa, what is the new temperature? 10. The pressure in an automobile tire is 1.88atm at 25.0⁰C. What will be the pressure if the temperature warms up to 37.0⁰C? 11. Helium gas in a 2.00L cylinder is under 1.12atm of pressure. At 36.5⁰C, that same gas sample has a pressure of 2.56atm. What was the initial temperature of the gas in the cylinder? 12. If a gas sample has a pressure of 30.7kPa at 0.00 ⁰ C, by how much does the temperature have to decrease to lower the pressure to 28.4kPa?

16. Gas Laws Review • Explain why gases such as the oxygen found in tanks used at hospitals are compressed. Why must care be taken to prevent compressed gases from reaching a high temperature? • A weather balloon of known initial volume is released. The air pressures at its initial and final altitudes are known. Why can’t you find it’s new volume by using these known variables and Boyle’s Law? • Determine which gas law you would use to calculate the following problem, then solve it: A gas at 20.0 ⁰ C occupies 1.00L. Assuming the pressure stays the same, what volume will it occupy at 30.0⁰C? 4. Why are baking instructions different at high altitudes than at low altitudes?

17. The Combined Gas Law The gas laws may be combined into a single law, called the combined gas law, that relates two sets of conditions of pressure, volume, and temperature by the following equation:

18. Applying the Combined Gas Law A sample of nitrogen monoxide has a volume of 72.6 mL at a temperature of 16.0°C and a pressure of 104.1 kPa. What volume will the sample occupy at 24.0°C and 99.3 kPa? Step 1: convert temperatures to Kelvin

19. Applying the Combined Gas Law Step 2: Substitute the known quantities and compute V2.

20. Combined Gas Laws Practice (p 430 # 19-21) • A helium-filled balloon at sea level has a volume of 2.1L at 0.998atm and 36⁰C. If it is released and rises to an elevation at which the pressure is 0.900atm and the temperature is 28⁰C, what will be the new volume of the balloon? • At 0.00⁰C and 1.00atm pressure, a sample of gas occupies 30.0mL. If the temperature is increased to 30.0⁰C and the entire gas sample is transferred to a 20.0mL container, what will be the gas pressure inside the container? • A sample of air in a syringe exerts a pressure of 1.02atm at a temperature of 22.0⁰C. The syringe is placed in a boiling water bath at 100.0⁰C. The pressure of the air is increased to 1.23atm by pushing the plunger in, which reduces the volume to 0.224mL. What was the original volume of air?

21. Avogadro’s Principle In the early nineteenth century, Avogadro proposed the idea that equal volumes of all gases at the same conditions of temperature and pressure contain the same number of particles. An extension of Avogadro’s principle is that one mole (6.02 x 1023 particles) of any gas at standard temperature and pressure (0°C and 1.00 atm pressure, STP) occupies a volume of 22.4 L. 22.4L/1mol or 1 mol/22.4L -allows you to interrelate mass, moles, pressure, volume, and temperature for any sample of gas.

22. Applying Avogadro’s Principle What is the volume of 7.17 g of neon gas at 24°C and 1.05 atm? Step 1: convert mass of neon to moles If given moles, skip step 1 and go to step 2 Step 2: determine the volume at STP of 0.355 mol Ne. If you needed volume at STP, you could stop here.

23. Applying Avogadro’s Principle What is the volume of 7.17 g of neon gas at 24°C and 1.05 atm? Step 3: use the combined gas law equation to determine the volume of the neon at 24°C and 1.05 atm pressure.

24. Avogadro’s Principle Practice (p 432 # 24-25;433 # 29-32) • Determine the volume of a container that holds 2.4 mol of gas at STP. • What size container do you need to hold 0.0459 mol of nitrogen gas at STP? • How many grams of carbon dioxide gas are in a 1.0L balloon at STP? • What volume in milliliters will 0.00922 g hydrogen gas occupy at STP? • What volume will 0.416 g of krypton gas occupy at STP?

25. The Ideal Gas Law The pressure, volume, temperature, and number of moles of gas can be related in a simpler, more convenient way by using the ideal gas law. The following is the law’s mathematical expression, where n represents the number of moles. PV = nRT The ideal gas constant,R, already contains the molar volume of a gas at STP along with the STP conditions. -value of R depends on the units in which the pressure of the gas is measured -These values are all equivalent. Use the one that matches the pressure units you are using.

26. Applying the Ideal Gas Law What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45°C? Step 1: change the temperature to kelvin Step 2: Substitute the known quantities and calculate P PV = nRT

27. Ideal Gas Law Practice (p 437 #41-44) 41. If the pressure exerted by a gas at 25⁰C in a volume of 0.044L is 3.81atm, how many moles of gas are present? 42. Determine the Celsius temperature of 2.49mol of gas contained in a 1.00L vessel at a pressure of 143kPa. 43. Calculate the volume that a 0.323 mol sample of a gas will occupy at 265K and a pressure of 0.900atm. 44. What is the pressure in atmospheres of a 0.108mol sample of helium gas at a temperature of 20.0⁰C if its volume is 0.505L?

28. Gas Stoichiometry Ammonium sulfate can be prepared by a reaction between ammonia gas and sulfuric acid as follows. What volume of NH3 gas, measured at 78°C and a pressure of 1.66 atm, will be needed to produce 5.00 x 103 g of (NH4)2SO4? Step 1: compute number of moles represented by 5.00 x 103 g of (NH4)2SO4. -molar mass of (NH4)2SO4= 132.14 g/mol

29. Gas Stoichiometry What volume of NH3 gas, measured at 78°C and a pressure of 1.66 atm, will be needed to produce 5.00 x 103 g of (NH4)2SO4? Step 2: determine the number of moles of NH3 that must react to produce 37.84 mol (NH4)2SO4. Step 3: use the ideal gas law equation to calculate the volume of 75.68 mol NH3 under the stated conditions.