Understanding Gas Pressure: Basic Concepts and Devices to Measure

1. Topic 13

2. Table of Contents Topic 13 Topic 13: Gases Basic Concepts Additional Concepts

3. Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? • The pressure of a gas is the force per unit area that the particles in the gas exert on the walls of their container. • As you would expect, more air particles inside the ball mean more mass inside. Click box to view movie clip.

4. Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? • From similar observations and measurements, scientists from as long ago as the 18th century learned that the pressure of a gas is directly proportional to its mass.

5. Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? • 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.

6. Gases: Basic Concepts Topic 13 Defining Gas Pressure—How are number of particles and gas pressure related? • Therefore the pressure is directly proportional to the number of particles. • For example, doubling the number of gas particles in a basketball doubles the pressure.

7. Gases: Basic Concepts Topic 13 How are temperature and gas pressure related? • At higher temperatures, the particles in a gas have greater kinetic energy. • They move faster and collide with the walls of the container more often and with greater force, so the pressure rises.

8. Gases: Basic Concepts Topic 13 How are temperature and gas pressure related? • If the volume of the container and the number of particles of gas are not changed, the pressure of a gas increases in direct proportion to the Kelvin temperature. • The volume of a gas at constant pressure is directly proportional to the Kelvin temperature.

9. Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer • One of the first instruments used to measure gas pressure was designed by the Italian scientist Evangelista Torricelli (1608-1647). • He invented the barometer, an instrument that measures the pressure exerted by the atmosphere.

10. Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer • His barometer was so sensitive that it showed the difference in atmospheric pressure between the top and bottom of a flight of stairs.

11. Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer • The height of the mercury column measures the pressure exerted by the atmosphere. • We live at the bottom of an ocean of air. • The highest pressures occur at the lowest altitudes. • If you go up a mountain, atmospheric pressure decreases because the depth of air above you is less.

12. Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer • One unit used to measure pressure is defined by using Torricelli’s barometer. • The standard atmosphere(atm) is defined as the pressure that supports a 760-mm column of mercury.

13. Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer • This definition can be represented by the following equation. • Because atmospheric pressure is measured with a barometer, it is often called barometric pressure.

14. Gases: Basic Concepts Topic 13 Devices to Measure Pressure—The Barometer • A barometer measures absolute pressure; that is, the total pressures exerted by all gases, including the atmosphere.

15. Gases: Basic Concepts Topic 13 Pressure Units • Atmospheric pressure is the force per unit area that the gases in the atmosphere exert on the surface of Earth. • The SI unit for measuring pressure is the pascal(Pa), named after the French physicist Blaise Pascal (1623-1662).

16. Gases: Basic Concepts Topic 13 Pressure Units • Because the pascal is a small pressure unit, it is more convenient to use the kilopascal. 1 kilopascal (kPa)is equivalent to 1000 pascals. • One standard atmosphere is equivalent to 101.3 kilopascals.

17. Gases: Basic Concepts Topic 13 Pressure Units • Because there are so many different pressure units, the international community of scientists recommends that all pressure measurements be made using SI units, but pounds per square inch continues to be widely used in engineering and almost all nonscientific applications in the United States.

18. Gases: Basic Concepts Topic 13 Pressure Conversions • You can use the table to convert pressure measurements to other units. • For example, you can now find the absolute pressure of the air in a bicycle tire.

19. Gases: Basic Concepts Topic 13 Pressure Conversions • Suppose the gauge pressure is 44 psi. • To find the absolute pressure, add the atmospheric pressure to the gauge pressure. • Because the gauge pressure is given in pounds per square inch, use the value of the standard atmosphere that is expressed in pounds per square inch. • One standard atmosphere equals 14.7 psi.

20. Gases: Basic Concepts Topic 13 Converting Barometric Pressure Units • In weather reports, barometric pressure is often expressed in inches of mercury. • What is one standard atmosphere expressed in inches of mercury? • You know that one standard atmosphere is equivalent to 760 mm of Hg. What is that height expressed in inches? • A length of 1.00 inch measures 25.4 mm on a meterstick.

21. Gases: Basic Concepts Topic 13 Converting Barometric Pressure Units • Select the appropriate equivalent values and units given. • Multiply 760 mm by the number of inches in each millimeter to express the measurement in inches.

22. Gases: Basic Concepts Topic 13 Converting Barometric Pressure Units • The factor on the right of the expression above is the conversion factor. • Notice that the units are arranged so that the unit mm will cancel properly and the answer will be in inches.

23. Gases: Basic Concepts Topic 13 Converting Pressure Units • The reading of a tire-pressure gauge is 35 psi. What is the equivalent pressure in kilopascals? • The given unit is pounds per square inch (psi), and the desired unit is kilopascals (kPa). • The relationship between these two units is 14.7 = 101.3 kPa.

24. Gases: Basic Concepts Topic 13 Converting Pressure Units

25. Gases: Basic Concepts Topic 13 Converting Pressure Units • Multiply and divide the values and units. • Notice that the given units (psi) will cancel properly and the quantity will be expressed in the desired unit (kPa) in the answer.

26. Gases: Basic Concepts Topic 13 The Gas Laws • 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.

27. Gases: Basic Concepts Topic 13 The Gas Laws • 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.

28. Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume • Robert Boyle (1627-1691), an English scientist, used a simple apparatus pictured to compress gases.

29. Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume • After performing many experiments with gases at constant temperatures, Boyle had four findings. • a) If the pressure of a gas increases, its • volume decreases proportionately. • b) If the pressure of a gas decreases, its • volume increases proportionately.

30. Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume • c) If the volume of a gas increases, its • pressure decreases proportionately. • d) If the volume of a gas decreases, its • pressure increases proportionately. • By using inverse proportions, all four findings can be included in one statement called Boyle’s law.

31. Gases: Basic Concepts Topic 13 Boyle’s Law: Pressure and Volume • Boyle’s law states that the pressure and volume of a gas at constant temperature are inversely proportional. Click box to view movie clip.

32. Gases: Basic Concepts Topic 13 Boyle’s Law • At a 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.

33. Gases: Basic Concepts Topic 13 Boyle’s Law • Thus, Boyle’s law states that at constant temperature, the pressure and volume of a gas are inversely related. • In mathematical terms, this law is expressed as follows.

34. Gases: Basic Concepts Topic 13 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? • Examine the Boyle’s law equation. You need to find P2, the new pressure, so solve the equation for P2.

35. Gases: Basic Concepts Topic 13 Applying Boyle’s Law • Substitute known values and solve.

36. Gases: Basic Concepts Topic 13 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.

37. Gases: Basic Concepts Topic 13 Charles’s Law Click box to view movie clip.

38. Gases: Basic Concepts Topic 13 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? • Start by converting the given temperature to kelvins.

39. Gases: Basic Concepts Topic 13 Applying Charles’s Law • Next, solve the Charles’s law equation for the new temperature, T2.

40. Gases: Basic Concepts Topic 13 Applying Charles’s Law • Then, substitute the known values and compute the result. • Finally, convert the Kelvin temperature back to Celsius. New Temperature = 323 – 273 = 50oC

41. Gases: Basic Concepts Topic 13 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. • With this equation, you can find the value of any one of the variables if you know the other five.

42. Gases: Basic Concepts Topic 13 Applying the Combined Gas Law • A sample of nitrogen monoxide has a volume of 72.6 mL at a temperature of 16°C and a pressure of 104.1 kPa. • What volume will the sample occupy at 24°C and 99.3 kPa? • Start by converting the temperatures to kelvins.

43. Gases: Basic Concepts Topic 13 Applying the Combined Gas Law • Next, solve the combined gas law equation for the quantity to be determined, the new volume, V2.

44. Gases: Basic Concepts Topic 13 Applying the Combined Gas Law • Substitute the known quantities and compute V2.

45. Gases: Basic Concepts Topic 13 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.

46. Gases: Basic Concepts Topic 13 Avogadro’s Principle • Given that the mass of a mole of any gas is the molecular mass of the gas expressed in grams, Avogadro’s principle allows you to interrelate mass, moles, pressure, volume, and temperature for any sample of gas.

47. Gases: Basic Concepts Topic 13 Applying Avogadro’s Principle • What is the volume of 7.17 g of neon gas at 24°C and 1.05 atm? • Start by converting the mass of neon to moles. • The periodic table tells you that the atomic mass of neon is 20.18 amu. Therefore, the molar mass of neon is 20.18 g.

48. Gases: Basic Concepts Topic 13 Applying Avogadro’s Principle • Next, determine the volume at STP of 0.355 mol Ne. • If you needed only the volume at STP, you could stop here. • Finally, use the combined gas law equation to determine the volume of the neon at 24°C and 1.05 atm pressure.

49. Gases: Basic Concepts Topic 13 Applying Avogadro’s Principle

50. Gases: Basic Concepts Topic 13 Question 1 – 3 Use the table and the equation 1.00 in. = 25.4 mm to convert the following measurements. Round answers to the nearest tenth.