The Gas Laws Chapter 14.1

Gas Laws Our current understanding of the nature of gases is based on the work a many scientists over many years. Boyle Charles Gay-Lussac

Kinetic Molecular Theory – describes the behavior of gases in terms of particles in motion gas particles are relatively far apart the volume of the particles in a gas is small compared to the empty space around the particles gases are compressible gas liquid solid

Kinetic Molecular Theory since gas particles are far apart, gas particles do NOT attract or repel each other gas particles are in constant random motion collisions between gas particles are elastic (no kinetic energy is lost when gas particles collide at the same temperature)

Kinetic Molecular Theory all particles of gas have the same average kinetic energy at the same temperature if the temperature increases, so will the KE (the particles will move faster) if the temperature decreases, so will the KE (the particles will move slower)

Factors Affecting Gas Behavior the number of particles (amount) temperature pressure volume These factors are interdependent. If one changes, it will affect one or more other factors.

Vocabulary Word Pressure: force per unit area Units of pressure kilopascal (kPa) mm Hg torr psi atmosphere (atm)

Instruments used to measure pressure barometer: used to measure air or atmospheric pressure

Instruments used to measure pressure manometer: used to measure gas pressure in a closed container

Volume If you squeeze a closed balloon, the volume decreases the number of particles remains the same the temperature remains the same the pressure increases (the particles are closer together, so they collide more frequently)

Volume When you release the balloon, the volume increases so the pressure decreases

Boyle’s Law Robert Boyle (1627-1691) was an Irish chemist that studied the effects of volume and pressure on gases in a closed cylinder.

Boyle’s Law He showed that at constant temperature doubling the pressure (from 2 atm to 4 atm) would decrease the volume by 1/2 (from 5 L to 2.5 L).

Boyle’s Law He also showed that at constant temperature decreasing the pressure by half (from 2 atm to 1 atm) would increase the volume by 2 fold (from 5 L to 10 L).

Boyle’s Law Boyle concluded that volume and pressure are inversely related Since the product of pressure and volume at any point on the line = 10 atm•L P1V1 = P2V2

Vocabulary Word Boyle’s Law: P1V1 = P2V2 the volume of a gas varies inversely with pressure (at a constant temperature).

Using Boyle’s Law Air in a cylinder occupies 145.7 mL at 1.08 atmospheres (atm) of pressure. If the pressure increased to 1.43 atm, what would the new volume be? P1V1 = P2V2 (1.08)(145.7) = (1.43)(V2) 157.36 = 110 mL 1.43

Jacques Charles Jacques Charles (1746-1823) studied the relationship btwn volume and temperature at constant pressure. He found that as temperature increased, so did pressure.

Jacques Charles As temperature increases the gas particles move faster. This increases the number of collisions. In order to maintain the same pressure, gas particles must spread out. This increases the volume.

Jacques Charles Temperature and pressure are directly proportional. The graph predicts where the volume should equal 0 (lowest theoretical temperature), -273.15oC or 0 K.

Charles’ Law V1 = V2 T1 T2 Note: temperature must be in degrees Kelvin

Vocabulary Word Charles’ Law: states that the volume of a given mass of gas is directly proportional to its kelvin temperature at constant pressure V1 = V2 T1 T2 To convert btwn Celsius and Kelvin: Tk = Tc + 273

Charles’ Law Using Charles’ Law in calculations: a gas at 89oC has a volume of 0.67L. If the volume increases to 1.12L, what is the temperature? V1 = 0.67 L V2 = 1.12 L T1 = 89 + 273 = 362 T2 = ?

Charles’ Law V1 = 0.67 L V2 = 1.12 L T1 = 89 + 273 = 362 T2 = ? 0.67 = 1.12 362 T2 (0.67) T2 = (1.12) (362)

Charles’ Law (0.67) T2 = (1.12) (362) T2 = (1.12) (362) 0.67 = 605 K = 605 - 273 = 330oC

Joseph Gay-Lussac Joseph Gay-Lussac explored the relationship btwn temperature and pressure at constant volume. He found that it was a directly proportional relationship.

Vocabulary Word 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

Gay-Lussac’s Law using Gay-Lussac’s law in calculations The pressure in a tire is 1.88 atm at 25oC. If the temperature increases to 37oC, what will the pressure be? P1 = P2 1.88 = P2 T1 T2 298 310

Gay-Lussac’s Law 1.88 = P2 298 310 (1.88) (310) = (298) P2 298 310 (1.88) (310) = (298) P2 (1.88) (310) = P2 (298) 1.96 atm = P2