Gas pressure is due to the force of gaseous particles colliding with their container. Torricelli invented the barometer to measure atmospheric pressure. Units used: mmHg, atm, kPa, psi Using a manometer: gas pressure > air pressure P gas = P atm + h gas pressure < air pressure P gas = P atm – h

Describe the relationship between pressure and volume of a gas. Describe the relationship between temperature and volume of a gas at a constant pressure. Define absolute zero. Solve problems for both Boyle’s and Charles’ Law.

Pressure (kPa) Volume (mL) BOYLE’S LAW – Pressure vs. Volume

BOYLE’S LAW: The volume of a given amount of gas (held at a constant temperature) varies inversely with the pressure. P α1 V

What will be the volume of 40 L of gas (held at a constant temperature) if the pressure is doubled? Reduced to 1/3 rd ? P α1 V 1/3 α 1 1/3 2 α1 2 1 = 3 1/3 120 L 20 L

PV = k = P1V1P1V1 P2V2P2V2 P α1 V

If 3 L of gas is initially at a pressure of 1 atm, what would be the new pressure required for a volume of 0.5 L? 6 atm of pressure will change 3 L of a gas at 1 atm to 0.5 L. = P1V1P1V1 P2V2P2V2 = (1)(3)P2P2 (0.5)

A syringe contains 20 mL of a gas at 100 kPa. The pressure in the syringe is changed to 25 kPa. What is the new volume of the gas? The gas will expand to 80 mL. = P1V1P1V1 P2V2P2V2 = (100)(20)V2V2 (25)

Absolute Zero

Jacques Charles ( ) Volume of gas changed with only 1 o C change in temperature. An increase of 273°C, doubled the volume. V α T CHARLES’S LAW: Volume of a given gas (held at a constant pressure) varies directly with the temperature

Temperature ( o C) Volume (mL) CHARLES’S LAW – Temp vs. Volume

William Thomson ( ) Created Kelvin Scale where –273°C is the lowest temperature possible or Absolute Zero. “Hypothetical” – called an ideal gas model: predicts that with zero kinetic energy comes zero volume. T K = T C T C = T K Stated as “315 Kelvin”- no degrees.

Ideal Gas Model: engaged in random motion (normal) obey conservation of energy (normal) non-interacting particles (IMFs alter results) Most real gases behave like “ideal gases,” but formula fails at lower temperatures OR higher pressures.

= V1V1 V2V2 T2T2 T1T1 **All temperatures must be in Kelvin. V α T V = k T

What is the new volume of a gas if 100 mL of the gas at 25°C is cooled to –25°C? 25°C = 298 K –25°C = 248 K The new volume is 83.2 mL. = V1V1 V2V2 T2T2 T1T1 = 100 V2V = mL (248) 298

If the volume of a gas at –73°C is doubled to 48.0 L, calculate the final temperature in degrees Celsius. 400 K – 273 = 127°C –73°C = 200 K = V1V1 V2V2 T2T2 T1T1 = K (200)

Boyle described the inverse relationship between the pressure and volume of a gas at a constant temperature. Charles described the direct relationship between the temperature and volume of a gas at a constant pressure. William Thomson (Lord Kelvin) developed the Kelvin temperature scale. At zero Kelvin (absolute zero), the volume of a gas will theoretically be zero. When solving gas problems the temperature must always be converted to Kelvin.