Volume - Temperature: Charles’ Law

OUTCOME QUESTION(S): C11-2-07 UNITS AND RELATIONSHIPS Describe the various units used to measure pressure and convert between units. Include: atmospheres, kilopascals, millimetres of mercury Experiment to develop the relationship between the pressure and volume of a gas using visual, numeric, and graphical representations. Include: Boyle’s Law Experiment to develop the relationship between the volume and temperature of a gas using visual, numeric, and graphical representations. Include: Charles’ Law, Absolute zero, Kelvin scale, Ideal gas Develop the relationship between the pressure and temperature of a gas using visual, numeric, and graphical representations. Include: Gay-Lussac’s Law, Dalton’s Law Vocabulary & Concepts 

Volume and temperature show a constant direct relationship Jacques Charles: (1746 - 1823) Experimented with volume and temperature of a sample at constant pressure. Data plotted – as volume vs. temperature Linear relationship emerges (a straight line) Slope is constant and predictable rise = constant run V = constant T rise Volume and temperature show a constant direct relationship run

Predictions fail using negative Celsius temperatures William Thomas: (1824 - 1907) Also known as “Lord Kelvin” Recognized significance of the extrapolation… Created Kelvin Scale where 0 K represents the lowest possible temperature (–273°C) Called Absolute Zero Predictions fail using negative Celsius temperatures

Absolute temperature extrapolations lead to: Ideal Gas Model Predicts that with zero kinetic energy comes zero volume Suggest particles will be non-interacting not possible not true Model predictions are good approximations of real gas behaviours under normal conditions – fail at extreme low temperatures or high pressures

(when held at a constant pressure) Charles’ Law: The volume of a given amount of gas varies directly with the temperature in Kelvin. (when held at a constant pressure) V α T

Stated as “315 Kelvin”- no degrees Converting Kelvin scale - Celsius: TK = TC + 273 TC = TK - 273 Stated as “315 Kelvin”- no degrees Now solve Charles’ Law by converting to Kelvin and use the same ratio argument used in Boyle’s Law problems

What is the new volume of 40 L of gas if the temperature in Kelvin is doubled? A direct relationship suggests: 2 α 2 V α T 80 L Double the temperature will double the original volume If temperature is reduced to 1/3rd ? 1 3 α 1 3 13.3 L Decreased temperature will shrink volume to 1/3 the original Direct of a third is a third

= V1 T1 V2 T2 V1 T1 V2 T2 Charles’ Law Equation: V = constant T rise run **All temperatures must be in Kelvin. V = constant T V1 T1 V2 T2 Initial conditions always equal Final conditions when divided

What is the new volume of a gas if 100 mL of the gas at 25°C is cooled to –25°C? V1 = 100 mL T1 = 25oC + 273 = 298 K V2 = ? T2 = -25oC + 273 = 248 K Watch units… V1 = V2 Predicted result? T1 T2 (248) 100 83 mL = 298 Decreasing the temperature by 50 degrees will cause a decrease in volume to 83 mL

If the volume of a gas at –73°C is doubled to 48 If the volume of a gas at –73°C is doubled to 48.0 L, calculate the final temperature in degrees Celsius. V1 = 24 L T1 = -73oC + 273 = 200 K V2 = 48 L T2 = ? V1 = V2 T1 T2 Predicted result? = 48.0 (200) 400 K 24.0 400 K – 273 = 127°C Doubling volume will require doubling temperature (in Kelvin) or 127oC

CAN YOU / HAVE YOU? C11-2-07 UNITS AND RELATIONSHIPS Describe the various units used to measure pressure and convert between units. Include: atmospheres, kilopascals, millimetres of mercury Experiment to develop the relationship between the pressure and volume of a gas using visual, numeric, and graphical representations. Include: Boyle’s Law Experiment to develop the relationship between the volume and temperature of a gas using visual, numeric, and graphical representations. Include: Charles’ Law, Absolute zero, Kelvin scale, Ideal gas Develop the relationship between the pressure and temperature of a gas using visual, numeric, and graphical representations. Include: Gay-Lussac’s Law, Dalton’s Law Vocabulary & Concepts