Lecture 3: Thermodynamics and Thermochemistry

Lecture Overview

• Topic: Thermodynamics and Thermochemistry

• Key Learning Areas:

  • Enthalpy

  • Dealing with Precision and Uncertainty

  • Importance of Units

  • Heat of Reactions

• Instructor: Khashayar Ghandi (kghandi@uoguelph.ca)

State Variables and State Functions

• State of a system is characterized by a set of variables on which all properties depend:

  • Common State Variables: Pressure (P), Volume (V), Temperature (T), number of moles (n)

• Classification of State Variables:

  • Intensive Variables: Independent of size

  • Examples: Pressure (P), Temperature (T)

  • Extensive Variables: Dependent on size

  • Examples: Mass, Volume (V), number of moles (n)

• State Function:

  • Example: Altitude of a campsite (independent of the path taken to reach it)

• Gravitational Potential Energy:

  • Expression: mgh

  • Where:

    • m = mass (kg)

    • g = gravitational constant (9.80 m/s²)

    • h = height (m)

Enthalpy (H)

• Defined as: An extensive property of a substance used to obtain the heat absorbed or evolved in a chemical reaction at constant pressure

• Enthalpy Change (ΔH):

  • Formula: riangle H = H( ext{products}) - H( ext{reactants})

  • Most reactions conducted at constant pressure, thus: riangle H = q_P

• Equation for Heat of Reaction (ΔH_Rxn):

  • riangle H_ ext{Rxn} = ext{s}ú H ext{products} - ext{s}ú H ext{reactants}

Example Reaction Analysis

Example 1: Reaction Type

• Reaction:

  • 2 ext{ mol Na}(s) + 2 ext{ mol H}_2 ext{O}(l)

• Enthalpy Change (H):

  • H = -368.6 ext{ kJ}

  • Indicates: 368.6 kJ of heat is released (Exothermic reaction)

• Products of Reaction:

  • 2 ext{ mol NaOH}(aq) + 1 ext{ mol H}_2(g)

Thermochemical Equations

• Defined as: The chemical equation in stoichiometric molar form with the enthalpy of reaction written directly after the equation

• Standard Enthalpy Change (°):

  • Indicates pure reactants and products at standard conditions (1 bar, 100 kPa)

• Example of Thermochemical Equation:

  • ext{CH}4(g) + 2 ext{O}2(g) → ext{CO}2(g) + 2 ext{H}2 ext{O}(l); riangle H^ ext{°} = -890 ext{ kJ} ext{mol}^{-1}

Quantities in Chemistry

• Chemistry involves a vast range of quantities, from subatomic scale to global measurements

• Smallest Timeframes in Kinetics:

  • Example: Lifetimes of subatomic particles can be around 1/100,000,000,000,000,000,000,000 s

• Age of the Universe:

  • Approximately 15,000,000,000 ext{ years}

• Scientific Notation:

  • Used for convenient representation of these quantities

  • Example Representations:

  • 31416.5 = 3.14165 imes 10^{4}

  • 0.002718 = 2.718 imes 10^{-3}

  • 15,000,000,000 = 1.5 imes 10^{10}

SI Prefixes and Scientific Notation

• SI Prefixes:

  • Describe powers of 10

  • Different prefixes every three powers of 10:

  • Examples of Prefix Conversion:

  • 3.0 imes 10^{9} ext{ W} = 3.0 ext{ GW} (3 gigawatts)

  • 1.6 imes 10^{-8} ext{ m} = 16 ext{ nm} (16 nanometers)

Estimation: Orders of Magnitude

• Order of Magnitude:

  • Definition: Refers to how many powers of 10 a number has

  • Example Orders:

  • 10 has an order of magnitude of one

  • 100 has an order of magnitude of two

• Practical Use:

  • Useful for quick calculations

Example of Back-of-the-Envelope Calculation

• Scenario: Canada's yearly gasoline consumption estimation

• Inputs:

  • Population of Canada: 40 million

  • Estimated number of cars: 20 million (2×10^7 cars)

  • Average car mileage: 20,000 km (2×10^4 km)

  • Fuel Consumption: 10 L/100 km

• Calculation:

  • Yearly consumption per car:

  • ext{(20,000 km)} imes ext{(10 L/100 km)} = 2 imes 10^{3} ext{ L}

  • Total yearly gasoline consumption:

  • ext{(2 × 10}^{3} ext{ L/car)} imes ext{(2 × 10}^{7} ext{ cars)} = 4 × 10^{10} ext{ L} (Approx. 40 Giga L)

Importance of Units in Chemistry

• Units are crucial in chemistry to avoid errors

• Anecdote:

  • NASA lost a $125 million Mars orbiter due to mishandling of unit conversions (English vs Metric systems)

Converting Units

• Conversion Methodology:

  • Use conversion tables to relate physical quantities in different unit systems

  • Process: Multiply or divide such that the undesired units cancel out

• Example of Unit Conversion:

  • Convert 1 mile (5280 feet) to meters using the conversion factor: 1 ext{ ft} = 0.3048 ext{ m}

Example in Thermochemistry

• Reaction of Sulfur (S8):

  • Burns in air to produce sulfur dioxide (SO2)

  • ext{S}8(s) + 8 ext{O}2(g) → 8 ext{SO}_2(g)

  • Enthalpy change: Averages 9.31 kJ of heat per gram of sulfur

  • Conversion to heat per mole for thermochemical equation:

  • riangle H = –2.39 imes 10^{3} ext{ kJ}

  • The negative sign indicates exothermic nature of the reaction

Applying Stoichiometry to Heats of Reaction

• Conversion Framework:

  • Start from grams of substance A to moles of A

  • Calculate kilojoules (kJ) associated with either reactant or product using

  • Molar mass of A

  • Enthalpy of reaction

Significant Figures and Uncertainty

• All measurements include experimental error

• Significant Figures:

  • Indicate the precision of a measurement

  • Accuracy influenced by the measuring instrument's limitations

• Importance:

  • Proper reporting of data requires adherence to significant figures to avoid misleading conclusions

  • Estimation, accuracy, and precision are critical in thermodynamics and kinetics

Sources of Uncertainty

• Model Errors:

  • Approximations in theories used for estimations can introduce errors

• Statistical Errors:

  • Natural variations in measurements

• Instrumentation Errors:

• Intrinsic Uncertainty:

  • Resulting from quantum nature at a microscopic scale

Summary of Key Topics Discussed

• Introduction to thermodynamics laws

• Concepts of system and surroundings

• Overview of thermochemistry and enthalpy calculations

• Importance of significant figures and handling of uncertainty

• Methods for unit conversion and scientific notation usage

• Introduction to calorimetry

Calorimetry: Measurement Examples

• Energy from Food:

  • Three primary roles:

  1. Supplies substances for tissue growth and repair

  2. Supplies substances for regulatory compound synthesis

  3. Supplies energy for physical actions

• Energy content through combustion processes

Examples of Energy Content in Biological Compounds

• For Glucose (C6H12O6):

  • Combustion reaction:

  • C6 H{12} O6(s) + 6 O2(g) → 6 CO2(g) + 6 H2 O(l); riangle H_f° = –2803 ext{ kJ}

• For Glycerol Trimyristate:

  • Combustion reaction:

  • C{45} H{86} O6(s) + rac{127}{2} O2(g) → 45 CO2(g) + 43 H2 O(l); riangle H_f° = –27,820 ext{ kJ}

• Average Energy Values:

  • Carbohydrates: 4.0 kcal/g

  • Fats: 9.0 kcal/g

Fossil Fuels and Energy Production

• Formation of Fossil Fuels:

  • Originated from the burial and compression of aquatic plants and animals over millions of years

  • Converted by bacterial decay and pressure into petroleum, gas, and coal

• Combustion:

  • Long-used process to generate heat, work, and electricity

Electricity Production in Canada

• Canada utilizes cleaner methods for electricity production

• Natural Gas: Preferred due to cleanliness and convenience (primarily methanes)

• Petroleum: A mixture, including hydrocarbons (e.g., gasoline)

• Coal: Viewed as the least favorable energy source

Recommended Problems to Work On (10th Edition)

• Problems:

  • 6.11

  • 6.31

  • 6.35

  • 6.97

  • 6.135