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Thermochemistry Study Notes chapter 6

QUESTIONS IN THERMOCHEMISTRY

  • If you place a thermometer into a solution, why does it take time for the reading on the thermometer to correspond to a temperature of the solution?
    • It takes time for the thermometer to reach thermal equilibrium with the solution.
  • Why don’t all gases have the same speed at a given temperature?
    • Gas molecules have collisions with other molecules and with container walls.
    • Collisions may mean different trajectories, and energy can be transferred during collisions.
    • If a molecule has more collisions than another, it has lower energy and thus lower speed.
  • After it has just finished raining, why do pools of water disappear when the temperature is below the boiling point of water?
    • Molecules near the liquid-gas boundary may have enough speed (i.e. kinetic energy) to escape.
    • The kinetic energy needed to overcome interactions holding molecules together is reduced as escaping molecules remove kinetic energy (i.e. evaporative cooling; same as sweating).
  • Many texts refer to energy being released when high energy bonds in ATP are broken. Is this a reasonable statement? What do these texts really mean?
    • In a reaction, some bonds may be broken and some may be formed.
    • Comparison of the relative energies of bond formation and bond breakage will indicate whether energy is released or not.
    • In the energy-releasing reaction, a bond in ATP is broken and the products (ADP & inorganic phosphate) are more stable than the reactant.
    • Energy is released during this reaction, indicating that energy changes occur in chemical reactions.

THE NATURE OF ENERGY: KEY DEFINITIONS

Important Terms

  • Thermodynamics: The study of heat and its transformations.
  • Thermochemistry: The branch of thermodynamics that deals with the heat involved in chemical and physical changes.
  • System: The part of the universe that is being studied.
  • Surroundings: Everything outside the system.
    • Open system: A system that can freely exchange energy and matter with its surroundings.
    • Closed system: A system that exchanges energy but not matter with its surroundings.
    • Isolated system: A system that does not interact with its surroundings.

Energy Concepts

  • Energy: Work is the action of forces through distances.
  • Potential Energy: Stored energy based on position.
  • Kinetic Energy: Energy of motion.
  • Thermal Energy: Depends on the number of particles and the nature of the substance (i.e., type of atoms or molecules).
  • Chemical Energy: Energy stored in the bonds of chemical compounds.
  • Law of Conservation of Energy: Energy cannot be created or destroyed, only transformed.

UNITS OF ENERGY

  • The SI unit of energy is the joule (J), defined as:
    1 ext{ J} = 1 ext{ kg} imes ext{ m}^2 imes ext{ s}^{-2}
  • The calorie (cal) is the older unit defining the quantity of energy needed to raise the temperature of 1 g of water by 1 °C (from 14.5 °C to 15.5 °C):
    1 ext{ cal} = 4.184 ext{ J}
  • Kilojoule (kJ):
    1 ext{ kJ} = 1000 ext{ J} = 0.2390 ext{ kcal} = 239.0 ext{ cal}
  • Nutritional calorie (Cal): Used in diet tables, actually a kilocalorie.
  • British Thermal Unit (Btu): A unit in engineering indicating the output of appliances; it is the energy required to raise the temperature of 1 lb of water by 1 °F, equivalent to:
    ext{Btu} = 1055 ext{ J}

FIRST LAW OF THERMODYNAMICS: THERE IS NO FREE LUNCH

  • First Law of Thermodynamics:
    • The total energy of the universe (i.e., system + surroundings) is constant.
    • Energy of an isolated system is constant.
    • Law of conservation of energy applies here: ext{ΔU}{ ext{isolated system}} = 0 or ext{ΔU}{ ext{system}} = - ext{ΔU}_{ ext{surroundings}}

INTERNAL ENERGY

  • Internal Energy (U):
    • The sum of the potential and kinetic energy for all particles in a system.
    • The system contains only internal energy.
    • Heat (q) and work (w) are ways of transferring energy between the system and surroundings:
      ext{ΔU} = U{f} - U{i} = q + w
  • Thermodynamic Quantities:
    • Consist of two parts:
      a) A number giving the magnitude of the change.
      b) The sign giving the direction of flow:
    • Energy coming into the system is positive because the system ends up with more energy.
    • Energy going out from the system is negative because the system ends up with less energy.
    • First law of thermodynamics states: ext{ΔU}{ ext{isolated}} = 0 or ext{ΔU}{ ext{system}} = - ext{ΔU}_{ ext{surroundings}}

CONTRIBUTIONS TO INTERNAL ENERGY

  • Contributions can include:
    • Translation energy.
    • Bond vibrational energy.
    • Molecular rotational energy.
    • Chemical bond energy.
    • Intermolecular attractions.
    • Energy due to electrons.

STATE FUNCTIONS

  • State functions or functions of state:
    • A property that depends only upon the current state of the system (its composition, volume, pressure, temperature) and not on the path the system took to reach that state.
    • Examples of state functions: Internal energy, temperature, pressure, enthalpy, volume.
    • Therefore, changes in functions like ext{ΔU, ΔP, ΔV, ΔT depend only on the system’s initial and final states.
    • Examples of path-dependent functions/properties: Work, heat.

QUANTIFYING HEAT & WORK

  • Heat (q):
    • Energy transferred between a system and its surroundings as a result of a difference in temperature only.
    • Energy change involving thermal energy transfer, moving from the body of higher temperature to the lower temperature until equal.
    • Can be transferred across the system and surrounding boundary.

Heat Relationships

  • The quantity of heat (q) absorbed by an object is proportional to its temperature change:
    q ext{ is proportional to } ext{ΔT} or q = ext{constant} imes ext{ΔT} = ext{constant} imes (T{f} - T{i})
  • Heat Capacity (C): The quantity of heat required to change the temperature of a substance by 1 K or 1 °C.
    C = rac{q}{ ext{ΔT}} units of J/K or J/°C.
  • Specific Heat Capacity (Cs): The quantity of heat required to change the temperature of 1 g of substance by 1 K or 1 °C at constant pressure:
    C_s = rac{q}{ ext{mass} imes ext{ΔT}} = rac{q}{m imes ext{ΔT}}
    units of J/g/K or J/g/°C.
  • Molar Heat Capacity (Cp,m): The quantity of heat required to change the temperature of 1 mole of substance by 1 K or 1 °C at constant pressure:
    C_{p,m} = rac{q}{ ext{amount} imes ext{ΔT}} = rac{q}{n imes ext{ΔT}}
    units of J/mol/K or J/mol/°C.

CALCULATIONS EXAMPLES

Example 1: Determine if a shiny gold-like rock is gold

  • Given: 4.7 g sample of rock, 57.2 J of heat supplied, temperature rises from 25 °C to 57 °C.
    • Use the equation:
      q = mCs ΔT Where: Cs = 0.380 ext{ J/g/°C} (actual for gold is 0.128 J/g/°C), thus rock is not gold.

Example 2: Calculate final temperature of aluminum block

  • Given: 55.0 g aluminum block, initial temperature 27.5 °C, absorbs 725 J of heat.
    • C_s ext{ (Al)} = 0.903 ext{ J/g/°C};
    • Calculate temperature to reach 42.1 °C.

Example 3: Calculate heat required to raise temperature of mercury

  • Given: 2.50 ext{ kg} Hg from –20.0 to –6.0 °C, with density 13.6 g/mL and molar heat capacity 28.0 J/mol·°C. Answer: 4.89 kJ.

FIRST LAW OF THERMODYNAMICS

  • Energy Changes:
  • The total energy of an isolated system remains constant.
  • q{in} + q{out} = 0 ext{ (total heat exchange)}

HEAT OF REACTIONS & CALORIMETRY

  • Chemical Energy: Energy associated with chemical bonds and intermolecular interactions.
  • Heat of Reaction (qrxn): Quantity of heat exchanged when a chemical reaction occurs at constant temperature.
  • Calorimetry: The science of measuring heat, based on observations of temperature changes when energy is absorbed or discharged.
  • Types of Calorimetry:
    • Constant Volume Calorimetry (Bomb Calorimeter)
    • Constant Pressure Calorimetry (Coffee Cup Calorimeter)

ENTHALPY

  • Enthalpy (H): Defined as H = U + PV
  • Change in enthalpy ( ext{ΔH}) equals heat gained or lost at constant pressure.
  • Enthalpy change (ΔH) can be calculated using the concept of standard states, with defined conditions for gases, solutions, and pure substances.
  • Hess’s Law: The enthalpy change of an overall process is the sum of the enthalpy changes of its individual steps.

THERMODYNAMIC QUANTITIES VARIABILITY AND STANDARDS

  • Standard States:
    • For gases: 1 bar and temperature of interest; behaves ideally.
    • For aqueous solutions: 1 M concentration.
    • For pure substances: Most stable form at 1 bar and designated temperature.

EXAMPLES

  1. Calculate enthalpy required for the given reaction of sucrose combustion.
  2. Use standard enthalpies of formation to find the ΔH for reactions.
  3. Calculate heat produced in reactions such as photosynthesis and combustion based on stoichiometry.

OBJECTIVES

  1. Define the nature of energy including system types and energy changes.
  2. Understand and apply the first law of thermodynamics in real-world contexts.
  3. Quantify and differentiate heat-related properties: heat, heat capacities, and work calculations.
  4. Analyze reactions using calorimetry and apply Hess’s Law in energy calculations.
  5. Evaluate environmental considerations for energy use and sustainability.