Chemistry Study Notes: Thermochemistry

Chapter 6: Thermochemistry: Energy Flow and Chemical Change

6.1 Forms of Energy and Their Interconversion

• Thermodynamics is the study of energy and its transformations.

• Thermochemistry is a branch of thermodynamics that deals with the heat involved in chemical and physical changes.

• Energy transfer occurs from one object to another manifesting as work and/or heat.

6.2 A Chemical System and its Surroundings

• The system refers to the contents of the reaction flask.

• The surroundings comprise everything else including the flask itself.

6.3 Defining System and Surroundings

• A meaningful study of energy transfer requires clear definitions of both the system and surroundings.

• Equation: System + Surroundings = Universe.

• Internal energy, $E$, of a system is the sum of the potential and kinetic energies of all particles present:
  $E = E<em>{potential} + E</em>{kinetic}$

• The total energy of the universe remains constant.

• A change in the energy of the system must result in an equal and opposite change in the energy of the surroundings.

6.4 Transfer of Internal Energy

• Change in internal energy ($ riangle E$) is defined as:
  $riangle E = E<em>{final} - E</em>{initial}$

• This reflects the difference in energy between the products and the reactants.

6.5 Heat and Work: Two Forms of Energy Transfer

• Energy transfer occurs in two forms:

  • Heat ($q$): energy transferred due to temperature difference between system and surroundings.

  • Work ($w$): energy transferred when an object is moved by a force.

• Total change in a system's internal energy:
  $riangle E = q + w$

6.6 Sign Conventions for q, w, and ΔE

• For $q$ (heat):

  • $+$ indicates heat absorbed by the system from surroundings.

  • $-$ indicates heat released by the system to the surroundings.

• For $w$ (work):

  • $+$ indicates work done on the system by surroundings.

  • $-$ indicates work done by the system on surroundings.

6.7 The Law of Energy Conservation

• First law of thermodynamics states: the total energy of the universe is constant.

• Energy can neither be created nor destroyed, only transferred as heat or work.

• Equation:
  $riangle E<em>{universe} = riangle E</em>{system} + riangle E_{surroundings} = 0$

6.8 Units of Energy

• The SI unit of energy is the joule (J):
  $1 J = 1 ext{ kg m}^2/ ext{s}^2$

• The calorie is defined as the quantity of energy needed to raise the temperature of 1 g of water by 1°C:

  • Conversion:
    $1 ext{ cal} = 4.184 J$

• The nutritional Calorie (Kilocalorie):

  • Conversion:
    $1 ext{ Cal} = 1000 ext{ cal} = 1 ext{ kcal} = 4184 J$

• British thermal unit (Btu):

  • Conversion:
    $1 ext{ Btu} = 1055 J$

6.9 Some Quantities of Energy

• Daily solar energy falling on Earth: $10^{24} J$.

• Energy of a strong earthquake: $10^{18} J$.

• Daily electrical output of Hoover Dam: $10^{15} J$.

• Combustion of 1 mol of glucose: $10^{3} J$.

• 1 kilowatt-hour of electrical energy: $10^{6} J$.

• Energy from fission of one $^{235}U$ atom: $10^{-15} J$.

6.10 Two Different Paths for the Energy Change of a System

• The total $ riangle E$ remains the same although $q$ and $w$ differ for different paths taken through the system's states.

6.11 Pressure-Volume Work

• Expanding gas performs PV work on surroundings:
  $w = -P riangle V$

6.12 Enthalpy: Chemical Change at Constant Pressure

• Enthalpy ($H$) defined as:
  $H = E + PV$
  Thus:
  $riangle H = riangle E + P riangle V$

• Under constant pressure conditions, if the volume change is minimal,
  $riangle H ext{ is approximately equal to } riangle E.$

6.13 ΔH as a Measure of ΔE

• $ riangle H$ represents the change in heat for a system at constant pressure:
  $q_p = riangle E + P riangle V$

• For reactions that involve gases, when the amount of gas does not change, $ riangle H ext{ approximates } riangle E$.

6.14 Enthalpy of Exothermic and Endothermic Processes

• Exothermic: releases heat;

  • $ riangle H < 0$.

• Endothermic: absorbs heat;

  • $ riangle H > 0$.

6.15 Calorimetry

• Heat exchanged is represented by: $q = c imes m imes riangle T$ where:

  • $q$: heat lost or gained

  • $c$: specific heat capacity

  • $m$: mass in grams

  • $ riangle T = T{final} - T{initial}$.

6.16 Specific Heat Capacities of Elements and Compounds

• Common specific heat capacities (c) values at 298 K (25°C):

  • Aluminum (Al): 0.897 J/g K

  • Water (H2O(l)): 4.18 J/g K

  • Ethyl alcohol (C2H5OH(l)): 2.438 J/g K

  • Iron (Fe): 0.449 J/g K

6.17 Sample Problem 6.4: Heat and Temperature Change

• Problem: Calculate heat needed to raise temperature of 125 g of copper from 25°C to 90°C.

  • $ext{c (Cu)} = 0.385 J/g K$

  • $T<em>{final} = 90°C, T</em>{initial} = 25°C, riangle T = 65°C$

• Solution:
  $q_{Cu} = c imes m imes riangle T = 0.385 imes 125 imes 65 = 3.13 imes 10^{3} J$

• Repeat calculation for water:

  • $ext{c (H2O)} = 4.18 J/g K$

  • $q_{H2O} = 4.18 imes 125 imes 65 = 4.30 imes 10^{4} J$

• Reason for difference: heat required for water is 10.9 times that of copper due to specific heat capacity differences.

6.18 Calorimetry Techniques

• Constant-Pressure Calorimetry: Illustrated Colloquial setup includes coffee-cup calorimeter, which consists of:

  • Stirrer

  • Thermometer

  • Cork stopper

  • Nested Styrofoam cups for insulation

• A Bomb Calorimeter measures heat at constant volume.

6.19 Stoichiometry of Thermochemical Equations

• A thermochemical equation integrates enthalpy $ riangle H$.

• Sign of $ riangle H$: Indicates exothermic or endothermic reactions.

• Magnitude of $ riangle H$: Directly proportional to the amount of substance.

6.20 Sample Problem 6.8: Thermochemical Equations

• Problem: Decompose bauxite ($Al2O3$).

• Analyze heat transferred to grams of aluminum produced when 3.0 x 10² kJ is absorbed:
  $2 Al<em>2O</em>3 <br>ightarrow 4 Al + 3 O_2 + 1676 kJ$

• Plan: Use thermal relations with reactions to convert between moles and heat absorbed.

6.21 Sample Problem 6.8: Solutions

• Steps indicating conversion of heat kJ to grams:
  $ext{mass}(Al) = rac{3.0 imes 10^{3} kJ}{ rac{1676 kJ}{2 ext{ mol } Al}} imes 26.98 g = 32.20 g$

• Conversion heat absorbed for $Al2O3$ reaction:

  • Compute resultant from known $ riangle H$ values.

6.22 Hess’s Law

• Hess’s law: Enthalpy change of an overall process equals sum of changes of individual steps.
  $riangle H<em>{overall} = riangle H</em>1 + riangle H<em>2 + … + riangle H</em>n$

• $ riangle H$ values for individual steps can recompute overall $ riangle H$.

6.23 Calculating ΔH for Overall Process

• Identify target equation and analyze reactants and products.

• Manipulate known equations and their respective $ riangle H$ values.

• Reverse signs for negative changes and multiply accordingly.

6.24 Standard Enthalpy of Formation

• Standard enthalpy of formation, $f^ullet riangle H$, refers to the formation energy of 1 mol compound from elements in standard states.

• For elements:
  $f^\bullet riangle H = 0$

• Common compounds release heat when forming from elements, most have negative $f^ullet riangle H$ values.

6.25 Selected Standard Enthalpies of Formation

• At 25°C (298 K), common enthalpies include:

  • $Br_2 (l)
    ightarrow 0$

  • $CaCO_3(s)
    ightarrow -1207.6$ kJ

  • $H_2O(g)
    ightarrow -241.8$ kJ

6.26 Sample Problem 6.11: Using ΔH Values

• Problem: Calculate enthalpy change for the reaction of nitrogen dioxide with oxygen to form dinitrogen pentoxide.

• Utilize $f^ullet riangle H$ values to assess product and reactant conversions:
  $f^\bullet riangle H_{reaction} = ext{products} - ext{reactants}$

6.27 Sample Problem 6.11: Solution

• Compute reaction enthalpy changes based on established equations and known value manipulations leading to resultant $H_{rxn} = -219 kJ$.