thermochemistry

Student Learning Objectives (SLOs) - Thermochemistry Part 1

• Apply the First Law of Thermodynamics to determine signs on heat (q) and work (w).

• Differentiate between path and state functions.

• Differentiate between endothermic and exothermic processes.

• Apply stoichiometric relationships between enthalpy and a balanced chemical equation to determine unknowns, such as grams of product, moles of reactant, change in energy, etc.

Introduction to Thermochemistry

• Changes in matter accompanied by changes in energy.

• Thermochemistry: The study of heat involved in chemical reactions.

  • Example: The small chemical heater, which uses the exothermic reaction of magnesium (Mg) and water to produce heat without light or smoke. A ‘tea bag’ filled with Mg is used: just add water and wait 10 minutes for the temperature to reach 60° C (source: www.CEN-ONLINE.ORG).

Basic Concepts in Thermodynamics

• Thermodynamics: The study of energy and its interconversions.

• First Law of Thermodynamics: States that the total energy of the universe is constant, also known as the Law of Conservation of Energy.

  • Energy Transfer Equation: $E = q + w$

Heat and Work

• Heat (q): Energy transferred due to a change in temperature.

  • -q indicates that heat has left the system (heat is lost).

  • +q indicates that heat has entered the system (heat is gained).

• Work (w): Energy transferred when an object moves due to a force.

  • The relationship for energy in the context of thermodynamics is given as: $E = q + w$

Class Concept Check

• Predict the sign of q related to the system (and surroundings) using examples:

  • An ice cube melting in a beverage cools the drink (q is negative for the system).

  • Sweat evaporating on the skin cools the body (q is negative for the system).

Thermodynamic Functions

• There are two kinds of thermodynamic functions:

  • State Function: A property of the system fixed by its current conditions and independent of the system’s history.

  • Path Function: A property that depends on how a particular change occurred.

  • The energy is classified as a state function: $E = q + w$

Enthalpy (ΔH)

• Enthalpy (ΔH): Another state function representing the change in heat (q) experienced by the system at constant pressure.

• A thermochemical equation presents a chemical equation including the enthalpy of reaction:

  • Example: $2H<em>2O(l) ightarrow 2H</em>2(g) + 1O<em>2(g) \ \Delta H</em>{rxn} = 572 ext{ kJ}$

  • The sign on ΔH indicates whether heat is released (given off) or absorbed.

Exothermic vs. Endothermic Reactions

• Exothermic Reaction: A system that transfers heat to its surroundings, indicated by -ΔH.

  • Example Reaction: $CH<em>4(g) + 2O</em>2(g) <br>ightarrow CO<em>2(g) + 2H</em>2O(g) + ext{heat}$

• Endothermic Reaction: A reaction that absorbs heat from its surroundings, indicated by +ΔH.

  • Example Reaction: $N<em>2(g) + O</em>2(g) + ext{heat} <br>ightarrow 2NO(g)$

Using Thermochemical Equations

• Example: Given the reaction $2H<em>2O(l) ightarrow 2H</em>2(g) + 1O<em>2(g)$ with $riangle H</em>{rxn} = 572 ext{ kJ},$ units of ΔH relate to coefficients from the balanced equation.

  • Inverting the moles will change the heat associated with the reaction:

  • If 4 moles of $H_2O$ react, calculate heat (q) required.

  • If 286 kJ of heat is absorbed (as endothermic), determine how many moles of hydrogen gas form.

Distinction between Heat (q) and Enthalpy (ΔH)

• Heat (q) (measured in kJ) relates to the mass or moles you start with in a problem (like pantry items).

• ΔH (measured in kJ per mole from coefficient) is the rate of heat gain/loss during a process.

  • Relationship: $riangle H = rac{q}{n}$

Example Calculation of Heat Required

1. It takes 74 kJ to heat enough liquid for a cup of tea. Determine mass of methane (CH4) to burn for this heat.

   • Given Reaction: $CH<em>4(g) + 2O</em>2(g) <br>ightarrow CO<em>2(g) + 2H</em>2O(g), \ riangle H = -890 ext{ kJ}$ (exothermic).

Example Heat Exchange Calculation

1. Calculate heat exchanged when 11.0 g of $CO_2$ forms from the combustion of propane.

   • Given Reaction: $C<em>3H</em>8(g) + 5O<em>2(g) ightarrow 3CO</em>2(g) + 4H_2O(g), \ riangle H = -2.22 imes 10^3 ext{ kJ}$

Student Learning Objectives (SLOs) - Thermochemistry Part 2

• Calculate heat, temperature, mass, and heat capacity using the formulas: $q = mc riangle T$ and $q = riangle n H$ for both the system and surroundings (excluding pressure-volume work).

• Rank substances based on predicted temperature change using heat capacities.

• Solve for change in temperature in constant pressure calorimetry settings.

• Solve for ΔHrxn using Hess’s Law, ΔHf, and calorimetry.

Additional Methods for Determining ΔH

• Various methods to solve for ΔH:

  • Calorimetry

  • Hess’s Law

  • Heat of formation

Calorimetry Overview

• In laboratory measurements, q can be derived to determine ΔH:

  • Conduct the reaction at constant pressure.

  • Create surroundings to retain all heat produced or absorbed.

  • Measure temperature change (ΔT) using a thermometer and relate to heat quantity using the specific heat capacity of the substance.

  • Calorimetry: In a closed, insulated system (no energy entry or exit).

  • $q<em>{lost} = -q</em>{gained}$

Specific Heat Capacity

• Specific Heat Capacity (c): The amount of heat needed to increase the temperature of 1 gram of a substance by 1 K (or °C).

  • For liquid water, specific heat is: $4.184 ext{ J/gºC} ext{ or } 75.4 ext{ J/molºC}$

Mathematical Example of Specific Heat

• The relationship between heat (q), mass (m), and change in temperature (ΔT) is shown in the equation:

  • $q = mc riangle T$

Relating Heat of Surroundings and System

• The contents of the calorimeter represent the surroundings, hence: $q_{surr} = mc riangle T$

• The chemical reaction refers to the system, thus: $q_{sys} ext{ relates to } ΔH$

• A sign change is required to relate $q<em>{surr}$ and $q</em>{sys}$ for appropriate calculations, plus ensure units consistency (q in Joules but ΔH in kJ).

Calorimetry Calculations

• General formulas for calorimetry calculations:

  • $q_{surr} = mc riangle T$

  • $q_{sys} = n riangle H$

Example Problem of Calorimetry

• Example: Dissolution of 22.2 g of CaCl2 (molar mass = 111.08 g/mol) in water contained in a calorimeter, where the temperature of water rises by 7.14 °C. Compute ΔH for the dissolution process.

  • Given specific heat of water: $(c = 4.184 ext{ J/gºC})$

Further Example for Determining Temperature Changes

• Calculation involving 18.4 g of $SrCl_2$ (molar mass = 158.6 g/mol) added to 585 g of water at an initial temperature of 35.1 °C, where the reaction is:

  • $SrCl_2(s) <br>ightarrow Sr^{2+}(aq) + 2 Cl^{-}(aq), \ riangle H = -52.03 ext{ kJ}$

Student Learning Objectives (SLOs) - Thermochemistry Part 3

• Solve for ΔHrxn using Hess's Law, ΔHf, and calorimetry.

Hess's Law of Heat Summation

• Hess’s Law states that the ΔH of an overall process is the sum of the enthalpy changes of its different steps, represented as:

  • $riangle H<em>{rxn} = riangle H</em>1 + riangle H<em>2 + riangle H</em>3 + …$

• It allows us to break down an overall unknown process into individual steps with known ΔH values.

• A crucial advantage is that ΔH is a state function, allowing easy summation of changes.

• Thermochemical equations must be provided to calculate the target ΔH.

Empirical Application of Hess's Law

• Example Reactions to showcase Hess's Law:

  1. $C(s) + O<em>2(g) ightarrow CO</em>2(g), \ riangle H = -393.5 ext{ kJ}$

  2. $CO<em>2(g) ightarrow CO(g) + rac{1}{2}O</em>2(g), \ riangle H = +283.0 ext{ kJ}$

1. $C(s) + rac{1}{2}O_2(g) <br>ightarrow CO(g), \ riangle H = -110.5 ext{ kJ}$

Tricks for Thermochemical Equations and Hess's Law

• To manipulate thermochemical equations with Hess’s Law:

  1. Sign Change: If the direction of the reaction is reversed, the sign of ΔH must be reversed.

  2. Magnitude Change: If the amount of reactants or products is altered, then the magnitude of ΔH must be correspondingly adjusted.

  3. Fractional Coefficients: Allows for adjustments provided ΔH relationships are maintained due to the state function property.

• Example: Given $2H<em>2O(l) ightarrow 2H</em>2(g) + O<em>2(g) \ riangle H</em>{rxn} = 572 ext{ kJ/mol},$ - When reversed, becomes: $2H<em>2(g) + O</em>2(g) <br>ightarrow 2H<em>2O(l), \ riangle H</em>{rxn} = -572 ext{ kJ/mol}$

Advanced Calculation with Hess's Law

• Determine the enthalpy change via Hess’s law using known reactions:

  1. For example: $2WO<em>2(s) + O</em>2(g) <br>ightarrow 2WO_3(s), \ riangle H = -506 ext{ kJ}$

  2. $2W(s) + 3O<em>2(g) ightarrow 2WO</em>3(s), \ riangle H = -1686 ext{ kJ}$

  3. Query: $2W(s) + 2O<em>2(g) ightarrow 2WO</em>2(s), \ riangle H = ???$

Calculation Example of Enthalpy Change

• Calculate the enthalpy change for target:

  • Given the following equations:

  1. $3C<em>2H</em>2(g) <br>ightarrow C<em>6H</em>6(g), \ riangle H = ???$

  2. $2C<em>2H</em>2(g) + 5O<em>2(g) ightarrow 4CO</em>2(g) + 2H_2O(g), \ riangle H = -1692 ext{ kJ}$

  3. $2C<em>6H</em>6(g) + 15O<em>2(g) ightarrow 12CO</em>2(g) + 6H_2O(g), \ riangle H = -6339 ext{ kJ}$

Standard Enthalpy of Formation (ΔHºf)

• The Standard Enthalpy of Formation (ΔHºf) is defined as the enthalpy change when one mole of a substance in its standard state is created from its most stable form of constituents in their standard states.

  • The standard state for a substance means the pure form at 25ºC and 1 atm pressure (for solutions, it is 1M).

  • Example: Carbon exists as graphite rather than diamond.

  • Reactions:

  • $C(graphite) + O<em>2(g) ightarrow CO</em>2(g), \ riangle Hºf[CO_2(g)] = -393.51 ext{ kJ/mol}$

  • $H<em>2(g) + rac{1}{2}O</em>2(g) <br>ightarrow H<em>2O(g), \ riangle Hºf[H</em>2O(g)] = -285.83 ext{ kJ/mol}$

  • $H<em>2(g) ightarrow H</em>2(g), \ riangle Hºf[H_2(g)] = 0 ext{ kJ/mol}$

Reaction Enthalpy Calculation Using ΔHºf

• Reaction Calculation Formula: $riangle Hº<em>{rxn} = S</em>n riangle Hº<em>f[ ext{products}] - S</em>m riangle Hº_f[ ext{reactants}]$

  • Example: For reaction $P<em>4O</em>{10}(s) + 6H<em>2O(g) ightarrow 4H</em>3PO<em>4(s)$ - Calculation to find $riangle Hº</em>{rxn} = ???$ - Given Standard Enthalpy Data:

  • $P<em>4O</em>{10}(s): riangle Hº_f = -1640 ext{ kJ/mol}$

  • $H<em>2O(g): riangle Hº</em>f = -242 ext{ kJ/mol}$

  • $H<em>3PO</em>4(s): riangle Hº_f = -1279 ext{ kJ/mol}$

  • Another application: Solve for the enthalpy of formation for a compound given its ΔHrxn.