Thermochemistry and Enthalpy Changes

Thermochemical Equations

Thermochemical equations represent chemical reactions that include both the changes in matter and the associated energy changes. The sign of the enthalpy change (ΔH) indicates whether the reaction is endothermic or exothermic:

• Endothermic Reaction: Heat is absorbed, ΔH > 0.

• Exothermic Reaction: Heat is released, ΔH < 0.

• Example: Melting ice (H2O(s) → H2O(l), ΔH = +6.01 kJ/mol) is endothermic; combustion of methane (CH4(g) + 2O2(g) → CO2(g) + 2H2O(l), ΔH = -890.4 kJ/mol) is exothermic.

Enthalpy of Reaction

The enthalpy of reaction (ΔHrxn) is the heat change associated with a chemical reaction at constant pressure. Breaking chemical bonds requires energy, while forming bonds releases energy.

• ΔHrxn < 0: Exothermic reaction; products have lower enthalpy than reactants.

• ΔHrxn > 0: Endothermic reaction; products have higher enthalpy than reactants.

Enthalpy in Stoichiometry

ΔHrxn is proportional to the stoichiometric coefficients in the balanced chemical equation. For example, in the combustion of propane:

• C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g), ΔHrxn = -2044 kJ

• Each mole of C3H8 combusted releases -2044 kJ.

Constant Pressure Calorimetry

Constant pressure calorimetry ("coffee cup calorimetry") is used to measure ΔHrxn for reactions in solution. The system is the reaction, and the surroundings are the solution.

• qrxn = -qsoln

• qsoln = msoln × Cs,soln × ΔT

• ΔHrxn = qp / moles of reactant

Processes with Energy Change

Many physical and chemical processes involve energy changes, including combustion, boiling, freezing, and dissolving.

• Combustion: Exothermic process (heat released).

• Boiling: Endothermic process (heat absorbed).

• Freezing: Exothermic process (heat released).

• Dissolving: Can be endothermic or exothermic depending on the solute and solvent.

Types of Enthalpy Changes

Common ΔHrxn Types

Different types of enthalpy changes are associated with specific processes:

• ΔHsoln: Heat of solution (dissolving).

• ΔHc: Heat of combustion.

• ΔHn: Heat of neutralization.

• ΔHfus: Heat of fusion (melting).

• ΔHvap: Heat of vaporization (boiling).

• ΔHfo: Standard heat of formation.

Hess’s Law

Principle of Hess’s Law

Hess’s Law states that if a reaction can be expressed as the sum of a series of steps, the overall enthalpy change is the sum of the enthalpy changes for each step. This is a consequence of enthalpy being a state function.

• Mathematical Expression:

• Example: If A + 2B → C (ΔH1) and C → 2D (ΔH2), then A + 2B → 2D (ΔH3 = ΔH1 + ΔH2).

Manipulating Chemical Equations

When manipulating chemical equations, the enthalpy change must be adjusted accordingly:

• Multiplying: If the equation is multiplied by a factor, ΔHrxn is multiplied by the same factor.

• Reversing: If the equation is reversed, the sign of ΔHrxn is changed.

Standard Enthalpy of Formation

Definition and Calculation

The standard enthalpy of formation (ΔHfo) is the enthalpy change when one mole of a compound is formed from its elements in their standard states. For pure elements in their standard state, ΔHfo = 0.

• Standard State: Gas at 1 atm, liquid/solid in most stable form at 1 atm, solution at 1 M.

• Example: C(s, graphite) + 2 H2(g) → CH4(g), ΔHfo = -74.6 kJ/mol at 25°C.

Using Standard Heats of Formation

To calculate the enthalpy change for a reaction using standard heats of formation:

• Example: For 2 Al(s) + Fe2O3(s) → Al2O3(s) + 2 Fe(s):

Calculation:

• kJ/mol

Practice Problems and Applications

Heat of Formation Reactions

Writing the heat of formation reaction for a compound involves combining elements in their standard states to form one mole of the compound.

• Example: Mg(s) + C(s, graphite) + 3/2 O2(g) → MgCO3(s)

• 6 C(s, graphite) + 6 H2(g) + 3 O2(g) → C6H12O6(s)

Calculating ΔHrxn Using ΔHfo

For the reaction 4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(g):

Calculation:

• kJ/mol

Heat of Sublimation Example

For the reaction 2 Ti(s) + 3 I2(g) → 2 TiI3(s), with ΔHrxn = -839 kJ/mol and ΔHfo of TiI3(s) = -328 kJ/mol, the heat of sublimation of I2 (ΔHsub) can be calculated:

• ΔHsub = ΔHfo (I2(g)) - ΔHfo (I2(s)) = +61.0 kJ/mol

Summary Table: Enthalpy Calculations

Additional info: All equations are provided in LaTeX format for clarity and academic rigor. Images included are directly relevant to the explanation of enthalpy changes, calorimetry, Hess’s Law, and standard heats of formation.