Chemical Energy, Enthalpy of Formation, and Bond Enthalpy

Role of Heat in Reactions: Chemical reactions are observed through energy changes, primarily the transfer of heat.
- Exothermic Reactions: These reactions release heat into the surroundings.
- Endothermic Reactions: These reactions absorb heat from the surroundings.
Practical Importance of Chemical Energy:
- Driving vehicles (combustion of fuel).
- Powering electronics (battery chemistry in cell phones).
- Biological functions (metabolism for movement and cell survival).

Internal Energy vs. Enthalpy:
- At constant volume, measured heat reflects the change in internal energy ( $\Delta U$ ).
- At constant pressure, measured heat reflects the change in enthalpy ( $\Delta H$ ).
Thermochemical Equations: A complete thermochemical equation includes:
- Chemical formulas for reactants and products.
- Stoichiometric balancing coefficients.
- The standard enthalpy of reaction ( $\Delta H_{rxn}^{\circ}$ ), which represents the enthalpy change per mole under stoichiometric conditions.

Calorimetry: The experimental process of measuring the heat involved in a chemical reaction.
Fundamental Equation: The relationship between temperature change and heat is defined as: $q = m \times s \times \Delta T$
- $q$ : Heat involved.
- $m$ : Mass of the substance.
- $s$ : Specific heat capacity.
- $\Delta T$ : Change in temperature.

Definition: The enthalpy change that occurs when exactly one mole of a compound is formed from its constituent elements in their most stable standard states.
Standard States:
- Elements must be in the form most stable at $1\text{ atmosphere}$ pressure.
- Carbon: Standard state is graphite (not diamond).
- Diatomic Elements: Hydrogen ( $H_2(g)$ ), Oxygen ( $O_2(g)$ ), Chlorine ( $Cl_2(g)$ ), and Bromine ( $Br_2(l)$ ).
Properties of $\Delta H_f^{\circ}$ Values:
- For any element already in its standard state (e.g., beryllium solid, graphite, liquid bromine), $\Delta H_f^{\circ} = 0$ .
- Elements not in their standard state (e.g., carbon diamond) have small, non-zero values.
- Values can be positive (endothermic formation) or negative (exothermic formation).
Calculating $\Delta H_{rxn}^{\circ}$ from Formation Values:
- The standard enthalpy of a reaction is calculated by subtracting the sum of the enthalpy of formation of the reactants from that of the products: $\Delta H_{rxn}^{\circ} = \sum n \Delta H_f^{\circ}(\text{products}) - \sum m \Delta H_f^{\circ}(\text{reactants})$
- Where $n$ and $m$ are stoichiometric coefficients.

Reaction Path: Butane ( $C_4H_{10}$ ) reacts with oxygen in the air to produce carbon dioxide, water, and heat.
Balanced Thermochemical Equation: $2 C_4H_{10}(l) + 13 O_2(g) \rightarrow 8 CO_2(g) + 10 H_2O(l)$
Data Provided:
- $\Delta H_f^{\circ} [CO_2(g)] = -393.5\,kJ/mol$
- $\Delta H_f^{\circ} [H_2O(l)] = -285.8\,kJ/mol$
- $\Delta H_f^{\circ} [C_4H_{10}(l)] = -147.6\,kJ/mol$
- $\Delta H_f^{\circ} [O_2(g)] = 0\,kJ/mol$
Calculation: $\Delta H_{rxn}^{\circ} = [8(-393.5) + 10(-285.8)] - [2(-147.6)] = -5710.8\,kJ/mol$
Interpretation: The negative value indicates an exothermic reaction, releasing $5710.8\,kJ$ of heat when two moles of butane react.
Stoichiometric Conversion (Heat from 1 gram of butane):
1. Convert mass to moles: $1\,g \div 58.12\,g/mol = 0.0172\text{ moles of butane}$ .
2. Use $\Delta H_{rxn}$ as a conversion factor: $\frac{5710.8\,kJ}{2\text{ moles of butane}}$ .
3. Calculation: $0.0172\text{ moles} \times (5710.8\,kJ / 2\text{ moles}) = 49.1\,kJ$ .
- Result: $49.1\,kJ$ of heat is generated into the surroundings from the combustion of $1\text{ gram}$ of butane.

Mechanism of Reaction: Reactions involve breaking reactant bonds (absorbing energy) and forming product bonds (releasing energy).
Hydrogen Molecule ( $H_2$ ) Energy Profile:
- Graphing energy vs. distance between two hydrogen atoms shows a minimum at the bond distance of $74\text{ picometers}$ .
- At infinite separation, energy is defined as zero.
- As atoms approach, attractive forces (electron-nucleus) reduce potential energy until it reaches $-436\,kJ/mol$ (the minimum).
- Closer than $74\,pm$ , nuclear repulsion forces energy to spike.
- To dissociate one mole of $H_2$ into atoms requires adding $436\,kJ$ of energy.
Predicting $\Delta H_{rxn}$ using Bond Enthalpies: $\Delta H_{rxn} = \sum(\text{bond enthalpies of broken bonds}) - \sum(\text{bond enthalpies of formed bonds})$
Reaction Examples:
- Exothermic: More energy is released during product bond formation than was absorbed to break reactant bonds (e.g., $H_2 + Cl_2 \rightarrow 2 HCl$ ).
- Endothermic: More energy is required to break reactant bonds than is released when forming products (e.g., dissociation of ammonia: $2 NH_3 \rightarrow N_2 + 3 H_2$ ).

Reaction: $CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O$
Bonds Processed:
- Broken: 4 $C-H$ single bonds, 2 $O=O$ double bonds.
- Formed: 2 $C=O$ double bonds, 4 $O-H$ single bonds.
Solving for Unknowns (Oxygen Difluoride Example):
- Instructor demonstrated calculating the unknown Bond Enthalpy of $O-F$ bonds by comparing total enthalpy absorbed vs. released.
- In the provided whiteboard exercise, the calculation led to an $O-F$ bond energy of $188\,kJ/mol$ .

Experimental Measurement: Using calorimetry to measure heat ( $q$ ).
Standard Enthalpies of Formation: Taking the difference between products and reactants (Products minus Reactants).
Average Bond Enthalpies: Taking the difference between bond energy in reactants and products (Broken minus Formed).

Question: Why did you use an 18 earlier in the butane equation?
Response: The instructor corrected themselves, clarifying they should have written 10 for the water coefficient based on the balancing of the butane equation ( $C_4H_{10}$ providing 10 hydrogens total).
Question: When choosing between water liquid or water vapor for combustion calculations, which do we use?
Response: If the condition is room temperature, water is initially liquid. If the problem specifies the vapor phase, use the $\Delta H_f^{\circ}$ for water gas, as the values are significantly different and will change the final $\Delta H_{rxn}$ .