Chemical Reactions: Energy, Rates, and Equilibrium

Energy and Chemical Reactions

Concepts in Context: Food and Energy
- Food contains stored chemical potential energy that is released during cellular metabolic processes.
- Energy content in food is measured in units of Calories (caloric content).
- The primary energy-yielding biomolecules present in food are:
- Carbohydrates
- Proteins
- Fats
Energy Content of Biomolecules
- Biomolecules utilized for cellular energy possess high potential energy stored primarily in their $C-C$ and $C-H$ covalent bonds.
- During metabolic processing or combustion, these biomolecules react with oxygen ( $O_2$ ) to convert into carbon dioxide ( $CO_2$ ) and water ( $H_2O$ ), which are low potential energy products.

Cellular respiration energy pathway

Units of Energy
- Calorie (cal): The amount of heat energy required to raise the temperature of $1\,\text{g}$ of water by $1\,^\circ\text{C}$ .
- Nutritional Calorie (Cal): Written with a capital C, equivalent to $1\,\text{kilocalorie (kcal)}$ or $10^3\,\text{cal}$ ( $1,000\,\text{cal}$ ).
- Joule (J): The standard International System of Units (SI) unit of energy, defined as the energy required to lift a mass of $1\,\text{kg}$ by a height of $10\,\text{cm}$ .
- Exact Conversion Factor: $1\,\text{cal} = 4.184\,\text{J}$ (exact definition).
Energy Conversion Examples
- Converting kilocalories to calories ( $5.79\,\text{kcal}$ ): $5.79\,\text{kcal} \times \frac{10^3\,\text{cal}}{1\,\text{kcal}} = 5,790\,\text{cal}$
- Converting joules to calories ( $48.8\,\text{J}$ ): $48.8\,\text{J} \times \frac{1\,\text{cal}}{4.184\,\text{J}} = 11.7\,\text{cal}$
Exothermic and Endothermic Reactions
- First Law of Thermodynamics: Energy can neither be created nor destroyed; energy is conserved in all physical and chemical processes.
- Matter contains both kinetic energy (energy of motion) and potential energy (stored energy).
- Chemical reactions involve differences in potential energy between reactants and products, resulting in energy transfers to or from the surroundings.
- Exothermic Reactions:
- Reactants have higher potential energy than products.
- Heat energy is released to the surroundings ( $\Delta H_{rxn} < 0$ ).
- As a consequence, the temperature of the surroundings increases.
- Endothermic Reactions:
- Reactants have lower potential energy than products.
- Heat energy is absorbed from the surroundings ( $\Delta H_{rxn} > 0$ ).
- As a consequence, the temperature of the surroundings decreases.

Energy diagrams for exothermic and endothermic reactions

Energy Transformations in Real-World Systems
- Internal Combustion Engine: Gasoline combusts to release energy; a portion is converted into mechanical work to move the vehicle, while the remainder is dissipated as heat into the environment.
- Biological Cells: Glucose undergoes multi-step combustion (cellular respiration); most energy is captured in usable chemical energy forms (such as ATP) for cellular work, while the remaining portion is released as body heat.
Bond Energy and Bond Strength
- Forming chemical bonds releases energy (exothermic process) because bonded atoms exist at a lower potential energy state.
- Breaking chemical bonds requires energy input (endothermic process).
- Bond Energy: Defined as the amount of energy required to break $1\,\text{mole}$ of a specific bond type in the gas phase.
- Average Bond Energies Table:
- $C-H$ bond: $414\,\text{kJ/mol}$
- $O-H$ bond: $464\,\text{kJ/mol}$
- $C-C$ single bond: $347\,\text{kJ/mol}$
- $C=C$ double bond: $611\,\text{kJ/mol}$
- Trends in Bond Strength:
- Higher bond energy corresponds to a stronger bond and lower potential energy.
- Compounds containing weaker bonds have higher potential energy and are generally more chemically reactive.
- Multiple bonds are stronger than single bonds between the same atoms: triple bonds > double bonds > single bonds.
Heat of Reaction ( $\Delta H_{rxn}$ )
- Total energy change accompanying a chemical reaction.
- Can be estimated from bond energies: $\Delta H_{rxn} = (\text{Sum of bond energies of bonds broken}) - (\text{Sum of bond energies of bonds formed})$
- Alternatively expressed in energy diagrams as: $\Delta H_{rxn} = \text{Energy of Products} - \text{Energy of Reactants}$
- Exothermic reactions: $\Delta H_{rxn} < 0$ (negative sign indicating energy release).
- Endothermic reactions: $\Delta H_{rxn} > 0$ (positive sign indicating energy absorption).
Examples of Specific Chemical Reactions
- Combustion of Propane (Exothermic): $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(g) + \text{heat energy}$
- Requires an initial spark to ignite.
- Releases substantial heat once initiated: $\Delta H = -2,010\,\text{kJ/mol}$ .
- Decomposition of Aluminum Oxide (Endothermic): $2Al_2O_3(s) + \text{heat energy} \rightarrow 4Al(s) + 3O_2(g)$
- Requires continuous heat input to sustain the reaction: $\Delta H = +1,676\,\text{kJ/mol}$ .
Practice Examples: Classifying Thermochemical Reactions
- Hydrogen sulfide decomposition: $8H_2S(g) \rightarrow 8H_2(g) + S_8(s)$ (heat absorbed)
- Classification: Endothermic.
- Carbon dioxide decomposition: $2CO_2(g) \rightarrow 2CO(g) + O_2(g)$ ( $\Delta H = +566\,\text{kJ}$ )
- Classification: Endothermic.
Calorimetry and Food Energy Content
- A calorimeter (specifically a bomb calorimeter) is an experimental device used to measure the heat of reaction ( $\Delta H_{rxn}$ ) for combustion processes and establish caloric values of foods.
- Operation Procedure:
1. A food sample is dried and weighed inside a sealed inner reaction chamber.
2. Oxygen ( $O_2$ ) gas is introduced into the chamber under pressure.
3. An electrical spark via ignition wires ignites the sample.
4. The heat generated by combustion transfers to a known volume of water surrounding the reaction chamber in an insulated outer vessel.
5. A thermometer monitors the temperature increase ( $\Delta T$ ) of the water.
6. $\Delta H_{rxn}$ and total Calorie value are calculated from $\Delta T$ .

Diagram of a bomb calorimeter

Caloric Values by Biomolecule Class
- Carbohydrates: Yield $4\,\text{Cal/g}$ (found in rice, potatoes, bread, vegetables, fruit, whole milk).
- Proteins: Yield $4\,\text{Cal/g}$ (found in fish, meat, dairy products).
- Fats: Yield $9\,\text{Cal/g}$ (found in oils, butter, margarine, animal fats, whole milk).
Standard Procedure for Calculating Caloric Values on Food Labels
1. Multiply the mass (in grams) of each biomolecule category by its respective energy factor ( $4\,\text{Cal/g}$ for carbs/protein, $9\,\text{Cal/g}$ for fat).
2. Sum the individual calorie contributions.
3. Round the resulting total to the nearest tens place.
Calculation Example (Yogurt Nutrition Label)
- Fat content: $1.5\,\text{g} \times 9\,\text{Cal/g} = 13.5\,\text{Cal}$
- Carbohydrate content: $30\,\text{g} \times 4\,\text{Cal/g} = 120\,\text{Cal}$
- Protein content: $5\,\text{g} \times 4\,\text{Cal/g} = 20\,\text{Cal}$
- Unrounded Sum: $13.5 + 120 + 20 = 153.5\,\text{Cal}$
- Standard Label Value: $150\,\text{Cal}$ (rounded to tens place).
Practice Example: Pasta Calorie Determination
- Pasta containing $32\,\text{g}$ carbohydrate, $5\,\text{g}$ protein, and $1\,\text{g}$ fat:
- Fat: $1\,\text{g} \times 9\,\text{Cal/g} = 9\,\text{Cal}$
- Carbohydrates: $32\,\text{g} \times 4\,\text{Cal/g} = 128\,\text{Cal}$
- Protein: $5\,\text{g} \times 4\,\text{Cal/g} = 20\,\text{Cal}$
- Total: $9 + 128 + 20 = 157\,\text{Cal}$
- Reported Label Value: $160\,\text{Cal}$ (rounded to tens place).
Metabolic Pathways: Catabolism vs. Anabolism
- Biochemical Pathway: A series of consecutive enzymatic chemical reactions that convert starting materials into specific products.
- Catabolic Pathways:
- Degrade complex, high-potential-energy biomolecules into smaller, simpler molecules.
- Release potential energy stored in chemical bonds, transferring it to energy-carrier molecules such as adenosine triphosphate ( $ATP$ ).
- Anabolic Pathways:
- Construct complex cellular structures (proteins, lipids, nucleic acids like DNA, biological membranes) from smaller monomeric precursor molecules.
- Require an input of energy supplied by catabolic pathways ( $ATP$ hydrolysis).

Catabolic vs anabolic pathways

Practice Examples: Classifying Metabolic Processes
- Synthesis of muscle proteins from individual amino acids: Anabolic pathway.
- Utilization and breakdown of fat stores by a hibernating bear: Catabolic pathway.

Rates of Chemical Reactions

Measuring Chemical Reaction Rates
- The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit of time.
- Can be monitored experimentally by tracking:
- The rate of disappearance of reactants.
- The rate of appearance of products.
- Reaction speeds vary widely, ranging from extremely fast (e.g., rapid decomposition of sodium azide in automobile air bags) to extremely slow (e.g., food spoilage or rusting).
Activation Energy ( $E_A$ )
- Definition: The minimum amount of kinetic energy colliding reactant molecules must possess for a reaction to take place.
- Represents the energy barrier that reactants must overcome to convert into products.
- Represented on an energy diagram as the energy difference between the starting reactants and the highest peak (transition state) along the y-axis.
- Relationship to Reaction Rate:
- High activation energy ( $E_A$ ) = higher energy barrier = fewer colliding molecules have sufficient energy = slower reaction rate.
- Low activation energy ( $E_A$ ) = lower energy barrier = more colliding molecules have sufficient energy = faster reaction rate.
- Independence from Heat of Reaction: Activation energy ( $E_A$ ) is completely independent of the overall heat of reaction ( $\Delta H_{rxn}$ ).

Effect of activation energy on reaction rate

Factors Influencing Chemical Reaction Rates
- Reactant Concentration:
- Increasing reactant concentration increases particle density, resulting in a higher frequency of intermolecular collisions per second.
- Higher collision frequency yields a faster reaction rate.
- As reactants are consumed over time, concentration decreases, causing the reaction rate to gradually slow down (shown as a flattening slope on concentration vs. time plots).

Concentration of reactants vs time graph

System Temperature:
- Elevating temperature increases the average kinetic energy and velocity of reacting particles.
- Particles collide more frequently and with greater kinetic energy, increasing the fraction of collisions that overcome $E_A$ .
- Empirical Rule of Thumb: For many chemical reactions, elevating the temperature by $10\,^\circ\text{C}$ approximately doubles the reaction rate.
- Lowering temperature decreases kinetic energy, reducing collision frequency and energy, thereby slowing the reaction.
Presence of a Catalyst:
- Accelerates reaction rates without being consumed or altered permanently in the process.
- Operates by providing an alternate reaction pathway with a lower activation energy ( $E_A$ ).
- Often acts by providing a molecular surface that binds reactants in optimal spatial orientations for bond breaking and formation.
- Does not alter the potential energy of reactants or products, and therefore has zero effect on the overall heat of reaction ( $\Delta H_{rxn}$ ).
- Indicated in chemical equations by writing the catalyst symbol or name above or below the reaction arrow.

Effect of catalyst on activation energy

Biological Catalysts: Enzymes
- Specialized, large, three-dimensional biological macromolecules (primarily proteins constructed from carbon, hydrogen, nitrogen, oxygen, sulfur, and sometimes metal cofactor ions such as $Zn^{2+}$ or $Mg^{2+}$ ).
- Dramatically enhance reaction rates under physiological conditions by factors of $10^5$ to $10^{17}$ .
- Essential for living organisms; uncatalyzed biological reactions are far too slow to sustain cellular life.
- Enzyme deficiencies lead to metabolic disorders:
- Lactose Intolerance: Caused by inadequate production or total absence of the digestive enzyme lactase.
- Lactase hydrolyzes lactose (disaccharide in dairy) into glucose and galactose: $\text{Lactose} + H_2O \xrightarrow{\text{Lactase}} \text{Glucose} + \text{Galactose}$
- Without lactase, undigested lactose passes into the lower gut, causing abdominal pain and discomfort.
Practice Examples: Predicting Rate Changes
- Adding heat to $2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$ :
- Explanation: Increasing temperature raises kinetic energy, producing more frequent and energetic collisions. Reaction rate increases.
- Adding sodium iodide ( $NaI$ ) catalyst to $2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$ :
- Explanation: $NaI$ acts as a catalyst to lower $E_A$ , providing a faster pathway. Reaction rate increases.

Chemical Equilibrium

Reversible Reactions and Dynamic Equilibrium
- Many chemical reactions are reversible, proceeding in both forward and reverse directions.
- Forward Reaction: Converts reactants into products ( $\text{Reactants} \rightarrow \text{Products}$ ).
- Reverse Reaction: Converts products back into reactants ( $\text{Products} \rightarrow \text{Reactants}$ ).
- Chemical Equilibrium State:
- Attained when the rate of the forward reaction equals the rate of the reverse reaction.
- At equilibrium, the concentrations of all reactants and products remain constant over time (though not necessarily equal in magnitude).
- Represents a dynamic state where reactions continuously occur in both directions at equal speeds.
- Corresponds to the minimum potential energy state for the chemical system mixture.

Chemical equilibrium potential energy curve

Equilibrium Position and the Equilibrium Constant ( $K_{eq}$ )
- Reversible reactions can achieve equilibrium starting from pure reactants, pure products, or any mixture of both.
- For a generalized simple reaction $A \rightleftharpoons B$ , the equilibrium constant expression is: $K_{eq} = \frac{[B]}{[A]}$ where brackets $[ ]$ denote molar concentrations at equilibrium.
- Interpretation of $K_{eq}$ Values:
- $K_{eq} > 1$ : Products are favored at equilibrium ( $[B] > [A]$ ). The equilibrium position lies far to the right.
- $K_{eq} < 1$ : Reactants are favored at equilibrium ( $[A] > [B]$ ). The equilibrium position lies far to the left.

Equilibrium position favoring reactants or products

Le Châtelier's Principle
- Core Definition: When a chemical system at equilibrium is subjected to an external disturbance (stress), the system shifts its equilibrium position in a direction that counteracts the disturbance and establishes a new equilibrium state.
Effects of Concentration Changes
- Adding Reactant: Increases forward reaction rate above reverse rate; equilibrium shifts to the right (toward products).
- Removing Reactant: Decreases forward reaction rate below reverse rate; equilibrium shifts to the left (toward reactants).
- Adding Product: Increases reverse reaction rate above forward rate; equilibrium shifts to the left (toward reactants).
- Removing Product: Decreases reverse reaction rate below forward rate; equilibrium shifts to the right (toward products).
Effects of Temperature Changes
- Heat is treated quantitatively as a chemical component in the reaction equation.
- Exothermic Reactions ( $\text{Reactants} \rightleftharpoons \text{Products} + \text{HEAT}$ ):
- Adding Heat (Heating): System shifts to the left to absorb added heat energy.
- Removing Heat (Cooling): System shifts to the right to generate replacement heat energy.
- Endothermic Reactions ( $\text{HEAT} + \text{Reactants} \rightleftharpoons \text{Products}$ ):
- Adding Heat (Heating): System shifts to the right to consume added heat energy.
- Removing Heat (Cooling): System shifts to the left to replace removed heat energy.
Biochemical Application: Oxygen Transport by Hemoglobin
- Hemoglobin ( $Hb$ ) binds oxygen gas ( $O_2$ ) reversibly to form oxyhemoglobin ( $HbO_2$ ): $Hb + O_2 \rightleftharpoons HbO_2$
- In the Lungs: High partial pressure/concentration of $O_2$ acts as a reactant stress, shifting the equilibrium to the right to saturate hemoglobin and form $HbO_2$ .
- In Metabolizing Tissues and Muscles: Low partial pressure/concentration of $O_2$ causes $O_2$ removal, shifting the equilibrium to the left to unload free $O_2$ into cells.

Hemoglobin oxygen binding equilibrium in lungs and tissues

Practice Examples: Carbonic Acid Blood Equilibrium
- Reversible blood buffering system equation: $H_2CO_3(aq) \rightleftharpoons CO_2(g) + H_2O(l)$
- Effect of extra cellular $CO_2$ waste in blood:
- Explanation: Carbon dioxide ( $CO_2$ ) is a product. Adding extra product increases reverse rate, shifting equilibrium to the left toward carbonic acid ( $H_2CO_3$ ).
- Effect of removing $CO_2$ via exhalation from lungs:
- Explanation: Exhalation removes product $CO_2$ . Decreasing product concentration shifts equilibrium to the right to replenish $CO_2$ .

Chemistry in Medicine: Calorimetry and Metabolic Energy

Direct Calorimetry in Humans
- Uses a human room calorimeter to measure energy expenditure directly.
- Subject stays inside a sealed, insulated chamber (often performing exercise on a treadmill).
- Heat radiated by the human body warms water flowing through surrounding cooling coils.
- Direct measurement of water temperature change provides exact total caloric heat output.

Human room calorimeter setup

Indirect Calorimetry
- Determines metabolic rate indirectly by measuring oxygen gas ( $O_2$ ) consumption rate.
- Based on the stoichiometry of glucose oxidation (cellular respiration): $C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O + \text{Heat}$
- A spirometer device measures exact volumes of inhaled and exhaled oxygen gas to calculate energy expenditure.
Clinical Management of Patients on Mechanical Ventilators
- Critically ill patients on mechanical respirators cannot self-regulate caloric intake.
- Risks of Underfeeding: Leads to starvation, severe muscle wasting, coma, and death.
- Risks of Overfeeding: Leads to excessive $CO_2$ production during cellular respiration, causing respiratory muscle fatigue and acute respiratory failure.
- Clinical Utility: Indirect calorimetry measures precise daily energy expenditure, allowing healthcare providers to formulate optimal caloric feeding plans.