# 6.1 Energy in Chemical Reactions Energy, often in the form of heat, is either evolved or absorbed during a chemical reaction. This occurs because chemical reactions involve the breaking of old chemical bonds and the formation of new ones. * **Bond Breaking:** Always consumes energy. * **Bond Making:** Always releases energy. The net energy change depends on the balance between these two processes. * If energy released from bond formation is greater than energy consumed by bond breaking, the reaction releases energy to the surroundings (**exothermic**). * If energy consumed by bond breaking is greater than energy released from bond formation, the reaction absorbs energy from the surroundings (**endothermic**). Thus, in chemical reactions, there is always an energy transfer between the **system** (the reaction itself) and the **surroundings**. --- ## 6.1.1 Units of Thermal Energy The standard unit of heat or thermal energy in the SI system is the **Joule (J)**. Another common unit is the **calorie (cal)**. * **Definition:** The thermal energy required to raise the temperature of one gram of water from $14.5^\circ\mathrm{C}$ to $15.5^\circ\mathrm{C}$. * **Conversion:** $$1\ \text{calorie} = 4.184\ \text{Joules}$$ --- ## 6.1.2 Thermochemical Reactions A **thermochemical reaction** is a chemical reaction that proceeds with the evolution or absorption of heat. The study of these heat changes is called **thermochemistry**. A **thermochemical equation** is a balanced chemical equation that includes the heat change (enthalpy change, $\Delta H$). **Example:** $$\mathrm{C_{(s)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}} \quad \Delta H^\circ = -393.5\ \text{kJ}$$ This equation indicates that when one mole of solid carbon reacts with one mole of oxygen gas to form one mole of carbon dioxide gas, 393.5 kJ of heat is released. ### (1) Exothermic Reactions An **exothermic reaction** is a chemical reaction that proceeds with the *evolution of heat* ($\Delta H$ is negative). In these reactions, the system transfers energy to the surroundings. **Examples:** * Combustion of Carbon: $$\mathrm{C_{(s)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}} \quad \Delta H^\circ = -393.5\ \text{kJ}$$ * Formation of Water: $$2\mathrm{H_{2(g)}} + \mathrm{O_{2(g)}} \rightarrow 2\mathrm{H_2O_{(l)}} \quad \Delta H^\circ = -571.6\ \text{kJ}$$ * Formation of Carbon Monoxide: $$\mathrm{C_{(s)}} + \frac{1}{2}\mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{(g)}} \quad \Delta H^\circ = -110.5\ \text{kJ}$$ ### (2) Endothermic Reactions An **endothermic reaction** is a chemical reaction that proceeds with the *absorption of heat* ($\Delta H$ is positive). In these reactions, the system absorbs heat from the surroundings. **Examples:** * Formation of Hydrogen Iodide: $$\mathrm{H_{2(g)}} + \mathrm{I_{2(g)}} \rightarrow 2\mathrm{HI_{(g)}} \quad \Delta H^\circ = +53.8\ \text{kJ}$$ * Steam Reforming of Carbon: $$\mathrm{C_{(s)}} + \mathrm{H_2O_{(g)}} \rightarrow \mathrm{CO_{(g)}} + \mathrm{H_{2(g)}} \quad \Delta H^\circ = +131.4\ \text{kJ}$$ * Formation of Nitric Oxide: $$\mathrm{N_{2(g)}} + \mathrm{O_{2(g)}} \rightarrow 2\mathrm{NO_{(g)}} \quad \Delta H^\circ = +180.5\ \text{kJ}$$ --- ## 6.1.3 Heat of Reaction ($\Delta H$) The **heat of reaction** is the amount of heat evolved or absorbed in a chemical reaction, corresponding to the molar quantities shown in the balanced chemical equation. The **standard enthalpy change ($\Delta H^\circ$)** is the heat of reaction measured under standard conditions: * **Temperature:** $25^\circ\mathrm{C}$ (298 K) * **Pressure:** 1 atmosphere (atm) **Important Note:** If a reaction is reversed, the magnitude of $\Delta H^\circ$ remains the same, but its sign changes. * **Forward Reaction (Exothermic):** $$\mathrm{C_{(s)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}} \quad \Delta H^\circ = -393.5\ \text{kJ}$$ * **Reverse Reaction (Endothermic):** $$\mathrm{CO_{2(g)}} \rightarrow \mathrm{C_{(s)}} + \mathrm{O_{2(g)}} \quad \Delta H^\circ = +393.5\ \text{kJ}$$ --- ## 6.1.4 Relation between Enthalpy Change and Heat of Reaction For reactions occurring at constant pressure, the heat change is equal to the change in **enthalpy ($\Delta H$)**. Enthalpy change is the difference between the enthalpies of the products and the reactants. $$\Delta H = H_{\text{products}} - H_{\text{reactants}}$$ * For an **exothermic** process, heat is released, so $H_{\text{products}} < H_{\text{reactants}}$, and **$\Delta H$ is negative**. * For an **endothermic** process, heat is absorbed, so $H_{\text{products}} > H_{\text{reactants}}$, and **$\Delta H$ is positive**. --- ## 6.1.5 Standard States and Standard Enthalpy Changes To ensure consistency, enthalpy changes are often reported for reactions where all substances are in their **standard state**. **Conditions for Standard States:** 1. **Gas:** A pure gas at 1 atm pressure. 2. **Element/Compound:** The most stable physical state (solid, liquid, or gas) at 1 atm and $25^\circ\mathrm{C}$ (298 K). 3. **Aqueous Solution:** A substance at a 1 M concentration. --- ## Types of Standard Enthalpies ### 1. Standard Enthalpy of Reaction ($\Delta H_r^\circ$) The enthalpy change when molar quantities of reactants as shown in the balanced equation react to form products, with all substances in their standard states. **Example:** Methane Combustion $$\mathrm{CH_{4(g)}} + 2\mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}} + 2\mathrm{H_2O_{(l)}} \quad \Delta H_r^\circ = -890.4\ \text{kJ}$$ ### 2. Standard Enthalpy of Formation ($\Delta H_f^\circ$) The enthalpy change that accompanies the formation of **one mole** of a compound from its constituent elements, with all substances in their standard states. **Table 6.1: Standard Enthalpies of Formation ($\Delta H_f^\circ$) in kJ mol⁻¹** | Compound | $\Delta H_f^\circ$ | Compound | $\Delta H_f^\circ$ | Compound | $\Delta H_f^\circ$ | | :--- | :---: | :--- | :---: | :--- | :---: | | $\mathrm{H_2O_{(g)}}$ | -245.1 | $\mathrm{Fe_2O_{3(s)}}$ | -824.2 | $\mathrm{C_{graphite}}$ | 0 | | $\mathrm{H_2O_{(l)}}$ | -285.8 | $\mathrm{SiO_{2(s)}}$ | -910.9 | $\mathrm{C_{diamond}}$ | +1.9 | | $\mathrm{NH_{3(g)}}$ | -46.1 | $\mathrm{CaCO_{3(s)}}$ | -1207 | $\mathrm{CH_{4(g)}}$ | -74.8 | | $\mathrm{HCl_{(g)}}$ | -92.3 | $\mathrm{NaOH_{(s)}}$ | -425.6 | $\mathrm{C_2H_{6(g)}}$ | -84.7 | | $\mathrm{CO_{(g)}}$ | -110.5 | $\mathrm{KOH_{(s)}}$ | -424.8 | $\mathrm{C_3H_{8(g)}}$ | -103.9 | | $\mathrm{CO_{2(g)}}$ | -393.5 | $\mathrm{HNO_{3(l)}}$ | -174.1 | $\mathrm{C_6H_{6(l)}}$ | +49.0 | | $\mathrm{SO_{2(g)}}$ | -296.8 | $\mathrm{H_2SO_{4(l)}}$ | -814.0 | $\mathrm{CH_3OH_{(l)}}$ | -238.7 | | $\mathrm{SO_{3(g)}}$ | -395.7 | $\mathrm{NaCl_{(s)}}$ | -411.2 | $\mathrm{C_2H_5OH_{(l)}}$ | -277.7 | | $\mathrm{CaO_{(s)}}$ | -635.1 | $\mathrm{KCl_{(s)}}$ | -436.8 | $\mathrm{CH_3COOH_{(l)}}$ | -484.5 | ### 3. Standard Enthalpy of Combustion ($\Delta H_c^\circ$) The enthalpy change when **one mole** of a substance is completely burned in excess oxygen under standard conditions. Combustion is always exothermic. **Table 6.2: Standard Enthalpies of Combustion ($\Delta H_c^\circ$) in kJ mol⁻¹** | Substance | $\Delta H_c^\circ$ | Substance | $\Delta H_c^\circ$ | | :--- | :---: | :--- | :---: | | $\mathrm{H_{2(g)}}$ | -285.8 | $\mathrm{C_2H_{4(g)}}$ | -1411 | | $\mathrm{C_{graphite}}$ | -393.5 | $\mathrm{C_2H_{2(g)}}$ | -1300 | | $\mathrm{CH_{4(g)}}$ | -890.4 | $\mathrm{C_2H_5OH_{(l)}}$ | -1367 | | $\mathrm{C_2H_{6(g)}}$ | -1560 | $\mathrm{C_6H_{12}O_{6(s)}}$ | -2802 | ### 4. Standard Enthalpy of Atomization ($\Delta H_{at}^\circ$) The enthalpy change when **one mole of gaseous atoms** is formed from an element in its standard state. This process is always endothermic. **Examples:** * Hydrogen: $$\frac{1}{2}\mathrm{H_{2(g)}} \rightarrow \mathrm{H_{(g)}} \quad \Delta H_{at}^\circ = +218\ \text{kJ mol}^{-1}$$ * Chlorine: $$\frac{1}{2}\mathrm{Cl_{2(g)}} \rightarrow \mathrm{Cl_{(g)}} \quad \Delta H_{at}^\circ = +121\ \text{kJ mol}^{-1}$$ ### 5. Standard Enthalpy of Neutralization ($\Delta H_n^\circ$) The amount of heat evolved when **one mole of $\mathrm{H^+}$ ions** from an acid combines with **one mole of $\mathrm{OH^-}$ ions** from a base to form one mole of water under standard conditions. For strong acids and bases, this value is approximately constant. $$\mathrm{H^+_{(aq)}} + \mathrm{OH^-_{(aq)}} \rightarrow \mathrm{H_2O_{(l)}} \quad \Delta H_n^\circ = -57.4\ \text{kJ mol}^{-1}$$ ### 6. Standard Enthalpy of Solution ($\Delta H_{sol}^\circ$) The enthalpy change when **one mole of a substance** is dissolved in a large excess of solvent under standard conditions. This can be endothermic or exothermic. **Examples:** * Ammonium Chloride (Endothermic): $$\mathrm{NH_4Cl_{(s)}} \xrightarrow{\mathrm{H_2O}} \mathrm{NH^+_{4(aq)}} + \mathrm{Cl^-_{(aq)}} \quad \Delta H_{sol}^\circ = +15.1\ \text{kJ mol}^{-1}$$ * Hydrogen Chloride (Exothermic): $$\mathrm{HCl_{(g)}} \xrightarrow{\mathrm{H_2O}} \mathrm{H^+_{(aq)}} + \mathrm{Cl^-_{(aq)}} \quad \Delta H_{sol}^\circ = -75\ \text{kJ mol}^{-1}$$ ### 7. Standard Enthalpy of First Electron Affinity ($\Delta H_{E.A.}^\circ$) The energy released when **one mole of gaseous atoms** gains one mole of electrons to form one mole of gaseous ions with a single negative charge. **Example:** $$\mathrm{Cl_{(g)}} + e^- \rightarrow \mathrm{Cl^-_{(g)}} \quad \Delta H_{E.A.}^\circ = -349\ \text{kJ mol}^{-1}$$ ### 8. Lattice Energy ($\Delta H_{lattice}^\circ$) The energy released when **one mole of a solid ionic compound** is formed from its constituent gaseous ions. It is a measure of the strength of the ionic bonds. **Example:** $$\mathrm{Na^+_{(g)}} + \mathrm{Cl^-_{(g)}} \rightarrow \mathrm{NaCl_{(s)}} \quad \Delta H_{lattice}^\circ = -787\ \text{kJ mol}^{-1}$$ --- ## Worked Examples ### Example 6.1 Write the thermochemical equation for the formation of $\mathrm{H_2O_{(l)}}$, $\mathrm{SO_{3(g)}}$, and $\mathrm{H_2O_{2(l)}}$. **Solution:** 1. **For $\mathrm{H_2O_{(l)}}$:** ($\Delta H_f^\circ = -285.8\ \text{kJ mol}^{-1}$) $$\mathrm{H_{2(g)}} + \frac{1}{2}\mathrm{O_{2(g)}} \rightarrow \mathrm{H_2O_{(l)}} \quad \Delta H_f^\circ = -285.8\ \text{kJ mol}^{-1}$$ 2. **For $\mathrm{SO_{3(g)}}$:** ($\Delta H_f^\circ = -395.7\ \text{kJ mol}^{-1}$) $$\mathrm{S_{(s)}} + \frac{3}{2}\mathrm{O_{2(g)}} \rightarrow \mathrm{SO_{3(g)}} \quad \Delta H_f^\circ = -395.7\ \text{kJ mol}^{-1}$$ 3. **For $\mathrm{H_2O_{2(l)}}$:** ($\Delta H_f^\circ = -187.8\ \text{kJ mol}^{-1}$) $$\mathrm{H_{2(g)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{H_2O_{2(l)}} \quad \Delta H_f^\circ = -187.8\ \text{kJ mol}^{-1}$$ ### Example 6.2 Write the thermochemical equation for the combustion of Carbon (graphite), Methane ($\mathrm{CH_4}$), and Hydrogen ($\mathrm{H_2}$). **Solution:** 1. **For Carbon (graphite):** ($\Delta H_c^\circ = -393.5\ \text{kJ mol}^{-1}$) $$\mathrm{C_{(s)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}} \quad \Delta H_c^\circ = -393.5\ \text{kJ mol}^{-1}$$ 2. **For Methane ($\mathrm{CH_4}$):** ($\Delta H_c^\circ = -890.4\ \text{kJ mol}^{-1}$) $$\mathrm{CH_{4(g)}} + 2\mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}} + 2\mathrm{H_2O_{(l)}} \quad \Delta H_c^\circ = -890.4\ \text{kJ mol}^{-1}$$ 3. **For Hydrogen ($\mathrm{H_2}$):** ($\Delta H_c^\circ = -285.8\ \text{kJ mol}^{-1}$) $$\mathrm{H_{2(g)}} + \frac{1}{2}\mathrm{O_{2(g)}} \rightarrow \mathrm{H_2O_{(l)}} \quad \Delta H_c^\circ = -285.8\ \text{kJ mol}^{-1}$$ --- ## Possible Questions/Answers **Concept Assessment Exercise 6.1** * **Q:** Classify the following processes as exothermic or endothermic. * (a) Freezing of water * (b) Combustion of methane * (c) Sublimation of dry ice * (d) $\mathrm{H_2O_{(g)}} \rightarrow \mathrm{H_2O_{(l)}}$ * (e) Decomposition of limestone * **A:** * (a) **Exothermic** (heat is released to freeze) * (b) **Exothermic** (burning releases heat) * (c) **Endothermic** (heat is absorbed to go from solid to gas) * (d) **Exothermic** (condensation releases heat) * (e) **Endothermic** (requires heat to break down, e.g., $\mathrm{CaCO_3} \rightarrow \mathrm{CaO} + \mathrm{CO_2}$) **Concept Assessment Exercise 6.2** * **Q:** Which of the following equations describes a reaction for which $\Delta H^\circ$ is equal to the enthalpy of formation of a compound, $\Delta H_f^\circ$? * (a) $4\mathrm{Al_{(s)}} + 3\mathrm{O_{2(g)}} \rightarrow 2\mathrm{Al_2O_{3(s)}}$ * (b) $2\mathrm{Al_{(s)}} + \frac{3}{2}\mathrm{O_{2(g)}} \rightarrow \mathrm{Al_2O_{3(s)}}$ * (c) $\mathrm{CO_{(g)}} + \frac{1}{2}\mathrm{O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}}$ * **A:** **(b)** is the correct answer. * *Reasoning:* The definition of $\Delta H_f^\circ$ requires the formation of **one mole** of the compound from its **elements** in their standard states. * (a) is incorrect because it forms 2 moles of $\mathrm{Al_2O_3}$. * (c) is incorrect because a reactant ($\mathrm{CO}$) is a compound, not an element. * (b) correctly shows the formation of 1 mole of $\mathrm{Al_2O_3}$ from its elements, Al and $\mathrm{O_2}$. ---