Calorimetry, Enthalpy, and Hess’s Law: Energy in Chemical Reactions

Energy and Chemical Reactions

Introduction to Energy in Chemistry

Energy plays a central role in chemical reactions, influencing both the direction and extent of chemical change. At the molecular level, energy released or absorbed during a reaction is associated with changes in the arrangement and motion of atoms and molecules.

• Internal energy (E): The sum of kinetic and potential energies for all particles in a system.

• Change in internal energy: $\Delta E = q + w$, where q is heat and w is work.

• The First Law of Thermodynamics: The total energy of the universe is constant.

• Enthalpy (H): The heat lost or gained at constant pressure, $\Delta H = q$.

• For most chemical reactions under constant pressure, $\Delta H \approx \Delta E$.

• Expansion work: $w = -P\Delta V$.

Calorimetry

Experimental Measurement of Heat Changes

Calorimetry is the experimental technique used to measure the heat exchanged in chemical reactions. Since heat cannot be measured directly, temperature changes are monitored and used to calculate heat.

• Calorimeter: An insulated device that isolates the system and surroundings, allowing accurate measurement of temperature changes.

• Temperature change of water or an aqueous mixture (the surroundings) is used to calculate the heat gained or lost by the reaction (the system).

• Calorimetry experiments are designed to measure $q$ indirectly via temperature changes.

Example: Simple Calorimeter

A typical calorimeter consists of a reaction mixture in an insulated container (such as nested styrofoam cups) with a thermometer and stirrer to ensure uniform temperature.

Heat Capacity

Definitions and Calculations

Heat capacity quantifies how much heat an object or substance can absorb before its temperature changes.

• Heat capacity (C): The amount of heat required to raise the temperature of an object by 1°C.

• Specific heat capacity (s): The amount of heat required to raise the temperature of 1 g of a substance by 1°C. $q = s \cdot m \cdot \Delta T$

• Molar heat capacity (C_m): The amount of heat required to raise the temperature of 1 mol of a substance by 1°C. $q = C_m \cdot n \cdot \Delta T$

• The value of heat capacity depends on both the identity and amount of the substance.

Table: Specific Heats and Molar Heat Capacities at 25°C

Substance	Specific Heat (J/g·°C)	Molar Heat Capacity (J/mol·°C)
Aluminum	0.897	24.2
Copper	0.385	24.4
Gold	0.129	25.4
Mercury	0.140	28.0
NaCl	0.859	50.2
Water (s)	2.03	36.6
Water (l)	4.184	75.3

Energy Units

Units of Heat and Energy

Heat is commonly measured in joules (J) or kilojoules (kJ), the SI units of energy. Sometimes, calories (cal) are used.

• Conversion: $1 \text{ cal} = 4.184 \text{ J}$

Calorimetry Calculations

Sample Problems and Applications

Calorimetry problems involve calculating the heat exchanged using measured temperature changes, mass, and specific heat.

• General formula: $q = s \cdot m \cdot \Delta T$

• Example: What is the specific heat of silver if 667.0 J are required to raise the temperature of 248.99 g of Ag by 11.4°C? Rearranged: $s = \frac{q}{m \cdot \Delta T}$

Worked Example: Neutralization Reaction

When 100.0 mL of 0.500 M HCl is combined with 100.0 mL of 0.500 M NaOH in a calorimeter at 22.50°C, the temperature increases to 25.86°C. Assuming the specific heat of the mixture is 4.184 J/g·°C and density is 1.00 g/mL:

• Total mass = 100.0 g + 100.0 g = 200.0 g

• $q = 4.184 \text{ J/g·°C} \times 200.0 \text{ g} \times (25.86 - 22.50) \text{°C}$

• $q = 2810 \text{ J}$

• $\Delta H = -2.81 \text{ kJ}$ (heat released by reaction)

Additional info:

Similar calculations apply for dissolution, precipitation, and other reactions, adjusting for calorimeter heat capacity if necessary.

Thermochemical Equations

Heat of Reaction and Stoichiometry

A thermochemical equation is a balanced chemical equation that includes the enthalpy change ($\Delta H$) for the reaction.

• Example: $\mathrm{Br_2(l) + 2NaOH(aq) \rightarrow NaBr(aq) + NaOBr(aq) + H_2O(l)}$ $\Delta H = -41.3 \text{ kJ}$

• The magnitude of $\Delta H$ is proportional to the amount of substance reacting.

• Multiplying reaction coefficients by a factor multiplies $\Delta H$ by the same factor.

• The sign of $\Delta H$ depends on the direction of the reaction.

Exothermic and Endothermic Reactions

Classification of Reactions by Heat Flow

Chemical reactions are classified based on whether they release or absorb heat.

• Exothermic reaction: Releases heat; $\Delta H$ is negative. Example: $\mathrm{Br_2(l) + 2NaOH(aq) \rightarrow NaBr(aq) + NaOBr(aq) + H_2O(l)}$ $\Delta H = -41.3 \text{ kJ}$

• Endothermic reaction: Absorbs heat; $\Delta H$ is positive. Example: $\mathrm{NaBr(aq) + NaOBr(aq) + H_2O(l) \rightarrow Br_2(l) + 2NaOH(aq)}$ $\Delta H = +41.3 \text{ kJ}$

Hess’s Law

Calculating Enthalpy Changes for Complex Reactions

Hess’s Law states that the enthalpy change for an overall process is the sum of the enthalpy changes for its individual steps. This is possible because enthalpy is a state function.

• Hess’s Law: $\Delta H_{\text{overall}} = \sum \Delta H_{\text{steps}}$

• Allows calculation of $\Delta H$ for reactions that are difficult to measure directly.

• Physical states of reactants and products must be considered.

Example: Formation of SO3(g)

• $\mathrm{S(s) + 3/2 O_2(g) \rightarrow SO_3(g)}$

• Step 1: $\mathrm{S(s) + O_2(g) \rightarrow SO_2(g)}$ $\Delta H = -296.8 \text{ kJ}$

• Step 2: $\mathrm{SO_2(g) + 1/2 O_2(g) \rightarrow SO_3(g)}$ $\Delta H = -98.9 \text{ kJ}$

• Overall: $\Delta H = -395.7 \text{ kJ}$

Summary

• Calorimetry is used to experimentally determine $\Delta H$.

• Heat capacity, specific heat, and molar heat capacity are key concepts for quantifying heat changes.

• Exothermic reactions release heat; endothermic reactions absorb heat.

• Thermochemical equations relate stoichiometry to enthalpy changes.

• Hess’s Law enables calculation of enthalpy changes for complex reactions by summing the enthalpy changes of individual steps.

Additional info:

These topics are foundational for understanding thermochemistry and energy changes in chemical reactions, as covered in General Chemistry Chapter 9.