Unit 5: Thermochemistry – Energy, Heat, and Enthalpy in Chemical Processes

Energy Basics

Kinetic and Potential Energy

Energy is a fundamental concept in chemistry, describing the capacity to do work or produce heat. It exists in various forms, primarily as kinetic and potential energy.

• Kinetic Energy (KE): Energy associated with the motion of objects. The formula for kinetic energy is: $KE = \frac{1}{2}mv^2$ where m is mass and v is velocity.

• Potential Energy (PE): Energy stored due to an object's position or arrangement. In chemistry, this often refers to energy stored in chemical bonds.

• Total Energy: The sum of kinetic and potential energy in a system.

• Conservation of Energy: Energy cannot be created or destroyed, only transformed. For a system and its surroundings: $\Delta E_{system} + \Delta E_{surroundings} = 0$

• Ways to Increase a System's Energy: Work can be done on a system, or heat can be transferred into it.

Energy in Chemistry

Chemical Energy and Work

In chemical processes, energy is stored in chemical bonds and can be released or absorbed during reactions.

• Chemical Energy: Potential energy stored in chemical bonds.

• Work: Energy transfer due to force acting over a distance. In chemistry, expansion work is important: $w = -P\Delta V$ where P is pressure and ΔV is change in volume.

• Internal Energy (U): The total energy (kinetic + potential) of all particles in a system.

Kinetic Energy and Temperature

The kinetic energy of atoms and molecules is directly related to temperature.

• Temperature: A measure of the average kinetic energy of particles.

• Relationship: $KE \propto T$

• Heat (q): Energy transfer that changes the kinetic energy of atoms or molecules in a system.

• Sign Convention: $q > 0$ means heat is absorbed (endothermic); $q < 0$ means heat is released (exothermic).

• Thermal Equilibrium: When two objects reach the same temperature, heat transfer stops.

Heat Capacity

Units and Definitions

Heat capacity quantifies the amount of energy required to raise the temperature of a substance.

• Calorie (cal): Amount of energy required to raise the temperature of 1 g of water by 1°C.

• Joule (J): SI unit of energy. $1 \text{ cal} = 4.184 \text{ J}$

• Heat Capacity (C): Amount of heat needed to raise the temperature of an object by 1°C. $C = \frac{q}{\Delta T}$

• Specific Heat Capacity (c): Amount of heat needed to raise the temperature of 1 g of a substance by 1°C. $q = m c \Delta T$ where m is mass, c is specific heat, and ΔT is temperature change.

Example Calculation

Calculate the heat required to raise the temperature of 250 g of copper (specific heat = 0.385 J/g·°C) from 22°C to 100°C:

• $q = (250 \text{ g})(0.385 \text{ J/g·°C})(100 - 22 \text{°C}) = 7,546.5 \text{ J}$

Measuring Heat

Calorimetry

Calorimetry is the experimental technique used to measure heat changes in chemical reactions or physical processes.

• General Approach: Place a hot object in a water bath and measure temperature changes.

• Equation: $q_{object} + q_{surroundings} = 0$ or $q_{object} = -q_{surroundings}$

• Interpretation: Heat lost by the object is gained by the surroundings, and vice versa.

Extended Example Calculation

A 49.8 g piece of metal at 75.0°C is immersed in 100.0 g of water at 22.0°C. The system reaches equilibrium at 25.1°C.

• Heat absorbed by water: $q_{water} = (100.0 \text{ g})(4.184 \text{ J/g·°C})(25.1 - 22.0 \text{°C}) = 1,310.0 \text{ J}$

• Heat lost by metal: $q_{metal} = -q_{water} = -1,310.0 \text{ J}$

• Specific heat of metal: $c = \frac{q_{metal}}{m \Delta T} = \frac{-1,310.0 \text{ J}}{49.8 \text{ g} \times (25.1 - 75.0) \text{°C}} = 0.527 \text{ J/g·°C}$

Heat and Energy in Chemical Processes

Energy in Chemical Reactions

Chemical reactions involve the breaking and forming of bonds, which results in energy changes.

• Exothermic Processes: Release heat; chemical potential energy from bonds is converted to kinetic energy.

• Endothermic Processes: Absorb heat; kinetic energy is converted into potential energy.

Demonstrations

• Demo 1: Sodium acetate crystallization (liquid to solid).

• Demo 2: Ammonium nitrate dissolution (solid to liquid, below freezing point).

• Demo 3: Combustion reaction (high voltage, flammable liquid, increase in pressure).

Reactions at Constant Volume and Pressure

Calorimetry at Constant Volume

Bomb calorimeters are used to measure energy changes at constant volume.

• Energy at Constant Volume: All energy released is heat. $\Delta U = q_{v}$

Energy at Constant Pressure

Most chemical reactions occur at constant pressure (open containers).

• Energy at Constant Pressure: Includes work done by gases. $\Delta H = \Delta U + P\Delta V$ $q_{p} = \Delta H$

Reaction Enthalpy

Relationship Between Enthalpy and Heat

Enthalpy change ($\Delta H$) is the heat released or absorbed by a reaction at constant pressure.

• Notation: $\Delta H_{reaction}$

• Example: $2Na(s) + 2H_2O(l) \rightarrow 2NaOH(aq) + H_2(g)$ $\Delta H = -368.4 \text{ kJ}$

• Sign of $\Delta H$: Negative for exothermic (heat released), positive for endothermic (heat absorbed).

• Switching Reaction Direction: Changes the sign of $\Delta H$.

• Scaling Coefficients: Multiply $\Delta H$ by the factor used to scale the reaction.

Calculating Reaction Enthalpies

Using Enthalpies of Related Reactions

Reaction enthalpy can be determined by combining enthalpies of related reactions.

• Example: $2NO(g) + O_2(g) \rightarrow 2NO_2(g)$ $\Delta H = -114.2 \text{ kJ}$ $2NO_2(g) + 2NaOH(aq) \rightarrow 2NaNO_3(aq) + 2H_2O(l)$ $\Delta H = -158.2 \text{ kJ}$ $H_2SO_4(aq) + 2NaOH(aq) \rightarrow 2H_2O(l) + Na_2SO_4(aq)$ $\Delta H = -111.2 \text{ kJ}$

Standard Enthalpy of Formation

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change for producing 1 mole of a substance from its elements in their standard states.

• Example: $2NO(g) + O_2(g) \rightarrow 2NO_2(g)$ $\Delta H_f^\circ = -114.2 \text{ kJ}$

Hess's Law

Combining Reaction Enthalpies

Hess's Law states that if a reaction can be expressed as the sum of two or more reactions, the enthalpy change for the overall reaction is the sum of the enthalpy changes for the individual reactions.

• General Steps:

  1. Write the target reaction as a sum of known reactions.

  2. Adjust enthalpies for reaction direction and scaling coefficients.

  3. Sum the adjusted enthalpies.

• Example: Given: $2SO_2(g) + O_2(g) \rightarrow 2SO_3(g), \Delta H = -198 \text{ kJ}$ $SO_3(g) + H_2O(l) \rightarrow H_2SO_4(aq), \Delta H = -130 \text{ kJ}$ Find $2SO_2(g) + 2H_2O(l) + O_2(g) \rightarrow 2H_2SO_4(aq)$ $\Delta H = -198 + 2(-130) = -458 \text{ kJ}$

Additional info: These notes cover key concepts from Chapter 5: Thermochemical Aspects of Chemical Reactions, including energy forms, heat capacity, calorimetry, enthalpy, and Hess's Law, with relevant equations and examples for General Chemistry students.