Thermochemistry and Energy in Chemical Reactions (CHY 102)

Thermochemistry and Energy in Chemical Reactions

Chapter Outline

• The Nature of Energy: Key Definitions

• First Law of Thermodynamics: There is No Free Lunch

• Quantifying Heat and Work

• ΔU for Chemical Reactions: Constant-Volume Calorimetry

• The Heat Evolved in a Chemical Reaction at Constant Pressure

• Constant-Pressure Calorimetry: Measuring ΔH

• Relationships Involving ΔH

• Enthalpies of Reaction from Standard Enthalpies of Formation

The Nature of Energy: Key Definitions

What is Energy?

Energy is a fundamental concept in chemistry, describing the capacity to do work or produce heat. The study of energy and its transformations is called thermochemistry.

• Energy: The capacity to do work.

• Work: The result of a force acting through a distance.

• Heat: The transfer of energy caused by a temperature difference.

Example: In curling, energy is transferred from the player to the stone, resulting in work and heat.

Types of Energy

Energy can exist in various forms, each relevant to chemical processes:

• Kinetic Energy: Energy associated with motion.

• Thermal Energy: Energy associated with temperature.

• Potential Energy: Energy associated with position or composition.

• Chemical Energy: A form of potential energy associated with the positions of electrons and nuclei in a system.

Example: A ball held above the ground has mechanical potential energy; when released, it gains kinetic energy.

Systems and Surroundings

In thermochemistry, it is essential to distinguish between the system (the part of the universe under study) and the surroundings (everything else).

• System: The portion of the universe singled out for investigation.

• Surroundings: Everything with which the system can exchange energy.

Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only be transferred from one object or system to another.

Units and Measurement of Energy

Energy is measured in joules (J), the SI unit. Other units include calories (cal), kilocalories (kcal), and kilowatt-hours (kWh).

• Kinetic Energy Formula:

$E_k = \frac{1}{2}mv^2$

• Unit Conversions:

Unit	Equivalent in Joules (J)
1 calorie (cal)	4.184 J
1 kilocalorie (kcal)	4184 J
1 kilowatt-hour (kWh)	3.60 × 106 J

First Law of Thermodynamics: There is No Free Lunch

Internal Energy and Its Change

The first law of thermodynamics states that the total energy of the universe is constant. The internal energy (U) of a system is the sum of its kinetic and potential energies.

• Internal Energy: $U = U_{kinetic} + U_{potential}$

• Change in Internal Energy: $\Delta U = q + w$

• q: Heat exchanged

• w: Work done

Signs of q and w:

• q > 0: System gains heat

• q < 0: System loses heat

• w > 0: Work done on the system

• w < 0: Work done by the system

Example: If a reaction releases 890 J of heat and does 450 J of work on the surroundings, $q = -890$ J, $w = -450$ J, $\Delta U = -1340$ J.

State Functions

A state function is a property whose value does not depend on the path taken to reach that specific value. Internal energy (U) is a state function.

Quantifying Heat and Work

Heat and Temperature

Heat (q) is not the same as temperature. Temperature measures the average kinetic energy of particles, while heat is the transfer of thermal energy.

• Specific Heat Capacity (c): The quantity of heat required to change the temperature of 1.0 g of a substance by 1°C. Units: J g-1 °C-1

• Heat Calculation:

$q = m c \Delta T$

• m: mass of substance (g)

• c: specific heat capacity

• $\Delta T$: change in temperature (°C or K)

Table: Specific Heat Capacities of Selected Substances

Substance	Specific Heat Capacity (J g-1 °C-1)
Lead	0.128
Gold	0.128
Silver	0.235
Copper	0.385
Iron	0.449
Aluminum	0.903
Ethanol	2.440
Water	4.184
Glass (Pyrex)	0.75
Granite	0.79
Sand	0.84

Types of Systems

• Open System: Both energy and matter can be exchanged with surroundings.

• Closed System: Only energy can be exchanged; matter cannot.

• Isolated System: Neither energy nor matter can be exchanged.

Heat Transfer and Thermal Equilibrium

When two substances at different temperatures are placed together, heat transfers from the hotter to the cooler substance until thermal equilibrium is reached.

• Heat Lost = Heat Gained:

$m_{metal} c_{metal} \Delta T_{metal} = m_{water} c_{water} \Delta T_{water}$

Work in Chemical Systems

Work is done when a system changes volume against an external pressure.

• Work Formula:

$w = -P \Delta V$

• P: external pressure

• $\Delta V$: change in volume

For reactions involving gases, the work can be related to the change in moles of gas:

$w = -\Delta n_{gas} RT$

• $\Delta n_{gas}$: change in moles of gas

• R: gas constant (8.314 J mol-1 K-1)

• T: temperature (K)

ΔU for Chemical Reactions: Constant-Volume Calorimetry

Bomb Calorimetry

Bomb calorimetry is used to measure the heat evolved in a chemical reaction at constant volume. The change in internal energy ($\Delta U$) is determined by measuring the heat transferred to the surroundings.

• At constant volume: $\Delta U = q_v$

• Heat absorbed by calorimeter: $q_{cal} = C_{cal} \Delta T$

Example: If 1.0 g of sucrose combusts and the temperature of the calorimeter increases, use the heat capacity and temperature change to calculate $\Delta U$.

The Heat Evolved in a Chemical Reaction at Constant Pressure

Enthalpy and Enthalpy Change

Enthalpy (H) is the sum of the internal energy and the product of pressure and volume:

$H = U + PV$

At constant pressure, the change in enthalpy ($\Delta H$) equals the heat exchanged:

$\Delta H = q_p$

• Exothermic Reaction: Releases heat ($\Delta H < 0$)

• Endothermic Reaction: Absorbs heat ($\Delta H > 0$)

Molecular Perspective of Exothermic Reactions

Exothermic reactions release energy due to the conversion of potential energy (from chemical bonds) into thermal energy.

Constant-Pressure Calorimetry: Measuring ΔH

Coffee-Cup Calorimeter

Used to measure the heat evolved or absorbed at constant pressure. The temperature change of the solution is used to calculate $q_p$ and thus $\Delta H$.

• For dilute aqueous solutions, assume density and heat capacity are similar to water.

• Calculation: $q_{solution} = m_{solution} c_{solution} \Delta T$

Relationships Involving ΔH

Manipulating Chemical Equations

Enthalpy changes are related to the stoichiometry of reactions. If a reaction is multiplied by a factor, $\Delta H$ is multiplied by the same factor. If a reaction is reversed, the sign of $\Delta H$ is reversed.

• Hess's Law: The enthalpy change for an overall reaction is the sum of the enthalpy changes for the individual steps.

Enthalpies of Reaction from Standard Enthalpies of Formation

Standard States and Enthalpy of Formation

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

• Standard state for a gas: pure gas at 1 bar and specified temperature (usually 25°C)

• Standard state for a solid or liquid: pure substance at 1 bar and specified temperature

• Standard state for a solution: concentration of 1 mol L-1

Table: Selected Standard Enthalpies of Formation

Compound	Formula	$\Delta H_f^\circ$ (kJ mol-1)
Isopropanol	C3H8O	-318.0
Glucose	C6H12O6	-1273.3
Sucrose	C12H22O11	-2220.0
CO2 (g)	CO2	-393.5
C2H5OH (l)	C2H5OH	-277.6

Additional info: Table values inferred and simplified for clarity.

Calculating Enthalpy Change for a Reaction

The standard enthalpy change for a reaction is calculated using the enthalpies of formation:

$\Delta H^\circ_{rxn} = \sum \Delta H^\circ_f \text{(products)} - \sum \Delta H^\circ_f \text{(reactants)}$

Example: For the fermentation of glucose:

$C_6H_{12}O_6 (s) \rightarrow 2 C_2H_5OH (l) + 2 CO_2 (g)$

$\Delta H^\circ_{rxn} = [2 \times (-277.6) + 2 \times (-393.5)] - [-1273.3] = 3.9$ kJ mol-1

Energy Use and the Environment

Combustion and Energy Production

Fossil fuels undergo combustion reactions that release large amounts of heat, used to generate electricity. However, excess CO2 emissions contribute to climate change, and fossil fuels are non-renewable.

• Alternative Energy: Solar energy is abundant and could potentially replace fossil fuels if efficiently harvested.

Example: The sun irradiates the Earth with 4.2 million exajoules of energy annually.

Additional info: Some values and examples inferred for completeness and clarity.