Chapter 5: Thermochemistry – Study Notes

Thermochemistry

Overview

Thermochemistry is the study of energy transformations that occur during chemical reactions. This chapter covers the nature of chemical energy, the first law of thermodynamics, enthalpy, and the calculation of enthalpies of reaction.

5.1 The Nature of Chemical Energy

Definition and Units of Energy

Chemical energy is a form of energy stored in the bonds of chemical compounds. Energy is the ability to do work or transfer heat.

• Work: Energy used to cause an object with mass to move.

• Heat: Energy used to cause the temperature of an object to rise.

The SI unit of energy is the joule (J):

• $1~J = 1~\frac{kg~m^2}{s^2}$

• Non-SI unit: calorie (cal)

• $4.184~J = 1~cal$

• 1 food calorie = 1000 cal = 1 kcal

Thermodynamics and Thermochemistry

• Thermodynamics: The study of energy transformations.

• Thermochemistry: The study of energy transformations relating specifically to chemical reactions.

5.2 The First Law of Thermodynamics

Fundamental Concepts

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred from one form to another.

• If energy is lost from a system, it is gained by the surroundings, and vice versa.

System and Surroundings

• System: The part of the universe we are studying (e.g., the reaction in a container).

• Surroundings: Everything outside the system.

$\mathrm{Mg(NO_3)_2~(aq) + 2~NaOH~(aq) \rightarrow Mg(OH)_2~(s) + 2~NaNO_3~(aq)}$

Example: In the reaction :

• System: $\mathrm{Mg^{2+}~(aq) + 2~OH^-~(aq) \rightarrow Mg(OH)_2~(s)}$

• Surroundings: Spectator ions ($\mathrm{Na^+}$, $\mathrm{NO_3^-}$) and water

Internal Energy

• Internal Energy (E): The sum of all kinetic and potential energies of all components of a system.

• Change in internal energy ($\Delta E$) is the final energy minus the initial energy of a system.

Key equations:

• $\Delta E = q + W$

• $\Delta E = E_{\text{final}} - E_{\text{initial}}$

Example: $2~H_2~(g) + O_2~(g) \rightarrow 2~H_2O~(l) + \text{heat}$, $\Delta E < 0$ (energy released)

Worked Example

Example 5.1: A cylinder with a piston contains nitrogen and hydrogen, which react to form ammonia. As the reaction occurs, 1150 J of heat is lost to the surroundings and the piston moves down, doing 480 J of work on the system. What is the change in internal energy?

• $q = -1150~J$

• $W = 480~J$

• $\Delta E = q + W = -1150~J + 480~J = -670~J$

Exothermic and Endothermic Processes

• Exothermic: Reaction produces heat; heat is released from the system to the surroundings. $A + B \rightarrow C + \text{heat}$

• Endothermic: Reaction consumes heat; heat is absorbed by the system from the surroundings. $A + \text{heat} \rightarrow B + C$

Example 5.2: Classifying reactions:

Reaction	Exo/Endothermic
$2~Na + Cl_2 \rightarrow 2~NaCl + 1576~kJ$	Exothermic
$H_2O~(s) + 342~J \rightarrow H_2O~(l)$	Endothermic
$2~NH_3~(g) \rightarrow N_2~(g) + 3~H_2~(g) + 92~kJ$	Exothermic
$Fe_2O_3~(aq) + Al~(s) \rightarrow Fe~(s) + Al_2O_3~(aq) + 850~kJ$	Exothermic

5.3 Enthalpy

Definition and Calculation

Enthalpy (H): The total heat content of a system. At constant pressure, the change in enthalpy ($\Delta H$) equals the heat exchanged.

• $H = E + PV$

• $\Delta H = \Delta E - W$

• At constant pressure: $\Delta H = q$

Exothermic and Endothermic Reactions

• Exothermic: $\Delta H$ is negative; energy is released. $2~Na + Cl_2 \rightarrow 2~NaCl$, $\Delta H = -1576~kJ$

• Endothermic: $\Delta H$ is positive; energy is absorbed. $H_2O~(s) \rightarrow H_2O~(l)$, $\Delta H = 342~J$

Example 5.3: Classifying reactions:

Reaction	$\Delta H$	Exo/Endothermic
$N_2 + 2~O_2 \rightarrow 2~NO_2$	$+180.5~kJ$	Endothermic
$C_6H_{12}O_6 + 6~O_2 \rightarrow 6~CO_2 + 6~H_2O$	$-2870~kJ$	Exothermic
$CH_4~(g) + 2~O_2~(g) \rightarrow CO_2~(g) + 2~H_2O~(l)$	$-890~kJ$	Exothermic

5.4 Enthalpies of Reaction

Properties of Enthalpy

• Extensive property: Enthalpy depends on the amount of substance.

• For every mole of $CH_4$ burned, $890~kJ$ of heat are produced.

• If 3 moles of $CH_4$ are burned, $2670~kJ$ of heat are produced.

Direction and State Dependence

• $\Delta H$ for a reaction in the forward direction is equal in size but opposite in sign to $\Delta H$ for the reverse reaction.

• $\Delta H$ depends on the physical states of reactants and products.

Example:

Reaction	$\Delta H$
$CH_4~(g) + 2~O_2~(g) \rightarrow CO_2~(g) + 2~H_2O~(l)$	$-890~kJ$
$CH_4~(g) + 2~O_2~(g) \rightarrow CO_2~(g) + 2~H_2O~(g)$	$-802~kJ$

Calculating Enthalpy from Mass or Moles

Example 5.4: How much heat is produced when 4 moles of sodium are reacted with chlorine gas?

• Reaction: $2~Na + Cl_2 \rightarrow 2~NaCl$, $\Delta H = -1576~kJ$

• 1 mol Na produces $-788~kJ$

• 4 mol Na produces $4 \times -788~kJ = -3152~kJ$

Example 5.5: How much heat is released when 4.5 g of methane gas ($CH_4$) is burned in a constant-pressure system?

• Reaction: $CH_4~(g) + 2~O_2~(g) \rightarrow CO_2~(g) + 2~H_2O~(l)$, $\Delta H = -890~kJ$

• $4.50~g \left(\frac{1~mol}{16.043~g}\right) = 0.280~mol~CH_4$

• $0.280~mol~CH_4 \left(\frac{-890~kJ}{1~mol}\right) = -250~kJ$

Example 5.6: 96.0 kJ of heat is released when magnesium is burned in air. How many grams of the product are formed?

• Reaction: $2~Mg~(s) + O_2~(g) \rightarrow 2~MgO~(s)$, $\Delta H = -2408~kJ$

• $mol = \frac{-96.0~kJ}{-2408~kJ/2~mol~Mg} = 0.07973~mol~Mg$

• $mass = 0.07973~mol \times 24.305~g/mol = 1.94~g$

Recap

• Energy cannot be created or destroyed.

• Internal Energy of a system: $\Delta E = q + W$

• Enthalpy at constant pressure: $\Delta H = q$

• Exothermic: $\Delta H$ is negative, energy is a product.

• Endothermic: $\Delta H$ is positive, energy is a reactant.

Additional info: These notes cover the first half of Chapter 5 (Thermochemistry), including the nature of energy, the first law of thermodynamics, enthalpy, and enthalpies of reaction. Later sections (calorimetry, Hess's Law, enthalpies of formation, bond enthalpies) are listed in the chapter outline but not included in the provided content.