Chapter 9 Student Notes

Thermochemistry: Chemical Energy

Introduction to Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, that occur during chemical reactions and changes of state. Understanding how energy is transferred and transformed is essential for predicting reaction behavior and designing chemical processes.

• Chemical energy is the energy stored in the bonds of chemical compounds.

• Energy changes in reactions can be measured and classified as heat (q) or work (w).

• Thermochemistry helps us understand the relationship between energy, heat, and work in chemical systems.

Key Terminology

• System: The part of the universe under study (e.g., the reactants and products in a reaction).

• Surroundings: Everything outside the system.

• State function: A property that depends only on the current state of the system, not on the path taken to reach that state (e.g., energy, pressure, temperature, volume).

• Path function: A property that depends on the specific pathway taken between two states (e.g., work, heat).

Forms of Energy

• Kinetic energy: Energy due to motion. $E_k = \frac{1}{2}mv^2$

• Potential energy: Energy due to position or composition.

• Thermal energy: Energy associated with the temperature of a substance (random motion of particles).

• Chemical energy: Energy stored in chemical bonds.

First Law of Thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. The total energy of the universe is constant.

• Mathematical expression:

$\Delta E = q + w$

• $\Delta E$ = change in internal energy of the system

• $q$ = heat exchanged

• $w$ = work done

Sign conventions:

• If $q$ or $w$ is positive, energy is added to the system.

• If $q$ or $w$ is negative, energy is lost from the system to the surroundings.

Heat, Work, and State Functions

• Heat (q): Energy transferred due to temperature difference.

• Work (w): Energy transferred when an object is moved by a force.

• State functions include energy, pressure, temperature, and volume.

• Path functions include heat and work.

Units of Energy

• Joule (J): SI unit of energy. $1\,\text{J} = 1\,\text{kg} \cdot \text{m}^2/\text{s}^2$

• Calorie (cal): Energy required to raise the temperature of 1 g of water by 1°C. $1\,\text{cal} = 4.184\,\text{J}$

Enthalpy (H)

Enthalpy is a state function that represents the heat content of a system at constant pressure. The change in enthalpy ($\Delta H$) is equal to the heat exchanged at constant pressure.

• $\Delta H = q_p$ (at constant pressure)

• $\Delta H = \Delta E + P\Delta V$

• For reactions at constant volume: $q_v = \Delta E$

• For reactions at constant pressure: $q_p = \Delta H$

Calorimetry

Calorimetry is the measurement of heat flow in chemical reactions. Calorimeters are devices used to measure heat changes.

• Coffee-cup calorimeter: Measures heat at constant pressure.

• Bomb calorimeter: Measures heat at constant volume.

Specific Heat Capacity

• Specific heat capacity (c): Amount of heat required to raise the temperature of 1 g of a substance by 1°C.

• Molar heat capacity (C): Amount of heat required to raise the temperature of 1 mol of a substance by 1°C.

Formula:

$q = mc\Delta T$

• $q$ = heat absorbed or released

• $m$ = mass of substance

• $c$ = specific heat capacity

• $\Delta T$ = change in temperature

Thermochemical Equations

Thermochemical equations show the enthalpy change ($\Delta H$) associated with chemical reactions. The enthalpy change is written as part of the equation and refers to the moles of reactants and products.

• Standard state: All gases, liquids, and solids at 1 atm pressure and 25°C.

• Reversing a reaction changes the sign of $\Delta H$.

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

Enthalpy of Formation

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

• For elements in their standard state, $\Delta H_f^\circ = 0$

• Formation reaction: Elements → Compound

Hess's Law

Hess's Law states that the enthalpy change for a reaction is the same, regardless of the pathway taken, as long as the initial and final conditions are the same. This allows calculation of $\Delta H$ for complex reactions by combining known enthalpy changes.

• If a reaction is reversed, $\Delta H$ changes sign.

• If a reaction is multiplied by a factor, $\Delta H$ is multiplied by the same factor.

• Sum the $\Delta H$ values for each step to get the overall $\Delta H$.

Sample Table: Standard Enthalpies of Formation

Substance	$\Delta H_f^\circ$ (kJ/mol)
CO$_2$(g)	-393.5
H$_2$O(l)	-285.8
CH$_4$(g)	-74.8
O$_2$(g)	0

Example Calculations

• Calculating heat absorbed: How many joules of heat must be removed from 100 g of H$_2$O to cool it from 20°C to its freezing point at 0°C? Use $q = mc\Delta T$.

• Using Hess's Law: Calculate $\Delta H$ for the reaction: $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$ using standard enthalpies of formation.

• Calorimetry problem: A 50.0 g chunk of lead is heated to 100.0°C and then dropped into a beaker with 100.0 g of H$_2$O at 25.0°C. Calculate the final temperature of the mixture.

Summary Table: Comparison of Calorimeters

Type	Condition	Measurement
Coffee-cup calorimeter	Constant pressure	Measures $q_p$ (heat at constant pressure)
Bomb calorimeter	Constant volume	Measures $q_v$ (heat at constant volume)

Important Equations

• $q = mc\Delta T$

• $\Delta E = q + w$

• $\Delta H = \Delta E + P\Delta V$

• For enthalpy of formation: $\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ \text{(products)} - \sum \Delta H_f^\circ \text{(reactants)}$

Additional info:

• Thermochemistry is foundational for understanding energy flow in chemical and physical processes.

• Mastery of calorimetry and enthalpy calculations is essential for laboratory and theoretical chemistry.