Thermo chem

1. Introduction to Thermochemistry

Thermochemistry is the study of heat changes that accompany chemical reactions and physical changes. It is a branch of thermodynamics.

2. Key Concepts and Definitions

• Energy ($E$): The capacity to do work or transfer heat.

  • Kinetic Energy ($KE$): Energy of motion, ${KE = \frac{1}{2}mv^2}$.

  • Potential Energy ($PE$): Stored energy, often due to position or composition.

• System: The specific part of the universe being studied (e.g., a chemical reaction).

• Surroundings: Everything outside the system.

• Universe: System + Surroundings.

• Heat ($q$): Thermal energy transfer between a system and its surroundings due to a temperature difference.

  • Endothermic Process: System absorbs heat from the surroundings (q > 0).

  • Exothermic Process: System releases heat to the surroundings (q < 0).

• Work ($w$): Energy transfer that is not heat, usually involving a force acting over a distance.

  • For gases, pressure-volume work: ${w = -P_{\text{ext}}\Delta V}$. If system expands, work is done by the system (w < 0).

3. The First Law of Thermodynamics

• Law of Conservation of Energy: Energy cannot be created or destroyed, only transferred or transformed.

• Internal Energy ($U$ or $E$): The total energy contained within a system.

  • Change in internal energy: ${ \Delta U = q + w }$

  • Where $q$ is heat added to the system and $w$ is work done on the system.

4. Enthalpy ($H$)

• Definition: A thermodynamic property of a system that is equal to the internal energy plus the product of pressure and volume: ${H = U + PV}$.

• Enthalpy Change ($\Delta H$): The heat absorbed or released by a system at constant pressure.

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

  • Endothermic Reaction: { \Delta H > 0 } (heat absorbed, system gains energy).

  • Exothermic Reaction: { \Delta H < 0 } (heat released, system loses energy).

• Standard Enthalpy Change ($\Delta H^{\circ}$): Enthalpy change measured under standard conditions ($1$ atm pressure for gases, $1$ M concentration for solutions, and a specified temperature, usually $298.15$ K ($25^{\circ}$C)).

5. Types of Enthalpies

• Standard Enthalpy of Formation ($\Delta H_f^{\circ}$): Enthalpy change when 1 mole of a compound is formed from its elements in their standard states.

  • ${ \Delta H_f^{\circ} }$ for elements in their standard states is $0$ kJ/mol.

• Standard Enthalpy of Reaction ($\Delta H_{rxn}^{\circ}$): The enthalpy change for a reaction under standard conditions.

  • Calculated using standard enthalpies of formation:
    ${ \Delta H<em>{rxn}^{\circ} = \sum n \Delta H</em>f^{\circ} (\text{products}) - \sum m \Delta H_f^{\circ} (\text{reactants}) }$
    (where $n$ and $m$ are stoichiometric coefficients).

• Standard Enthalpy of Combustion ($\Delta H_c^{\circ}$): Enthalpy change when 1 mole of a substance undergoes complete combustion with oxygen under standard conditions.

6. Calorimetry

• Definition: The experimental measurement of heat flow.

• Calorimeter: A device used to measure heat changes.

• Specific Heat Capacity ($c$ or $s$): The amount of heat required to raise the temperature of 1 gram of a substance by ${1^{\circ}}$C (or $1$ K).

  • ${q = mc\Delta T}$ (for a substance, where $m$ is mass, $\Delta T$ is temperature change).

• Heat Capacity ($C$): The amount of heat required to raise the temperature of an entire object by ${1^{\circ}}$C (or $1$ K).

  • ${q = C\Delta T}$.

• Bomb Calorimeter (Constant Volume Calorimeter): Measures ${ \Delta U }$ (or ${ q_v }$) for combustion reactions.

  • ${q<em>{calorimeter} = C</em>{calorimeter}\Delta T}$.

  • ${q<em>{reaction} = -q</em>{calorimeter}}$.

• Coffee-Cup Calorimeter (Constant Pressure Calorimeter): Measures ${ \Delta H }$ (or ${ q_p }$) for reactions in solution.

  • ${q<em>{solution} = m</em>{solution}c_{solution}\Delta T}$.

  • ${q<em>{reaction} = -q</em>{solution}}$.

7. Hess's Law

• Statement: If a reaction can be expressed as a series of steps, then the enthalpy change for the overall reaction is the sum of the enthalpy changes for each step.

• Application: Allows calculation of ${ \Delta H }$ for reactions that are difficult to measure directly, using known ${ \Delta H }$ values of other reactions.

  • Rules for manipulating reactions:

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

  • Multiplying a reaction by a coefficient multiplies ${ \Delta H }$ by the same coefficient.

8. Bond Energies

• Bond Energy: The energy required to break 1 mole of a specific type of bond in the gaseous state.

• Approximation of ${ \Delta H<em>{rxn} }$: ${ \Delta H</em>{rxn} \approx \sum (\text{bond energies of bonds broken}) - \sum (\text{bond energies of bonds formed}) }$

  • Breaking bonds is endothermic (requires energy, positive values).

  • Forming bonds is exothermic (releases energy, negative values).