SUPA Chem Unit 5

1. The Nature of Energy

• Energy: The capacity to do work or transfer heat.

  • Kinetic Energy ($E_k$): Energy associated with motion.

  • Formula: $E_k = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

  • Potential Energy ($E_p$): Energy associated with position or composition.

  • Chemical Potential Energy: Stored within the bonds of chemical substances.

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

• Units of Energy: Joule ($J$), calorie ($cal$), Calorie ($Cal$ = $1000$ calories).

  • Conversion: $1\ cal = 4.184\ J$

2. The First Law of Thermodynamics

• Law of Conservation of Energy: Energy can be converted from one form to another but cannot be created or destroyed.

• System: The specific part of the universe being studied.

• Surroundings: Everything outside the system.

• $q$ (Heat): Energy transfer due to a temperature difference.

  • Positive $q$: System gains heat (endothermic).

  • Negative $q$: System loses heat (exothermic).

• $w$ (Work): Energy transfer due to a force acting over a distance.

  • Positive $w$: Surroundings do work on the system.

  • Negative $w$: System does work on the surroundings (e.g., expansion work).

• Change in Internal Energy ($\Delta E$): The sum of heat and work exchanged between the system and surroundings.

  • Formula: $\Delta E = q + w$

3. Enthalpy ($H$) and Enthalpy Changes ($\Delta H$)

• Enthalpy: A thermodynamic property equal to the internal energy of the system plus the product of pressure and volume.

  • Formula: $H = E + PV$

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

  • Formula: $\Delta H = q_p$

  • Exothermic Reaction: \Delta H < 0, heat is released by the system to the surroundings.

  • Endothermic Reaction: \Delta H > 0, heat is absorbed by the system from the surroundings.

• Thermochemical Equations: Balanced chemical equations that include the associated $\Delta H$ value.

  • State Functions: Properties whose values depend only on the state of the system, not on the path taken to reach that state (e.g., E, H).

  • Extensive Properties: Properties that depend on the amount of substance present, such as mass and volume, in contrast to intensive properties that do not depend on the size of the sample.

• Thermodynamically favored reactions:

  • Reactions for which $\Delta H$ is large (about 100 kJ or more) and negative tend to be spontaneous.

  • Reactions for which $\Delta H$ is large and positive tend to be spontaneous only in the reverse direction.

4. Calorimetry

• Calorimetry: The measurement of heat flow.

• Heat Capacity ($C$): The amount of heat required to raise the temperature of a substance by $1$ Kelvin or $1$ degree Celsius.

  • Unit: $J/K$ or $J/°C$

• Specific Heat Capacity ($c$): The amount of heat required to raise the temperature of $1$ gram of a substance by $1$ Kelvin or $1$ degree Celsius.

  • Unit: $J/(g\cdot K)$ or $J/(g\cdot °C)$

  • Formula for heat transfer: $q = mc\Delta T$, where $m$ is mass, $c$ is specific heat, and $\Delta T$ is the change in temperature.

• Molar Heat Capacity ($C_m$): The amount of heat required to raise the temperature of $1$ mole of a substance by $1$ Kelvin or $1$ degree Celsius.

  • Unit: $J/(mol\cdot K)$ or $J/(mol\cdot °C)$

• Constant-Pressure Calorimetry (Coffee-Cup Calorimeter): Used to determine $\Delta H$ for reactions in solution.

  • Assumptions: No heat loss to surroundings; specific heat of solution is similar to water.

  • Calculation: $q<em>{reaction} = -q</em>{solution} = -(mc\Delta T)_{solution}$

• Constant-Volume Calorimetry (Bomb Calorimeter): Used to measure the heat of combustion.

  • The heat capacity of the calorimeter ($C_{cal}$) must be known.

  • Calculation: $q<em>{reaction} = -q</em>{calorimeter} = -C_{cal}\Delta T$

5. Hess's Law

• Hess's Law: If a reaction can be expressed as a series of steps, then the $\Delta H$ for the overall reaction is the sum of the $\Delta H$ values for each step.

  • Rules for manipulating thermochemical equations:

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

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

6. Standard Enthalpies of Formation ($\Delta H_f^°$)

• Standard State: The most stable form of a substance at $1$ atm pressure and a specified temperature (usually $25°C$ or $298.15\ K$).

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

• $\Delta H<em>f^°$ of an element in its standard state is zero (e.g., $\Delta H</em>f^°(O_{2(g)}) = 0$).

• Calculating $\Delta H_{reaction}^°$ using standard enthalpies of formation:

  • Formula: $\Delta H<em>{reaction}^° = \sum n\Delta H</em>f^°(products) - \sum m\Delta H_f^°(reactants)$

  • Where $n$ and $m$ are the stoichiometric coefficients from the balanced chemical equation.

7. Bond Enthalpies

• Bond Enthalpy (Bond Energy): The energy required to break a specific covalent bond in one mole of gaseous molecules.

  • Always positive (bond breaking is endothermic).

  • Average bond enthalpies are used for estimations.

• Estimating $\Delta H_{reaction}$ using bond enthalpies:

  • Formula: $\Delta H_{reaction} \approx \sum (bond\ enthalpies\ of\ bonds\ broken) - \sum (bond\ enthalpies\ of\ bonds\ formed)$

  • Bonds broken are on the reactant side, bonds formed are on the product side.

  • This method is an approximation because average bond enthalpies are used, and it's typically for gas-phase reactions.