Energy

Thermochemistry

Thermochemistry: Quantification of the energy of chemical rxns and changes. It is a subset of thermodynamics.

Internal energy (U): energy contained in a system.

\(\Delta U\) represents the change in energy, in other terms: \(U_{f} - U_{i}\)

Terminology:

• Universe – Everything

• System – The part of the universe that we are studying (we need to define it)

• Endothermic – When heat enters the system. That is to say, the change in energy is positive, as the system gains energy.

• Exothermic – When heat exits the system, into the surroundings. That is to say, the change in energy is negative, as the system loses energy.

Types of Systems

• Open: Matter and energy are exchanged w/ surroundings
• Closed: Only energy is exchanged w/ surroundings
• Isolated: Nothing exchanged

First Law of Thermo

\[ \Delta U = Q + W = Q - P \Delta V \]

Enthalpy:

\[ \Delta H = q \]

\(q\) is a path function, \(\Delta H\) is a state function

• Path functions depend on the path taken
• State functions don’t depend on path (only depend on the initial and final states regardless of the pathway that took place)

Changes in Enthalpy

• Due to temperature change
• Due to chemical rxn
• Due to phase changes
  • evaporation/boiling (system needs to absorb heat for phase change) or condensation (system needs to release heat for phase change)

\(\Delta H_{VAP}\): Enthalpy of vaporization:

Due to change between liquid and vapor, always reported as positive value.

• evaporation/boiling: liquid to gas is endothermic (system takes in heat)
• condensation: gas to liquid is exothermic (system loses heat). \(\Delta H = - \Delta H_{VAP}\)

\(\Delta H_{FUS}\): Enthalpy of fusion:

Due to change between solid and liquid

• melting: solid to liquid is endothermic (system takes in heat)
• freezing: liquid to solid is exothermic (system loses heat). \(\Delta H = - \Delta H_{FUS}\)

\(\Delta H_{SUB}\): Enthalpy of sublimation:

Change between solid and gas

• sublimation: solid to gas is endothermic (system takes in heat)
• deposition: gas to solid is exothermic (system loses heat). \(\Delta H = - \Delta H_{SUB}\)

\(\Delta H_{f}\): Enthalpy of formation:

Due to the chemical reaction in order to produce 1 mole of a substance from its elements in their reference (standard) states:

• 25 degrees Celsius
• 1 atm

Hess’s Law

Arrange formulas (reverse and apply coefficients, propagating changes to rxn enthalpy) to determine enthalpy of reaction (by summing the individual enthalpies) for specified formula.

If you have enthalpies of the individual compounds that also suffices, the enthalpy of a reaction is given by the enthalpy of the products (weighted by their coefficients) - enthalpy of the reactants (weighted by their coefficients).

Heat Capacity of a System

\[ q = C \Delta T = m c \Delta T \]

• \(C\) – Called the calorimeter constant. Units: J/Degree Celsius or J/Kelvin.

Heat Capacity: The amount of heat required to change to change the temperature of a system by 1 degree celsius (or K).

Specific Heat

\[ q = mc \Delta T \]

Amount of heat required to change the temperature of 1 gram of a substance by 1 degree celsius

Molar Heat Capacity

\[ q = Cn \Delta T \]

Where \(n\) is number of moles

Amount of heat required to change temperature of 1 mole of a substance by 1 degree celsius

\[ C = cm \]

Calorimetry Example

A coffee calorimeter (constant pressure) contains 100.0g of \(H_{2}O\)(l) initially at 25 degrees Celsius. A 72.00g piece of metal initially at 97.00 degrees Celsius is added t othe calorimeter. The final temperature of both the metal/water is 29.10 degrees Celsius.

\[ q_{system} = - q_{surroundings} \]

1. Find \(q_{surroundings}\) with \(q = mc \Delta T\)
2. Find \(q_{system}\)
3. Find \(c_{metal}\) from \(q_{system}\)

For a chemical reaction, the system could be the chemical reaction, and the surroundings could be the solution.