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Thermochemistry

Describe the changes in potential energy that accompany the formation and breaking of chemical bonds.

Energy can be stored and released in the breaking and formation of chemical bonds, affecting the potential energy. Forming chemical bonds releases energy while breaking chemical bonds consumes energy.

Distinguish between the system and the surroundings in thermodynamics.

The portion of the universe that we are studying at the moment is the system, everything else is the surroundings.

Calculate internal energy from heat and work and state the sign conventions of these quantities.

Internal energy, \(E\), of a system is the sum of all kinetic and potential energy of the system.

\[\Delta E = q + w\]

Sign conventions

Explain the concept of a state function and give examples.

The value of a state function is a property of a system that depends only on the present state of the system, not the path the system took to reach that state. For example, internal energy is a state function.

Calculate \(\Delta H\) from \(\Delta E\) and \(P \Delta V\).

Enthalpy, \(H\), is the internal energy plus the product of the pressure, \(P\), and volume, \(V\), of a system.

\[\Delta H = \Delta E + P\Delta V\quad\text{(constant pressure)}\]

Relate \(q_p\) to \(\Delta H\) and indicate how the signs of \(q\) and \(\Delta H\) relate to whether a process is exothermic or endothermic.

At constant pressure, the change in enthalpy equals the heat \(q_p\) gained or lost.

\[\Delta H = q_p\]

Sign conventions

Use thermochemical equations to relate the amount of heat energy transferred in reactions at constant pressure (\(\Delta H\)) to the amount of substance involved in the reaction.

\(\Delta H\) is measured in \(\pu{kJ/mol}\) so the conversion sequence is simple:

\[(\text{mass of substance}) \times (\text{molar mass}) \times \Delta H\]

Calculate the heat transferred in a process from temperature measurements together with heat capacities or specific heats (calorimetry).

Specific heat:

\[ \begin{aligned} \text{Specific heat} &= {\text{(quantity of heat transferred)}\over \text{(grams of substance)}\times \text{(temperature change)}} \\ C_s &= {q\over m \times \Delta T} \end{aligned} \]

Constant pressure calorimetry:

\[q_{soln} = \text{(specific heat of solution)}\times\text{(grams of solution)} \times \Delta T = -q_{rxn}\]

Bomb calorimetry (where \(C_{cal}\) is the total heat capacity of the calorimeter):

\[q_{rxn} = -C_{cal} \times \Delta T\]

Use Hess's law to determine enthalpy changes for reactions.

Hess's law states that if a reaction is carried out in a series of steps, \(\Delta H\) for the reaction equals the sum of \(\Delta H\) for the steps. Therefore:

\[\Delta H = \sum_{n=1}^k \Delta H_n = \Delta H_1 + \Delta H_2 \dotsm \Delta H_k\]

Use standard enthalpies of formation to calculate \(\Delta H^\circ\) for reactions.

The standard enthalpy of formation for a substance, \(\Delta H^\circ_f\), is the change in enthalpy for the reaction that forms one mole of the compound from its constituent elements, with all substances in their standard states. You can calculate enthalpies of reaction using these standard enthalpies of formation by using Hess's law (under standard conditions) and stoichiometry:

\[\Delta H^\circ_{rxn} = \sum n\Delta H_f^\circ\text{(products)} - \sum m\Delta H_f^\circ\text{(reactants)}\]

Use average bond enthalpies to estimate the reaction enthalpies of reactions where all reactants and products are in the gas phase.

\(\Delta H_{rxn} = \sum \text{(enthalpy of bonds broken)} - \sum \text{(enthalpy of bonds formed)}\) \(\;\)

Chemical Thermodynamics

Explain and apply the terms spontaneous process, reversible process, irreversible process, and isothermal process.

• A spontaneous process occurs on its own without outside assistance.
  • e.g. ice melting at room temperature
• A nonspontaneous process requires outside assistance to occur.
  • e.g. ice freezing at room temperature

Processes that are spontaneous in one direction are nonspontaneous in the opposite direction.

• A thermodynamically reversible process is one where you can restore the system to its original condition with no change to the surroundings.
• A thermodynamically irreversible process is one that changes the surroundings somehow when the system is restored to its original state.

There are pretty much no reversible processes, except for those which involve infinitesimally small changes in temperature.

• An isothermal process occurs at constant temperature.
  • e.g. a gas expanding at constant pressure

Define entropy and state the second law of thermodynamics.

Entropy is the tendency for energy to spread and disperse, reducing its ability to accomplish work, and reflects the degree of randomness or disorder in the particles that carry this energy.

The second law of thermodynamics is that the entropy of the universe increases for any spontaneous process.

Calculate \(\Delta S\) for a phase change.

For an isothermal process,

\[ \Delta S = {q_{rev}\over T}\]

Melting at the melting point and vaporization at the boiling point (and vice versa) are isothermal processes where \(q_{rev} = \Delta H\).

\[\Delta S_{fusion} = {q_{rev}\over T} = {\Delta H_{fusion}\over T}\]

Explain how the entropy of a system is related to the number of possible microstates.

The relationship between the number of microstates of a system, \(W\), and the entropy of the system, \(S\), where \(k = \pu{1.38 x 10^-23 J/K}\) is:

\[S = k \ln W\]

So as the number of microstates increases, entropy of the system increases as well.

Describe the kinds of molecular motion a molecule can possess.

• Translational motion is simple motion in at least one of the three dimensions.
• Rotational motion is motion in which the molecule spins about an axis.
• Vibrational motion is motion in which the atoms in the molecule move towards and away from one another periodically.

Predict the sign of \(\Delta S\) for physical and chemical processes.

Entropy will increase with the more kinds of motion, and therefore microstates, allowed. So a gas has more entropy than a liquid, which has more entropy than a solid. Entropy also increases when a solid dissolves in a liquid. And finally, entropy will increase when the number of gas molecules increases during a chemical reaction.

State the third law of thermodynamics.

The entropy of a pure, perfect crystalline substance at absolute zero is zero.

Compare the values of standard molar entropies.

• Unlike enthalpies of formation, standard molar enthalpies of elements at the reference temperature of 298 K are not zero.
• The standard molar entropies of gases are higher than liquids and solids.
• Standard molar entropies increase with increasing molar mass.
• Standard molar entropies increase with increasing molecular complexity.

Calculate standard entropy changes for a system from standard molar entropes.

Like with standard enthalpy,

\[\Delta S^\circ = \sum nS^\circ_\text{products} - \sum mS^\circ_\text{reactants}\]

Calculate the Gibbs free energy from the enthalpy change and entropy change at a given temperature.

\[\Delta G = \Delta H - T\Delta S\]

Use free-energy changes to predict whether reactions are spontaneous.

If \(\Delta G\) is negative, the reaction will be spontaneous.

Calculate standard free-energy changes using standard free energies of formation.

Like with standard entropy and standard enthalpy, \(\Delta G^\circ = \sum nG^\circ_{f \text{(products)}} - \sum mG^\circ_{f \text{(reactants)}}\)

Predict the effect of temperature on spontaneity given \(\Delta H\) and \(\Delta S\).

Sign conventions

Calculate \(\Delta G\) under nonstandard conditions.

Under any other condition (not pure solid/liquid, not gas under 101.3 kPa/1 atm pressure, not 1M concentration solution, not an element in standard state):

\[\Delta G = \Delta G^\circ + RT \ln Q\]

where \(R\) is the ideal gas constant, \(\pu{8.314 J/mol * K}\), \(T\) is the absolute temperature, and \(Q\) is the reaction quotiend for the reaction mixture of interest. If \(Q = K\), the reaction is at equilibrium.

Relate \(\Delta G^\circ\) and the equilibrium constant.

Since at equilibrium, \(Q = K\) and \(\Delta G = 0\), you can rearrange the equation to be:

\[\Delta G^\circ = -RT \ln K \\ K = e^{-\Delta G^\circ \over RT}\]

Laws of thermodynamics

1. Energy can be converted from one form to another, but it is neither created nor destroyed.
2. The entropy of the universe increases for any spontaneous process.
3. The entropy of a pure, perfect crystalline substance at absolute zero is zero.

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Chemical Kinetics

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Chemical Equilibrium

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Acid-Base Equilibria

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