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Chemistry Review

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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

Quantity Positive Negative
\[q\] system gains heat system loses heat
\[w\] work done on system work done by system
\[\Delta E\] net gain of energy by system net loss of energy by system

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

Quantity Positive Negative
\[q\] Endothermic Exothermic
\[\Delta H\] Endothermic Exothermic

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.

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

Equations

Equation Definition
\( w = F \times D \) Work related to force and distance
\( E_{el} = {\kappa Q_1Q_2 \over d} \) Electrostatic potential energy
\(\Delta E = E_\text{final} - E_\text{initial} \) Change in internal energy
\(\Delta E = q + w\) Change in internal energy related to heat and work
\(H = E + PV\) Enthalpy
\(w = -P\Delta V\) Work done by an expanding gas at constant pressure
\(\Delta H = \Delta E + P\Delta V = q_p\) Enthalpy change at constant pressure
\(q = C_s \times m \times \Delta T\) Change in heat based on specific heat, mass, and temperature change
\(q_{rxn} = -C_{cal} \times \Delta T\) Heat exchanged between reaction and calorimeter
\(\Delta H^\circ_{rxn} = \sum n\Delta H^\circ_{f\text{(products)}} - \sum m\Delta H^\circ_{f\text{(reactants)}}\) Standard enthalpy change of a reaction
\(\Delta H_{rxn} = \sum H_\text{bonds broken} - \sum H_\text{bonds formed}\) Reaction enthalpy using bond enthalpies in the gas phase

Chemical Thermodynamics

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

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

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

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.

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.

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

\(\Delta H\) \(\Delta S\) \(-T\Delta S\) \(\Delta G\) Reaction Characteristics
- + - - Spontaneous at all temperatures
+ - + + Nonspontaneous at all temperatures
- - + + or - Spontaneous at low \(T\), nonspontaneous at high \(T\)
+ + - + or - Spontaneous at high \(T\), nonspontaneous at low \(T\)

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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Equations

Equation Definition
\(\Delta S = {q_{rev}\over T}\quad\text{(constant T)}\) Relating change in entropy to heat absorbed or released in a reversible process
\(\begin{rcases}\text{Reversible:} &\Delta S_{univ} = \Delta S_{sys} + S_{surr} = 0 \\ \text{Irreversible:} &\Delta S_{univ} = \Delta S_{sys} + S_{surr} > 0 \end{rcases}\) The second law of thermodynamics
\(S = k \ln W\) Relating entropy to the number of microstates
\(\Delta S^\circ = \sum nS^\circ_\text{products} - \sum mS^\circ_\text{reactants}\) Calculating standard entropy from standard molar entropies
\(\Delta S_{surr} = {-\Delta H_{sys}\over T}\) The entropy change of the surroundings for a process
\(\Delta G = \Delta H - T \Delta S\) Calculating Gibbs free-energy change from entropy and enthalpy changes at constant temperature
\(\Delta G^\circ = \sum nG^\circ_{f (\text{products})} - \sum mG^\circ_{f (\text{reactants})}\) Calculating standard free energy change from standard free energies of formation
\(\begin{rcases} \text{Reversible:} &\Delta G = \Delta H_{sys} - T \Delta S_{sys} = 0 \\ \text{Irreversible:} &\Delta G = \Delta H_{sys} - T \Delta S_{sys} < 0\end{rcases}\) Relating the free eergy change to reversibility of a process at constant temperature and pressure
\(\Delta G = -w_{max}\) Relating the free-energy change to the maximum work a system can perform
\(\Delta G = \Delta G^\circ + RT \ln Q\) Calculating free-energy change under nonstandard conditions
\(\Delta G^\circ = -RT ln K\) Relating standard free-energy change and the equilibrium constant

Chemical Kinetics

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Equations

Equation Definition
\(\text{Rate} = -{1\over a} {\Delta \text{[A]} \over \Delta t} = -{1\over b} {\Delta \text{[B]} \over \Delta t} \) Definition of reaction rate for the chemical equation \(\ce{a A -> b B}\)
\(\text{Rate} = k\text{[A]}^m\text{[B]}^n\) General form of a rate law for the reaction \(\ce{A + B -> products}\)
\(\begin{aligned}\ln \text{[A]}_t - \ln\text{[A]}_0 &= -kt \\\text{or}\; \ln {\text{[A]}_t\over\text{[A]}_0} &= -kt\end{aligned}\) Integrated form of a first-order rate law for \(\ce{A -> products}\)
\({1\over\text{[A]}_t} = kt + {1\over\text{[A]}_0}\) Integrated form of a second-order rate law for \(\ce{A->products}\)
\(\text{[A]}_t = -kt + \text{[A]}_0\) Integrated form of a zero-order rate law for \(\ce{A -> products}\)
\(t_{1/2} = {0.693\over k}\) The half life and rate constnant for a first order reaction
\(k = Ae^{-E_a\over RT}\) The Arrhenius equation, which expresses how rate constant depends on temperature
\(\ln k = -{E_a\over RT} + \ln A\) Logarithmic form of the Arrhenius equation

Chemical Equilibrium

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Equations

Equation Definition
\(K_c = {[\text{D}]^d[\text{E}]^e\over[\text{A}]^a[\text{B}]^b}\) The equilibrium constant expression for a general reaction of type \(\ce{a A + b B <=> d D + e E}\) where concentrations are equilibrium concentrations
\(K_p = {P_\text{D}^dP_\text{E}^e \over P_\text{A}^aP_\text{B}^b}\) The equilibrium constant expression in terms of equilibrium partial pressures
\(K_p = K_c(RT)^{\Delta n}\) Relating the equilibrium constant based on partial pressures to the equilibrium constant based on concentrations
\(Q_c = {[\text{D}]^d[\text{E}]^e\over[\text{A}]^a[\text{B}]^b}\) The reaction quotient; concentrations are for any time during a reaction. At equilibrium, \(Q_c = K_c\)

Acid-Base Equilibria

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Equations

Equation Definition
\(K_w = \ce{[H3O+][OH-]} = \ce{[H+][OH-]} = \pu{1.0 x 10^-14}\) Ion-product constant of water at \(\pu{25 \degree C}\)
\(\ce{pH} = -\log \ce{[H+]}\) Definition of pH
\(\ce{pOH} = -\log \ce{[OH-]}\) Definition of pOH
\(\text{pH} + \text{pOH} = 14.00\) Relationship between pH and pOH
\(K_a = {\ce{[H3O+][A-]}\over\ce{[HA]}}\) Acid-dissociation constant for a weak acid, HA
\(\text{Percent ionization} = {\text{[H}^+]_\text{equilibrium}\over [\text{HA}]_\text{initial} } \times 100 \%\) Percent ionization of a weak acid
\(K_b = {\ce{[BH+][OH-]}\over\ce{[B]}}\) Base-dissociation constant for a weak base, B
\(K_a \times K_b = K_w\) Relationship between acid- and base-dissociation constants for a conjugate acid-base pair
\(\text{p}K_a = -\log K_a \;\text{and}\; \text{p}K_b = -\log K_b\) Definitions of pKa and pKb

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