Chemistry Equilibrium and Reaction Kinetics

Activation Energy

• Activation energy is the barrier to entry for a chemical reaction.
• Concentration, pressure, and temperature affect the activation energy.
• Increasing energy increases the reaction rate; temperature is synonymous with energy.
• Electrical stimulus can increase reaction rate by, effectively, adding energy to the system.

Concentration and Collisions

• Increasing concentration increases the number of collisions per unit time, thus increasing the likelihood of statistically successful collisions.
• Lessening the amount of interacting substances reduces the likelihood of successful reactions due to fewer interactions.

Temperature and Collision Success

• Increasing temperature increases the energy of collisions, making more collisions successful and speeding up the reaction.

Pressure

• Increasing pressure has the same effect as increasing concentration, increasing the number of reactions per unit time and total successful outcomes.

Reversible Reactions and Equilibrium

• Almost all chemical processes are reversible, with very few exceptions with extremely high $K_{eq}$ values (e.g. $10^{1000}$) that are considered essentially irreversible.
• Even in highly efficient reactions, some starting material always remains.

Equilibrium Definition

• Equilibrium is reached when the forward reaction rate equals the reverse reaction rate.
• Initially, the forward reaction rate is very fast due to high initial concentrations.

Static Concentrations and Molecular Changes

• At equilibrium, apparent concentrations are static, but reactions continue at equal rates.
• Isotopic labeling experiments (using deuterium, hydrogen with one proton and one neutron, with an atomic mass of 2 instead of 1) can demonstrate constant reactions despite static concentrations.

Equilibrium Constant ($K_{eq}$)

• $K<em>{eq}$ is the equilibrium constant, with special cases like $K</em>w$ (auto-protolysis of water).
• At 25 degrees Celsius and atmospheric pressure, $K_w$ is always $10^{-14}$, representing two water molecules forming hydronium and hydroxide ions.

General Equilibrium Equation

• For a general equation, $K_{eq}$ equals the product of the concentrations of the products, each raised to the power of their stoichiometric coefficients, divided by the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients.
• $K_{eq} = [Products]^\text{stoichiometric coefficients} / [Reactants]^\text{stoichiometric coefficients}$
• Missing coefficients are implied to be one.

Interpreting $K_{eq}$ Values

• Larger $K_{eq}$ values indicate that products are favored.
• Smaller $K_{eq}$ values indicate that reactants are favored.

Mathematical Basis for $K_{eq}$ Interpretation

• Increasing product concentrations increases $K<em>{eq}$. Decreasing reactant concentrations also increases $K</em>{eq}$. Decreasing product concentrations and increasing reactant concentrations decrease $K_{eq}$.
• Small $K<em>{eq}$ equates to an unfavorable reaction; large $K</em>{eq}$ equates to a favorable reaction.

Examples of $K_{eq}$ Values

• HBr formation is a very favorable reaction.
• NO formation from $N<em>2$ and $O</em>2$ is not favorable; low atmospheric concentration is beneficial due to NO's toxicity as a free radical and potent greenhouse gas (thousands of times more potent than $CO_2$).

Qualitative Assessment of Equilibrium

• A $K_{eq}$ of one means the total amount of products equals the total amount of reactants, resulting in roughly a fifty-fifty mixture, accounting for stoichiometric coefficients.
• $K<em>{eq}$ > 1 favors products; $K</em>{eq}$ < 1 favors reactants.

Quantitative Benchmarks for Equilibrium

• (Approximation) $K_{eq}$ ≥ 1000 guarantees ≥ 99% products.
• (Approximation) $K_{eq}$ ≤ 0.001 guarantees ≥ 99% reactants.

Exclusion of Solids and Liquids from Equilibrium Calculations

• For example, $CaCO<em>3(s) \rightleftharpoons CaO(s) + CO</em>2(g)$. Solids, pure liquids, and gases are not considered in equilibrium calculations; only things in solution are.
• This is because solids and gases lack a concentration.

Equilibrium Calculations

• Equilibrium problems involve generating the equilibrium equation and plugging in given concentrations.

Example

• Given initial concentrations and temperature, plug into the $K_{eq}$ equation after raising the products to their stoichiometric coefficients.
• More challenging questions require figuring out all the concentrations.
• If given $K_{eq}$, rearrange the equilibrium equation to solve for the missing variable.

Le Chatelier's Principle

• Any stimulus applied to a chemical reaction will cause the reaction to adjust to alleviate the stress.
• Stimulus to reactants shifts equilibrium towards products; stimulus to products shifts equilibrium towards reactants.

Population Analogy

• Molecules tend to move from high to low concentrations to equilibrate.

Applying Stimuli

• Adding $NO_2$ shifts the reaction back to the starting materials.
• Adding more starting material shifts the reaction toward the product.
• Le Chatelier's principle only indicates what happens at equilibrium, not the kinetics or process.

Volume and Pressure Effects on Gases

• Volume is only important when dealing with gases.
• Increasing pressure increases force, favoring the side with the least moles of gas.
• Decreasing pressure favors the side with more moles of gas, as there is less force on the molecules, allowing them to take up more space.
• For solids and liquids, density must be considered.

Exothermic and Endothermic Reactions

• Heat can be treated as a reactant or product.
• Exothermic reaction: $A + B \rightleftharpoons C + \Delta$ (heat is released as a product).
• Endothermic reaction: $A + B + \Delta \rightleftharpoons C$ (heat is taken in as a reactant).

Temperature Effects on Equilibrium

• Increasing temperature disfavors products in exothermic reactions, favoring starting materials.
• Increasing temperature favors products in endothermic reactions, as energy is added to the starting materials.
• Removing heat has the opposite effects.

Haber-Bosch Process

• An exothermic reaction that occurs at 600 degrees Celsius.
• High temperature disfavors product formation.

Implications of Temperature Control

• Lowering the temperature could drive the reaction to a higher extent.
• Changing the temperature in a sealed container can change the relative composition of elements.
• Equilibrium constants are temperature-dependent and must be experimentally determined.

Summary of Le Chatelier's Principle

• Exothermic and endothermic reactions behave differently with temperature changes.
• The reaction equilibrates away from the applied stimulus.
• Consider PV=NRT effects for volume and pressure and equilibrium constant effects for temperature.

Solubility (KSP)

• A specialized equilibrium equation.
• Pure solids are not considered.
• Example: $CaF_2(s) \rightleftharpoons Ca^{2+}(aq) + 2F^-(aq)$

KSP Equation

• $Keq = \frac{[Ca^{2+}][F^-]^2}{[CaF_2]}$
• For solids and pure liquids, set their concentration equal to one, making the denominator equal to one.
• $Ksp = [Ca^{2+}][F^-]^2$

Reaction Rates and Activation Energy

• Activation energy is the energy required to cause a chemical reaction.
• Lower activation energy leads to a faster reaction rate, and vice versa.

Reaction Landscapes and Energy Diagrams

• Show the energy levels of reactants and products.
• If reactants start higher in energy than products, the reaction is exothermic.
• The energy of activation does not affect the energy given off by an exothermic reaction.

Catalysts

• Modulate activation energy.
• Good catalysts lower the energy of activation.
• Inhibitors raise the activation energy.
• Enzymes are the best catalysts because they are the most complicated catalysts that exist; alter the reaction pathway.

Complex Enzymes in Biology

• Evolved to have the most efficient chemistry.
• Can force molecules into places that aren't naturally possible with smaller molecules.
• Can be incredibly active and target one specific molecule out of hundreds of different atoms.
• For example, a specific ligase protein or enzyme can cleave sucrose at just the oxygen carbon linkage; chemists, like inorganic chemists, spend their lives just trying to figure out how they can mimic biology because everything biology does is better than what we do.
• The binding pocket of an enzyme pulls molecules together for specific excitation, which leads to the cleavage of one bond.

Review

• Concentrate primarily on equilibrium reactions and equations.
• There are certain specialized Keqs, such as Ksp and Kw; focus on general ones.
• Focus conceptually on understanding Le Chatelier's principle.
• Know the relationship between the molecules have to actually interact to cause a chemical reaction and that they have to hit with sufficient energy to have a reaction.

Le Chatelier's Principle Reaction Examples:

$N<em>2 + 3H</em>2 \rightleftharpoons 2NH_3$ (Exothermic Reaction)

• Pressure Increase: Shift to products (right).
• Pressure Decrease: Shift to reactants (left).
• Add $H<em>2$ or $N</em>2$: Shift to products (right).
• Add $NH_3$: Shift to reactants (left).
• Add Heat: Shift to reactants (left).
• Subtract Heat: Shift to products (right).

$CuSO<em>4 \cdot 5H</em>2O \rightleftharpoons CuSO<em>4 + 5H</em>2O$ (Endothermic Reaction)

• Add $CuSO_4$ (anhydrous): Shift to reactants (left).
• Add $CuSO<em>4 \cdot 5H</em>2O$: Shift to products (right).
• Pressure Increase: Shift to reactants (left) (favors liquid).

Reaction: $NH<em>4OH \rightleftharpoons NH</em>3 + HNO<em>3$, where $NH</em>3$ is a Gas

• Heat Added: Favors Products.
• Pressure Increased: Favors Products.
• Add Reactant: Favors Products.
• Add Product: Favors Reactants.

KSP problem Example: AB

• $Ksp = [A] * [B]$
• Example problem: $H<em>2SO</em>4 \rightleftharpoons 2H^+ + SO_4^{2-}$
• $Ksp = [H^+]^2 *[SO_4^{2-}]$
• If Ksp is $10^5 = (2X)^2 * X$
• Then X squared becomes 4x cubed. Taking the cube root gives the concentrations.