chm 12901 general chemistry with a biological focus unit 5 study guides

Key Concepts and Definitions

• Chemical kinetics studies the rates of chemical reactions and the factors that influence them
• Reaction rate measures the speed at which reactants are consumed or products are formed per unit time
• Rate law expresses the relationship between the reaction rate and the concentrations of reactants
• Reaction order indicates how the reaction rate depends on the concentration of each reactant
• Rate constant ($k$) is a proportionality constant that relates the reaction rate to the concentrations of reactants
• Activation energy ($E_a$) represents the minimum energy required for reactants to overcome and initiate a chemical reaction
• Catalyst lowers the activation energy of a reaction without being consumed in the process
• Chemical equilibrium occurs when the rates of forward and reverse reactions are equal, resulting in no net change in concentrations

Reaction Rates and Rate Laws

• Reaction rates can be determined by measuring the change in concentration of reactants or products over time
• Rate laws are typically expressed as $\text{Rate} = k[\text{A}]^m[\text{B}]^n$, where $k$ is the rate constant, $[\text{A}]$ and $[\text{B}]$ are the concentrations of reactants, and $m$ and $n$ are the reaction orders
• The overall reaction order is the sum of the individual reaction orders for each reactant
• Zero-order reactions have rates independent of reactant concentrations ($\text{Rate} = k$)
• First-order reactions have rates directly proportional to the concentration of one reactant ($\text{Rate} = k[\text{A}]$)
• Second-order reactions have rates proportional to the square of the concentration of one reactant ($\text{Rate} = k[\text{A}]^2$) or the product of the concentrations of two reactants ($\text{Rate} = k[\text{A}][\text{B}]$)
• Integrated rate laws describe the concentration of reactants or products as a function of time for different reaction orders
  • For a first-order reaction: $\ln[\text{A}]_t = -kt + \ln[\text{A}]_0$
  • For a second-order reaction: $\frac{1}{[\text{A}]_t} = kt + \frac{1}{[\text{A}]_0}$

Factors Affecting Reaction Rates

• Temperature increases reaction rates by providing more energy for reactants to overcome the activation energy barrier
  • A general rule is that reaction rates double for every 10°C increase in temperature
• Concentration of reactants affects reaction rates according to the rate law
  • Higher concentrations lead to more frequent collisions between reactants, increasing the reaction rate
• Surface area of solid reactants influences reaction rates by determining the number of available reaction sites
  • Smaller particle sizes or more finely divided solids have higher surface areas and faster reaction rates
• Catalysts accelerate reaction rates by providing an alternative reaction pathway with a lower activation energy
  • Enzymes are biological catalysts that facilitate chemical reactions in living organisms
• Pressure affects the reaction rates of gaseous reactants by altering their concentrations
  • Higher pressures compress gases, increasing their concentrations and reaction rates

Reaction Mechanisms

• Reaction mechanisms describe the step-by-step sequence of elementary reactions that lead to the overall chemical reaction
• Elementary reactions are the simplest chemical reactions that occur in a single step and cannot be broken down further
• The slowest step in a reaction mechanism is called the rate-determining step, as it controls the overall reaction rate
• Reaction intermediates are species formed during the reaction mechanism but not present in the overall balanced equation
• The molecularity of an elementary reaction refers to the number of reactant molecules involved in the reaction step
  • Unimolecular reactions involve a single reactant molecule (e.g., decomposition reactions)
  • Bimolecular reactions involve the collision of two reactant molecules (e.g., many gas-phase reactions)
• The rate law for an elementary reaction can be determined directly from the molecularity of the reaction step

Chemical Equilibrium

• Chemical equilibrium is a dynamic state in which the rates of forward and reverse reactions are equal
• At equilibrium, the concentrations of reactants and products remain constant, but the reactions continue to occur in both directions
• The equilibrium constant ($K$) is a quantitative measure of the extent of a reaction at equilibrium
  • For the general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant is expressed as $K = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$
• The magnitude of the equilibrium constant indicates the relative amounts of reactants and products at equilibrium
  • $K > 1$ means the equilibrium favors the products
  • $K < 1$ means the equilibrium favors the reactants
• The reaction quotient ($Q$) has the same mathematical expression as the equilibrium constant but uses instantaneous concentrations instead of equilibrium concentrations
  • Comparing $Q$ to $K$ predicts the direction of a reaction to reach equilibrium

Le Chatelier's Principle

• Le Chatelier's principle states that when a system at equilibrium is subjected to a disturbance, the system will shift its equilibrium position to counteract the disturbance
• Changes in concentration, pressure, volume, or temperature can disturb a system at equilibrium
• Adding reactants or removing products will shift the equilibrium towards the products to consume the added reactants or replace the removed products
• Removing reactants or adding products will shift the equilibrium towards the reactants to replace the removed reactants or consume the added products
• Increasing the pressure or decreasing the volume of a gaseous equilibrium will shift the equilibrium towards the side with fewer moles of gas to reduce the pressure
• Decreasing the pressure or increasing the volume will shift the equilibrium towards the side with more moles of gas
• Increasing the temperature will shift the equilibrium in the endothermic direction to absorb the added heat
• Decreasing the temperature will shift the equilibrium in the exothermic direction to release heat

Equilibrium Constants

• The equilibrium constant ($K$) is a quantitative measure of the position of equilibrium for a specific reaction at a given temperature
• The value of $K$ is independent of the initial concentrations of reactants and products
• For a general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant expression is $K = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$
• The equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant for the forward reaction
• The equilibrium constant for a reaction that is the sum of two or more reactions is the product of the equilibrium constants for the individual reactions
• The solubility product constant ($K_{sp}$) is a special case of the equilibrium constant that applies to the dissolution of slightly soluble ionic compounds
  • For a general dissolution reaction $\text{A}_a\text{B}b(s) \rightleftharpoons a\text{A}^{b+}(aq) + b\text{B}^{a-}(aq)$, the solubility product constant is $K{sp} = [\text{A}^{b+}]^a[\text{B}^{a-}]^b$

Biological Applications and Examples

• Enzyme kinetics studies the rates of enzyme-catalyzed reactions and the factors that influence them
  • The Michaelis-Menten equation describes the relationship between the reaction rate and substrate concentration for enzyme-catalyzed reactions
• Hemoglobin-oxygen binding is an example of a biological equilibrium
  • Hemoglobin (Hb) binds reversibly with oxygen (O2) to form oxyhemoglobin (HbO2): $\text{Hb}(aq) + \text{O}_2(aq) \rightleftharpoons \text{HbO}_2(aq)$
  • The oxygen dissociation curve shows the relationship between the partial pressure of oxygen and the fraction of hemoglobin saturated with oxygen
• pH homeostasis in the human body relies on chemical equilibria involving buffer systems
  • The bicarbonate buffer system helps maintain the blood pH around 7.4: $\text{H}_2\text{CO}_3(aq) \rightleftharpoons \text{H}^+(aq) + \text{HCO}_3^-(aq)$
• Calcium phosphate equilibrium is crucial for bone formation and remodeling
  • Hydroxyapatite, a calcium phosphate mineral, is the main component of bone: $\text{Ca}_5(\text{PO}_4)_3\text{OH}(s) \rightleftharpoons 5\text{Ca}^{2+}(aq) + 3\text{PO}_4^{3-}(aq) + \text{OH}^-(aq)$
• Nitrogen fixation is a process by which atmospheric nitrogen is converted into biologically usable forms, such as ammonia
  • The Haber-Bosch process is an industrial method for ammonia synthesis: $\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$
  • Biological nitrogen fixation is carried out by certain bacteria and archaea using the enzyme nitrogenase