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5.1 Rates, Equilibrium and pH - Coggle Diagram

- - - - A rate equation is a mathematical expression that shows how the rate of a chemical reaction depends on the concentrations of the reactants. For a general reaction: A + B ➔ C + D
      - The rate equation takes the form:
        Rate = k[A]m[B]n
        
        Where:
        
        Rate is the reaction rate (mol dm-3 s-1).
        
        k is the rate constant.
        
        [A] and [B] are the concentrations of reactants A and B (mol dm-3).
        
        m and n are the orders of reaction with respect to A and B.
    - - Zero order - The rate is independent of the reactant concentration. Doubling or tripling the concentration has no effect on the rate. [A]0 = 1, so zero order terms are often written without the concentration term.
      - First order - The rate is directly proportional to the reactant concentration. Doubling the concentration doubles the rate, tripling the concentration triples the rate.
      - Second order - The rate is proportional to the square of the reactant concentration. Doubling the concentration quadruples the rate (22 = 4), tripling the concentration increases the rate ninefold (32 = 9).
    - - The rate constant, k, is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants at a specific temperature.
      - A larger k value indicates a faster rate of reaction.
      - k remains constant for a given reaction at a fixed temperature.
      - Increasing the temperature exponentially increases the value of k, as collisions between reactant molecules are more frequent and more energetic.
  - - - To determine the reaction order with respect to the concentration of a specific reactant, you can use two main methods:
        
        Initial rates method - This involves measuring how the initial rate changes when you alter the initial concentration of the reactant in question.
        
        Continuous monitoring - This involves tracking the change in concentration of the reactant over time and plotting a rate-concentration graph.
      - In both strategies, ensure that the concentrations of any other reactants remain substantially constant (in large excess) throughout the experiment. This approach helps ensure that any observed changes in rate are solely due to the reactant being studied.
    - - The initial rate of a reaction refers to the rate at the very beginning of the reaction (time = 0) and is found by calculating the gradient of the tangent to the concentration-time graph at t = 0.
      - The steps involved in the initial rates method are:
        
        Perform the reaction several times, each time changing the initial concentration of one reactant while keeping the others constant.
        
        Calculate the initial rate from the concentration-time data for each experiment.
        
        Analyse how the initial rates change with varying initial concentrations to deduce the order of the reaction with respect to each reactant.
        
        Use these findings to assemble the overall rate equation.
    - - Rather than finding initial rates, some reactions can be continuously monitored as they proceed to completion. The amounts of reactant or product are determined at regular intervals to see how the rate varies over the course of the reaction.
      - Numerous methods can be used depending on what property changes during the reaction:
        
        Measuring the volume of gas evolved.
        
        Measuring the mass loss as a gas escapes.
        
        Measuring pH changes.
        
        Using colorimetry to quantify colour changes
    - - Colorimeters measure the absorbance of a specific wavelength of light by a solution. If the reactant and product have different absorbances at a chosen wavelength, the change in absorbance can be used to monitor the reaction.
      - Colorimetry involves the following steps:
        
        Select the appropriate wavelength for monitoring the target species.
        
        Calibrate the colorimeter using a blank sample (e.g., distilled water) to set the absorbance to zero.
        
        Withdraw samples from the reaction mixture at fixed time points and measure their absorbance.
      - To convert absorbance readings into concentrations, a calibration curve must be prepared. This involves the following steps:
        
        Prepare a series of standard solutions with known concentrations of the analyte (reactant or product).
        
        Measure the absorbance of each standard solution using the colorimeter.
        
        Plot the absorbance values against the corresponding concentrations.
        
        Fit a trendline to the data points to obtain the calibration curve.
    - - The shape of a rate-concentration graph can reveal the reaction order with respect to a particular reactant.
      - Zero order - A horizontal line indicates that the reaction rate is independent of the reactant concentration.
        The rate equation is: rate = k.
      - First order - A straight line passing through the origin signifies that the reaction rate is directly proportional to the reactant concentration.
        The rate equation is: rate = k[X].
      - Second order - A curved plot indicates that the reaction rate is proportional to the square of the reactant concentration.
        The rate equation is: rate = k[X]2.
    - - The half-life ( t 1/2) of a reaction is the time taken for the concentration of a reactant to decrease to half of its initial value.
      - For first-order reactions:
        
        The half-life is independent of the initial concentration.
        
        Each successive half-life is the same duration.
        
        The half-life can be read directly from the concentration-time graph.
  - - - The rate-determining step (also known as the rate-limiting step) is the slowest step in a multi-step reaction mechanism. It dictates the overall rate of the reaction.
      - Each step in a reaction mechanism can have a different rate, but the step with the slowest rate controls how fast the reaction proceeds overall.
    - - The rate equation provides valuable insights into the mechanism of a chemical reaction, particularly in identifying which reactants are involved in the rate-determining step.
      - key points:
        
        If a reactant appears in the rate equation, it must be involved in the rate-determining step, either directly or via a substance derived from it.
        
        Conversely, if a reactant is absent from the rate equation, neither it nor any substance derived from it participates in the rate-determining step.
        
        The rate-determining step is not always the first step in the mechanism.
        
        The reaction mechanism usually cannot be deduced solely from the balanced equation.
    - - The order of reaction with respect to a particular reactant indicates how many molecules of that reactant are involved in the rate-determining step.
      - For instance, if a reaction is second-order with respect to reactant X, then two molecules of X must be present in the rate-determining step.
      - Example:
        
        The mechanism for the reaction between chlorine radicals and ozone (O3) consists of two steps:
        
        Step 1 (slow): Cl• + O3 ➔ ClO• + O2
        
        Step 2 (fast): ClO• + O3 ➔ Cl• + 2O2
        
        To predict the rate equation:
        
        Both Cl• and O3 appear in the slow, rate-determining step, so both must be in the rate equation.
        
        There is one Cl• radical and one O3 molecule in this step, so the reaction is first-order with respect to each.
        
        Therefore, the rate equation takes the form: rate = k[Cl•][O3]
    - - Mechanism 1 (single-step)
        
        A one-step process where the OH- nucleophile directly substitutes the Cl atom in a single transition state.
      - Mechanism 2 (two-step)
        
        Step 1 (slow) - The C-Cl bond breaks, forming a carbocation intermediate and Cl-. This is likely the rate-determining step as breaking a strong C-Cl bond requires significant energy.
        
        Step 2 (fast) - The positively charged carbocation rapidly reacts with the negatively charged OH- nucleophile to form the final product. If the OH- concentration is high, this step should occur quickly once the carbocation forms.
      - The experimentally determined rate equation is:
        rate = k[CH3Cl]
        The absence of [OH-] in this equation indicates that OH- is not involved in the rate-determining step. This supports mechanism 2 being correct, where OH- only appears in the fast second step.
    - - In some cases, the rate-determining step may involve an intermediate species that is formed and consumed during a reaction, but does not appear in the overall balanced equation.
      - Consider this example:
        
        The reaction 2NO(g) + O2(g) ➔ 2NO2(g) proceeds via a two-step mechanism:
        
        Step 1: 2NO ➔ N2O2
        
        Step 1 cannot be the rate-determining step as it does not involve O2. Although step 2 doesn't contain the reactants in the stoichiometry expected from the rate equation, it does involve the intermediate N2O2. This intermediate is derived from 2NO molecules, matching the rate equation.
        
        Step 2: N2O2 + O2 ➔ 2NO2
        
        Therefore, step 2 is the rate-determining step, even though it involves the intermediate N2O2 rather than the reactants shown in the overall equation.
        
        The rate equation tells us that the rate-determining step must involve:
        
        2 molecules of NO
        
        1 molecule of O2
  - - - The Arrhenius equation is a mathematical formula that connects the rate constant (k) of a chemical reaction with the temperature (T) and the activation energy (Ea). This equation helps us understand how these factors affect the rate of a chemical reaction.
      - Arrhenius Equation: K= Ae^ (-Ea/RT)
        
        Where:
        
        k = rate constant.
        
        A = pre-exponential factor (also known as the Arrhenius constant).
        
        e = mathematical constant (the base of natural logarithms).
        
        Ea = activation energy (J mol-1).
        
        R = gas constant (8.31 J K-1 mol-1).
        
        T = temperature (K).
    - - The Arrhenius equation reveals important relationships between the rate constant, activation energy, and temperature:
        
        Activation energy (Ea):
        
        The higher the Ea, the lower the rate constant (k) becomes.
        
        A high activation energy means that fewer reactant molecules have sufficient kinetic energy to overcome the energy barrier and react successfully.
        
        Consequently, a reaction with a high Ea will have a slower rate.
        
        Temperature (T):
        
        An increase in temperature leads to an exponential increase in the rate constant (k).
        
        At higher temperatures, reactant molecules move faster, resulting in more frequent collisions.
        
        Additionally, higher temperatures provide greater kinetic energy to reactant molecules, allowing a higher proportion to exceed the activation energy barrier.
        
        Both of these factors contribute to the increased reaction rate when temperature increases.
    - - To calculate either the rate constant (k) or activation energy (Ea) when other variables are known, we often use the logarithmic form of the Arrhenius equation:
        
        lnK = -Ea/RT + ln(A)
        
        Where:
        
        y= ln(k)
        
        x = 1/T
        
        Gradient = - Ea/ RT
        
        y-interpect = ln(A)
- - - - Homogeneous - All reactants and products are in the same physical state.
        
        For homogeneous systems, all reactants and products are included in the Kc expression.
      - Heterogeneous - Reactants and products are in different physical states.
        
        For heterogeneous systems, only gases and aqueous substances are included in the Kc expression. Solids and pure liquids are omitted because their concentrations stay relatively constant and do not affect the position of equilibrium.
  - - - The mole fraction (χ) of a gas is the proportion of the total gas mixture that is made up of that particular gas.
      - This can be represented by the equation:
        mole fraction of gas = number of gas/ total number of moles in the mixture
    - - Partial pressure (p) is the pressure exerted by each individual gas component in a gaseous mixture. The total pressure exerted by the gas mixture equals the sum of the partial pressures.
      - This can be represented by:
        
        p(total) = ∑p(components)
        
        where ∑ = sum of
    - - We can use mole fractions to determine the partial pressures of gases in a mixture if the total pressure is known.
      - The equation for the partial pressure of a gas is:
        Partial pressure of a gas = mole fraction of that gas x total pressure
    - - Unlike liquids, it's easier to measure gas amounts using pressure rather than concentration.
      - Kp is calculated in the same way as Kc, but using partial pressures instead of concentrations.
      - Units for Kp are pressure units e.g. kPa or atm.
      - Solids and liquids do NOT get included in Kp expressions.
    - - For the general equilibrium reaction:
      - aA(g) + bB(g) ⇌ dD(g) + eE(g)
      - The Kp expression for this equilibrium is:
      - Kp+ (pD)^d pC)^c/ pA)^a pB)^b
  - - - The position of equilibrium depends on temperature according to Le Chatelier's principle:
        
        For an exothermic reaction, increasing temperature shifts the equilibrium towards the reactants (left).
        
        For an endothermic reaction, increasing temperature shifts the equilibrium towards the products (right).
    - - The equilibrium constant (Kc) is influenced solely by temperature. Changes in concentration or pressure have no impact on Kc.
        
        When the position of equilibrium is altered due to a temperature shift:
        
        A decrease in the amount of product at equilibrium causes Kc to decrease.
        
        An increase in the amount of product at equilibrium causes Kc to increase.
        
        This ensures that the value of Kc aligns with the new position of equilibrium.
      - Exothermic Reactions
        
        Temperature Increase
        
        Equilibrium Position shift to left
        
        Decrease Kp
        
        Temperature Decrease
        
        Equilibrium position shifts to right
        
        Increases Kp
      - Endothermic Reactions
        
        Temperature Increase
        
        Equilibrium Position shift to right
        
        Increase Kp
        
        Temperature Decrease
        
        Equilibrium Position shift to left
        
        Decrease Kp
    - - While shifts in concentration or pressure can move the equilibrium position, altering the quantities present to counteract the change, Kc remains unchanged at a specific temperature.
      - For Example:
        
        N2(g) + 3H2(g) ⇌ 2NH3(g)
        
        Adding more N2 leads to an increased formation of NH3 at the new equilibrium. However, the equilibrium ratio of [NH3]2 to [N2][H2]3 still remains equal to keep value of Kc constant.
        
        Thus, changes in concentration and pressure do not directly influence Kc - its value is only determined by temperature.
    - - Catalysts increase the rate of both the forward and reverse reactions, reducing the time needed to reach equilibrium following a change.
      - However, catalysts neither alter the equilibrium position nor the value of Kc.
      - The effects of changing reaction conditions on the position of equilibrium and the value of Kc:
        
        Concentration
        
        Changes Equilibrium Position
        
        Kc remains the same
        
        Pressure
        
        Changes Equilibrium Position
        
        Kc remains the same
        
        Temperature
        
        Changes Equilibrium Position
        
        Kc chamges
        
        Concentration
        
        Equilibrium Position remains the same
        
        Kc remains the same
    - - The equilibrium constant Kp changes with temperature in the same way as the equilibrium constant Kc.
      - Increasing temperature causes Kp to increase for endothermic reactions and decrease for exothermic reactions.
      - Decreasing temperature has the opposite effects on Kp.
      - Changes in pressure and adding a catalyst do not affect the value of Kp, only shifting the equilibrium position. The value of Kp itself depends only on temperature, just like Kc.
      - Exothermic Reactions
        
        Temperature Increase
        
        Equilibrium Position shift to left
        
        Decrease Kp
        
        Temperature Decrease
        
        Equilibrium position shifts to right
        
        Increases Kp
      - Endothermic Reactions
        
        Temperature Increase
        
        Equilibrium Position shift to right
        
        Increase Kp
        
        Temperature Decrease
        
        Equilibrium Position shift to left
        
        Decrease Kp