Overview of Kinetics
The last unit of the semester is kinetics. The connection between thermodynamics and kinetics:
- Thermodynamics deals with whether a reaction proceeds on its own (delta G).
- Kinetics has to do with the rate at which a reaction occurs.
Key Concepts
- Stable vs. Unstable: Refers to the spontaneous tendency and delta G. Something is stable when the delta G of formation is negative.
- Inert: Describes a reaction's rate. If something has existed for a long time but isn't necessarily stable, a chemist might call it inert.
- Rate Matters: Using the revolution speed of a ferris wheel as an example.
Chemical Kinetics
Chemical kinetics calculates the rates of chemical reactions, frequently by tracking a substance's change in concentration over time.
Elements Influencing Reaction Rates
- Temperature
- Catalysts
- Environmental factors, such as pressure and the type of material (solid, gas, etc.)
- Mechanism (number of steps, phase changes involved)
- Material concentration (applies in some cases depending on mechanism/reaction type)
Example: Oscillating Clock Reaction
An example of an oscillating clock reaction that incorporates kinetics, chemical equilibrium, oxidation-reduction, acid-base, and thermodynamics consists of several steps that have been condensed into two primary steps for discussion.
Step 1
Takes place when the concentration of I2 is low. A clear solution (iodide in some oxidation states) turns amber when exposed to acidic conditions (H+) because I2 is created. When I2 accumulates too much, this reaction stops.
Step 2
Takes place when there is a high concentration of I2. Amber turns blue as a result of the formation of a blue complex. I2 is consumed in this step, which lowers its concentration once more.
The Oscillation Cycle
Step 1 is triggered by low I2 (clear to amber), I2 builds up, step 2 is triggered by high I2 (amber to blue), I2 is consumed, I2 concentration falls again, step 1 is triggered by low I2, and so on. One reaction's product serves as the other reaction's substrate.
Oxidation-Reduction in the Reaction
- Iodate shifts the oxidation state in I2 from +5 to 0.
- In I2, iodide transforms its oxidation state from -1 to 0.
- Hydrogen peroxide's oxygen content fluctuates between -1 and 0.
- Water's oxygen content is -2.
Hydrogen Peroxide's Role
Its large positive standard reduction potential makes its reduction spontaneous (negative delta G), making it an excellent oxidizing agent.
Temperature Sensitivity
Temperature has an impact on the rate of reaction.
Demonstration of the Oscillating Clock
The oscillating clock demonstration involves adding hydrogen peroxide (solution A) and solution B, which contains iodate. The iodine is supplied by Solution B.
As anticipated from step 1, the first color shift is yellowish/amber. When solution D is added, the color changes to blue.
The reaction was able to oscillate and change color.
Effect of Temperature Demo
Using solutions stored in ice, the same reaction is demonstrated. In comparison to the reaction at higher temperatures, the reaction at lower temperatures (in ice) proceeds much, much slower. This exemplifies how temperature affects reaction rate.
Eventually, the rapid reaction will either cease or turn dark brown.
Types of Reaction Rates
- Average Rate: Concentration change over a given time period (delta concentration / delta T). An example plot of NO concentration versus time is used to demonstrate.
- Instantaneous Rate: The rate at a specific moment in time.
- Initial Rate: The instantaneous rate at time equals zero.
Rate Laws vs. Rate Expressions
Rate Expressions: Compare the rate at which reactants vanish or products appear to the rate at which a reaction occurs.
- The rate is equal to the negative rates of NO2 disappearance (-d[NO2]/dt), CO disappearance (-d[CO]/dt), NO appearance (d[NO]/dt), and CO2 appearance (d[CO2]/dt) for a reaction such as NO2 + CO -> NO + CO2.
- If there are no intermediates that materially alter the overall rate, these are equal.
- The rate expression for a generic equation aA + bB -> cC + dD takes stoichiometry into account: Rate = -1/a (d[A]/dt) = -1/b (d[B]/dt) = 1/c (d[C]/dt) = 1/d (d[D]/dt).
Rate Laws
A rate constant (little k) connects them. The equilibrium constant (big K) is not the same as this.
A + B -> C + D in general form: Rate = k [A]^m [B]^n, where m and n are the order of the reaction with respect to A and B, respectively, k is the rate constant, and [A] and [B] are concentrations.
Facts regarding Rate Laws
- Unless it is an elementary reaction, you cannot determine the order (m, n) from the stoichiometric coefficients (a, b) by simply looking at the equation.
- It is necessary to conduct an experiment in order to ascertain the rate law.
- Although product concentrations (such as [C] in the example A + B -> C + D), which are also ascertained experimentally, can occasionally be included in the rate law, it is typically expressed in terms of reactant concentrations.
- The order exponents (m, n) may be positive, negative, fractions, or integers.
Reaction Order (based on single reactant A -> products)
Determining Order: Experimentally ascertained by observing how the rate varies when a reactant's concentration is altered while holding the others constant.
First Order (m=1)
Rate = k[A]. The rate doubles when [A] is doubled.
Second Order (m=2)
Rate = k[A]^2. Doubling [A] quadruples the rate (2^2 = 4 times). Nine times the rate is obtained by tripling [A] (3^2 = 9 times).
Order m=-1
Rate = k[A]^-1. Doubling [A] cuts the rate in half (2^-1 = 0.5 times).
Order m=-1/2
Rate = k[A]^-1/2. The rate is 2^-1/2 (about 0.707) times the rate when [A] is doubled.
Half Order (m=1/2)
Rate = k[A]^1/2. The rate increases by 2^1/2 (about 1.4) when [A] is doubled.
Understanding Reaction Rates
The rate is equal to the rate constant.
The rate remains unchanged when [A] is doubled.
The sum of the exponents (orders) in the rate law is the overall order of reaction.
For instance, the overall order of Rate = k[A]^2[B]^1 is 2 + 1 = 3 (third order).
- The rate constant's units are determined by the overall order and are frequently more complicated.
Integrated Rate Laws
A different approach to measuring kinetics, integrated rate laws are particularly helpful when:
- Determining initial rates is challenging
- Concentration variations are slight
They directly represent concentrations as a function of time.
Integrated First Order Rate Law
Integrated First Order Rate Law (for A → products):
The process of derivation involves:
- Separating variables
- Integrating
- Setting the rate expression (-d[A]/dt) equal to the rate law (k[A])
The outcome is either ln([A]t) - ln([A]0) = -kt or ln([A]t / [A]0) = -kt.
Another way to express it is: [A]t = [A]0 * e^(-kt), where:
- t is time
- k is the rate constant
- [A]0 is the initial concentration
- [A]t is the concentration at time t
Graphical Method to Find k
Plot ln([A]t) versus time. This plot will be a straight line if the reaction is first order.
The line's y-intercept is ln([A]0).
The line's slope is -k. This allows for determining the rate constant experimentally.
First Order Process Half-Life (t1/2)
The time it takes for half of the original material to disappear is defined as t1/2.
The integrated rate law ln([A]t/[A]0) = -kt is derived by substituting [A]t = [A]0/2 and t = t1/2.
The outcome is t1/2 = ln(2) / k or t1/2 = 0.693 / k using ln(2) ≈ 0.693.
The first-order key point is that concentration has no effect on half-life.
The rate constant (k), which is dependent on the material, is the only factor that affects half-life.
For instance, the concentration changes from 0.8 to 0.4 take the same amount of time as the concentration changes from 0.4 to 0.2 for the same first-order material.
An example of successive half-lives is as follows: 0.5 of the initial concentration is left after one half-life, 0.25 after two, and 0.125 after three.
One instance of a first-order process is radioactive decay.
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