Chemistry Kinetics: How Fast is "Fast"?
Welcome to Kinetics! This chapter is all about understanding the speed of chemical reactions. Why do some reactions, like an explosion, happen instantly, while others, like the rusting of iron, take years?
Kinetics helps chemists control reactions, making industrial processes faster (and cheaper!) or preventing dangerous reactions from running wild. Don't worry if this seems tricky at first; we'll break it down using simple ideas like car crashes and gates!
Part 1: The Foundations of Rate (AS Level)
3.1.6 Collision Theory and Activation Energy
A chemical reaction can only occur if the reacting particles (atoms, ions, or molecules) successfully collide. This is the core idea of Collision Theory.
Why Most Collisions Fail
For a collision to be successful and lead to a reaction, two conditions must be met:
- Sufficient Energy: The particles must collide with energy equal to or greater than the Activation Energy ($E_a$).
- Correct Orientation: The particles must collide facing the correct way so that the necessary bonds can break and new bonds can form.
Key Term: Activation Energy ($E_a$)
$E_a$ is the minimum energy required by colliding particles for a reaction to occur.
Analogy: The Hill Climb
Think of a reaction as driving a car over a hill. The valley floor is the starting reactants, and the other side is the products. The height of the hill is the $E_a$. If your car (the colliding particle) doesn't have enough kinetic energy to reach the top of the hill, it just rolls back down (an unsuccessful collision).
Quick Review: Successful Reaction Criteria
- Collision occurs.
- Energy $\geq E_a$.
- Correct alignment/orientation.
3.1.6.2 The Maxwell-Boltzmann Distribution
Not all particles in a gas or liquid move at the same speed, so they don't all have the same energy. The Maxwell-Boltzmann (MB) Distribution curve shows the range of energies held by the molecules in a sample at a specific temperature.
- The area under the curve represents the total number of molecules.
- The peak of the curve represents the most probable energy (the energy possessed by the largest number of molecules).
- The curve approaches the energy axis but never touches it, meaning theoretically, some molecules have extremely high energies.
Effect of Temperature on the MB Distribution
When you increase the temperature (T):
- The curve flattens and broadens.
- The peak shifts to the right (higher energy).
- Crucially: The number of molecules with energy $\geq E_a$ increases significantly.
Why a small temperature increase causes a large rate increase (3.1.6.3):
A small rise in temperature does not just slightly increase the average energy; it causes an exponential increase in the number of particles that exceed the $E_a$ threshold. If you shift the entire curve slightly to the right, the area under the curve past the $E_a$ line gets dramatically larger.
3.1.6.4 Factors Affecting Reaction Rate (Qualitative)
The rate of reaction is defined as the change in concentration of a reactant or product per unit time (e.g., mol dm$^{-3}$ s$^{-1}$).
Factors we can manipulate to change the rate include:
1. Concentration (Solutions) / Pressure (Gases)
- Effect: Increasing concentration (or pressure for gases) increases the reaction rate.
- Explanation: Higher concentration/pressure means there are more particles packed into the same volume. This increases the frequency of collisions (more collisions per second), therefore increasing the frequency of successful collisions.
2. Temperature
- Effect: Increasing temperature increases the reaction rate.
- Explanation: As explained with the MB curve, increasing temperature causes a massive increase in the proportion of molecules that possess energy $\geq E_a$. These are the particles capable of reacting successfully.
3. Surface Area (Solids)
- Effect: Increasing surface area (e.g., using powder instead of a lump) increases the reaction rate.
- Explanation: Reactions involving solids only occur at the exposed surface. Increasing the surface area increases the frequency of exposure between the reactant particles, leading to more collisions.
3.1.6.5 Catalysts
A catalyst is a substance that increases the rate of a chemical reaction without being used up in chemical composition or amount.
How Catalysts Work
A catalyst works by providing an alternative reaction route (or mechanism) that has a lower activation energy ($E_a$).
Analogy: The Tunnel
If the uncatalysed reaction is driving over a large hill ($E_a$), the catalyst provides a tunnel right through the hill (a much lower $E_a$ pathway). More cars (particles) now have enough energy to get through.
Catalysts and the Maxwell-Boltzmann Curve
When you draw the $E_a$ onto an MB curve, adding a catalyst means the required energy threshold ($E_a$) shifts significantly to the left (lower energy). This drastically increases the number of molecules that now have sufficient energy to react.
Types of Catalysts (AS Review)
- Homogeneous: Catalyst and reactants are in the same phase (e.g., liquid solutions). They often work by forming an intermediate species.
- Heterogeneous: Catalyst and reactants are in different phases (e.g., solid catalyst, gaseous reactants). Reactions occur at active sites on the catalyst surface (like V$_2$O$_5$ in the Contact process or Fe in the Haber process).
Key Takeaway (Part 1): Rate depends on successful collisions, which require energy $\geq E_a$ and correct orientation. Temperature and catalysts are the most powerful ways to increase rate because they increase the number of particles exceeding the $E_a$ barrier.
Part 2: Rate Equations and Mechanism (A2 Level)
For the AS section, we discussed the *qualitative* effects on rate. Now, in A2, we get mathematical. We will use experimental data to find the exact relationship between concentration and rate.
3.1.11.1 Rate Equations and Orders of Reaction
The relationship between the rate of reaction and the concentrations of the reactants is defined by the Rate Equation.
For a reaction $A + B \rightarrow Products$, the general rate equation is:
$$Rate = k[A]^m[B]^n$$Where:
- Rate: Measured in mol dm$^{-3}$ s$^{-1}$.
- \([A]\) and \([B]\): Concentrations of reactants (mol dm$^{-3}$).
- \(k\): The Rate Constant. Its value depends only on temperature and the catalyst used.
- \(m\) and \(n\): The Orders of Reaction with respect to A and B.
Important! The orders \(m\) and \(n\) must be determined experimentally. They are not necessarily the stoichiometric numbers from the balanced equation.
Order of Reaction (Limited to 0, 1, and 2)
The order of reaction defines how much the rate changes when the concentration of a specific reactant changes.
- Order 0 (m=0): $Rate = k[A]^0 = k$.
The rate is unaffected by a change in concentration of A. Doubling [A] has no effect on the rate. - Order 1 (m=1): $Rate = k[A]^1$.
The rate is directly proportional to [A]. Doubling [A] doubles the rate. - Order 2 (m=2): $Rate = k[A]^2$.
The rate is proportional to the square of [A]. Doubling [A] quadruples (2$^2$) the rate.
Overall Order: This is the sum of the individual orders: $m + n$.
3.1.11.2 Determination of Rate Equation (Experimental)
You will need to use experimental data (often initial rates) to find $m$ and $n$.
Step-by-step: Finding the Order from Initial Rate Data
Let's look at the reaction $A + B \rightarrow Products$ (Rate $= k[A]^m[B]^n$).
- To find $m$ (order with respect to A): Find two experiments where the concentration of B is kept constant, but [A] is changed.
Example: If you double [A] and the rate quadruples (x4), then the order $m=2$ ($2^2 = 4$). - To find $n$ (order with respect to B): Find two experiments where the concentration of A is kept constant, but [B] is changed.
Example: If you double [B] and the rate stays the same, then the order $n=0$ ($2^0 = 1$). - Write the Rate Equation: Once $m$ and $n$ are known, substitute them into the general equation.
- Calculate $k$: Substitute the concentrations and rate from any single experiment into your complete rate equation and solve for $k$.
Common Mistake to Avoid: You must state the units of $k$ (the rate constant). These units change depending on the overall order of the reaction!
Trick for k units: Use $Units\ of\ k = \frac{Units\ of\ Rate}{(Units\ of\ Conc)^{Overall\ Order}}$
- Overall Order 1: \(k\) units are s$^{-1}$.
- Overall Order 2: \(k\) units are dm$^3$ mol$^{-1}$ s$^{-1}$.
- Overall Order 3: \(k\) units are dm$^6$ mol$^{-2}$ s$^{-1}$.
Using Concentration-Time Graphs
If you are given a graph showing concentration vs. time, you can deduce the order of the reaction visually:
- Zero Order: The graph is a straight line with a negative gradient. Rate is constant.
- First Order: The graph shows an exponential decrease. The half-life is constant (takes the same time for concentration to halve, regardless of starting concentration).
- Second Order: The concentration drops very steeply initially. The half-life is not constant.
To find the rate at a specific time (e.g., the initial rate at $t=0$), you draw a tangent to the curve at that point and calculate its gradient (change in y / change in x).
3.1.11.2 Connecting Order to Reaction Mechanism
Most reactions happen in a series of small steps, called the reaction mechanism.
In any mechanism, one step is much slower than all the others. This slow step is called the Rate Determining Step (RDS) or Limiting Step.
The reactants involved in the Rate Determining Step are the only ones that appear in the Rate Equation.
Analogy: The Toll Booth
Imagine a chemical factory assembly line. If the first step (Step 1) involves two molecules of A colliding, but Step 2 is the slowest step (the toll booth), the overall production speed is limited by Step 2. If Step 2 involves one molecule of B and one molecule of C, then the rate equation will only show [B] and [C], regardless of what happened in Step 1.
Therefore, if a reactant is Zero Order, it means that reactant is not involved in the rate determining step (or is involved in a fast step after the RDS).
3.1.11.1 The Arrhenius Equation and Rate Constant (k)
We established that the rate constant $k$ is dependent on temperature (and $E_a$). The mathematical relationship is given by the Arrhenius Equation:
$$k = A e^{-E_a/RT}$$Where:
- \(k\): Rate constant.
- \(A\): The Arrhenius constant (related to collision frequency and orientation factor).
- \(E_a\): Activation energy (J mol$^{-1}$).
- \(R\): The gas constant (J K$^{-1}$ mol$^{-1}$). (Given in exam)
- \(T\): Temperature (must be in Kelvin, K).
Understanding the exponential term: The term $e^{-E_a/RT}$ is equivalent to the fraction of molecules that have energy $\geq E_a$. As T increases, this fraction (and therefore $k$) increases rapidly.
Linear Form of the Arrhenius Equation
To determine the activation energy ($E_a$) experimentally, the Arrhenius equation is usually rearranged into a linear form. If you take the natural logarithm ($\ln$) of both sides:
$$\ln k = -\frac{E_a}{R}\left(\frac{1}{T}\right) + \ln A$$This equation matches the straight-line form \(y = mx + c\):
- \(y\) axis: $\ln k$
- \(x\) axis: $1/T$ (Note: T must be in Kelvin!)
- \(c\) (y-intercept): $\ln A$
- \(m\) (gradient/slope): $-\frac{E_a}{R}$
Calculation Skill: By plotting $\ln k$ against $1/T$, you can calculate the gradient ($m$). Since $R$ is known, you can then solve for the activation energy $E_a$:
$$E_a = -R \times \text{Gradient}$$Key Takeaway (Part 2): The rate equation ($Rate = k[A]^m[B]^n$) is found experimentally, not from stoichiometry. The orders ($m, n$) relate directly to the molecules involved in the slowest step (the Rate Determining Step). The rate constant ($k$) is sensitive to temperature, a relationship mathematically described by the Arrhenius equation.