Chemical kinetics involves the study of reaction rates and the factors that influence them. In AS Chemistry, you learned how variables like temperature, pressure, concentration, and catalysts affect the rate of a reaction. In A-Level Chemistry, we express these relationships mathematically using rate equations and reaction orders.
🔑 Key Principle
The rate equation of a chemical reaction is determined experimentally. It cannot be deduced simply by looking at the stoichiometric coefficients of the balanced overall chemical equation.
What is the Rate of a Reaction?
The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time.
The speed at which reactants are converted into products. It is mathematically represented as:
\( \text{Rate} = \frac{\Delta[\text{Concentration}]}{\Delta t} \)
The standard units for reaction rate are \( \text{mol dm}^{-3}\text{s}^{-1} \).
The Rate Equation
For a general reaction where reactants \( A \) and \( B \) form products:
\( aA + bB \rightarrow \text{products} \)
The rate equation (or rate expression) takes the form:
Where:
- \( \text{Rate} \) is the reaction rate in \( \text{mol dm}^{-3}\text{s}^{-1} \).
- \( [A] \) and \( [B] \) represent the concentrations of reactants \( A \) and \( B \) in \( \text{mol dm}^{-3} \).
- \( m \) and \( n \) are the orders of reaction with respect to reactant \( A \) and reactant \( B \).
- \( k \) is the rate constant.
A proportionality constant in the rate equation that is specific to a particular reaction at a specific temperature. Its value and units vary depending on the reaction orders.
Orders of Reaction
The order of reaction with respect to a given reactant describes how the rate changes when the concentration of that reactant is changed. Reaction orders are typically integers: zero, first, or second.
| Order | Mathematical Effect | If Concentration Doubles (\( \times 2 \)) | If Concentration Triples (\( \times 3 \)) |
|---|---|---|---|
| Zero (0) | Rate is proportional to \( [\text{Reactant}]^0 \) | Rate is unchanged (\( \times 1 \)) | Rate is unchanged (\( \times 1 \)) |
| First (1) | Rate is proportional to \( [\text{Reactant}]^1 \) | Rate doubles (\( \times 2 \)) | Rate triples (\( \times 3 \)) |
| Second (2) | Rate is proportional to \( [\text{Reactant}]^2 \) | Rate quadruples (\( \times 2^2 = 4 \)) | Rate increases nine-fold (\( \times 3^2 = 9 \)) |
The sum of the individual reaction orders of the reactants in the rate equation:
\( \text{Overall Order} = m + n + \dots \)
Always state the orders of reaction clearly. A reactant that is zero order is omitted from the final rate equation because \( [X]^0 = 1 \). If the question asks for the rate equation, do not include zero-order reactants in your written expression.
Concentration-Time Graphs for Different Orders
If we monitor the concentration of a single reactant over time, the shape of the concentration-time curve reveals the order of the reaction with respect to that reactant:
How to Deduce the Units of the Rate Constant \( k \)
The rate constant \( k \) does not have a single fixed set of units. Its units depend on the overall order of the reaction. To find the units of \( k \):
- Rearrange the rate equation to make \( k \) the subject.
- Substitute the units of rate (\( \text{mol dm}^{-3}\text{s}^{-1} \)) and concentration (\( \text{mol dm}^{-3} \)) into the rearranged equation.
- Cancel out units common to both the numerator and the denominator.
Step 1: Rearrange for \( k \):
\( k = \frac{\text{Rate}}{[A][B]} \)
Step 2: Substitute standard units:
\( \text{Units of } k = \frac{\text{mol dm}^{-3}\text{ s}^{-1}}{(\text{mol dm}^{-3}) \times (\text{mol dm}^{-3})} \)
Step 3: Simplify the expression:
Cancel one \( \text{mol dm}^{-3} \) from the top and bottom:
\( \text{Units of } k = \frac{\text{s}^{-1}}{\text{mol dm}^{-3}} = \text{mol}^{-1}\text{dm}^3\text{s}^{-1} \)
Written in standard order: \( \text{dm}^3\text{mol}^{-1}\text{s}^{-1} \).
Step 1: Rearrange for \( k \):
\( k = \frac{\text{Rate}}{[C]^2[D]} \)
Step 2: Substitute standard units:
\( \text{Units of } k = \frac{\text{mol dm}^{-3}\text{ s}^{-1}}{(\text{mol dm}^{-3})^2 \times (\text{mol dm}^{-3})} = \frac{\text{mol dm}^{-3}\text{ s}^{-1}}{(\text{mol dm}^{-3})^3} \)
Step 3: Cancel and simplify:
\( \text{Units of } k = \frac{\text{s}^{-1}}{(\text{mol dm}^{-3})^2} = \frac{\text{s}^{-1}}{\text{mol}^2\text{dm}^{-6}} = \text{mol}^{-2}\text{dm}^6\text{s}^{-1} \)
Written in standard order: \( \text{dm}^6\text{mol}^{-2}\text{s}^{-1} \).
Effect of Temperature on the Rate Constant \( k \)
If you increase the temperature of a reaction, the rate increases. According to the rate equation:
\( \text{Rate} = k[A]^m[B]^n \)
Since the concentrations of the reactants remain unchanged, the only way the rate can increase is if the rate constant \( k \) increases. Therefore, \( k \) is temperature dependent and increases exponentially with temperature. This relationship is quantified by the Arrhenius equation, which you will study in a later lesson.
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