A-Level Chemistry AQA Notes

3.1.9 Rate Equations (A-Level)

Rate Equations (A-Level)
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Rate of Reaction
  • The rate of reaction is the change in concentration of a reactant or product per unit time.
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  • The rate of a reaction can be calculated by recording the amount of a reactant or a product at regular time intervals during a single reaction (continuous monitoring) or by determining the initial rate of several reactions and finding an average.
  • There are several methods for monitoring the rate of reaction:
    • Concentration change- take samples from a reaction at regular intervals in time and carry out a titration to measure the concentration
    • Gas evolving experiments- measure the volume of gas evolved, usually with a syringe, or set the system on a balance and measure the decrease in mass as the gas is released
    • Colour change- measure the colour change during an experiment with a colorimeter
    • pH change- use a pH meter to follow the pH change during a reaction

​Rate Equations
  • The rates of chemical reactions are dependent on the concentrations of the species involved in the reactions.
  • The rate equation is an expression which describes the dependence of the reaction rate on the concentrations of the species involved in the reaction.
For the reaction: A Products
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Rate = k[A]^x
For the reaction: A + B Products
Rate = k[A]^m[B]^n
k rate constant
m and n orders of reaction with respect to reactants A and B

  • The rate equation is experimentally determined– it cannot be determined from chemical equations.
  • The order of reaction with respect to a species tells us how the concentration of the species affects the rate
    • If the order of reaction is 0, a double in concentration of the species does not affect the rate rate = k[A]^0 = k
    • If the order of reaction is 1 a double in concentration of the species, doubles the rate rate = k[A]^1 = k[A]
    • If the order of reaction is 2 a double in concentration of the species, quadruples the rate rate = k[A]^2
  • The sum of the orders of all the reactants will give the overall order of the reaction
  • The order of reaction depends on the mechanism of a reaction and must be found experimentally
  • The units of rate constants are variable- they depend on the orders of the reactants involved. Rate constants can only be compared if they have the same units.

​The Effect of Temperature on Rate Constants
  • Temperature is a measure of the amount of energy that molecules have on average – the higher the temperature, the more energy molecules have.
  • Increasing the temperature increases the rate of reaction and therefore the rate constant increases too
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  • The Arrhenius equation:
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k is the rate constant
A is the Arrhenius constant
Ea is the activation energy (Jmol^-1)
​R is the gas constant (8.31 J K^-1mol^-1)
T is temperature (K)
  • For the rate constant to increase:
    • The temperature must increase
    • The activation energy must decrease
  • The Arrhenius rearrangement can be rearranged by taking the natural log of both sides of the equation:
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  • ​This is in the format of an equation for a straight line. By plotting ln(k) against 1/T
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  • The activation energy can be calculated by:
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  • The Arrhenius constant can be calculated from the y intercept
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Clock Reactions
  • Clock reactions allow determination of the rate of reaction for a specific concentration
  • The time taken for a certain amount of product to form is measured for a specific concentration of one of the reactants via an easily observable endpoint.
  • To calculate the initial rate, some assumptions are made:
    • The concentration of the reactant does not change significantly over the timescale
    • The temperature is constant
    • The endpoint has not been over-estimated by observing the colour change or precipitate formed too late
  • The time taken for precipitate formation can be monitored or the time taken for a distinct colour change to occur
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​Determination of Rate Equations
  • Rate-concentration graphs allow us to easily see how the concentration of a reactant affects the rate of reaction
  • Zero order reactions
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  • ​First order reactions. The gradient is equal to the rate constant.
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  • Second order reactions
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  • A concentration-time graph can be used to calculate the initial rate by drawing a tangent at t=0 and working out the gradient.
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  • The shape of a concentration-time graph will indicate the order of the reaction with respect to the reactant
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  • The rate-determining step is the slowest step in the reaction mechanism of a multistep reaction.
  • The slowest step in a reaction will dictate how fast the whole reaction will happen
  • For any reactant in the rate equation, the order indicates how many molecules of the reactant are involved in the rate-determining step (RDS), either directly or by forming an intermediate

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Rate Equations (A-Level)
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