10.3: The effect of concentration on rate

The effect of concentration on rate

The rate of a reaction is the change in concentration of a reactant or product divided by the time taken for the change to occur.
The rate of a reaction changes during the reaction as the reactants are used up.
Reactions are followed by measuring the change, with time, of a property that is proportional to the concentration of a reactant or product - e.g. pH of the reaction mixture, colour intensity if the reaction involves a coloured compound, volume of a gas given off.
A plot of this property against time is the progress curve for the reaction.
The half-life of a reaction is the time taken for the concentration of a reactant to decrease to one half of its initial value.
If the rate at which the reactant is used up in a reaction displays a constant half life, the reaction is first order with respect to that reactant.
The rate equation for a reaction shows how the rate of reaction varies with the concentration of each of the reactants.
Many reactions occur in a series of simple individual steps. If one step in a reaction mechanism is much slower than the others it is called the rate determining step.
Rate equations can only be predicted from the chemical equations for the individual steps in a reaction mechanism. They cannot be predicted from the overall equation for the reaction and must always be found experimentally.

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For the reaction of A with B, the rate equation is given by rate=k[A]"[B]", where k is the rate constant and "(m and n) are the orders of the reation with respect to A and B. The overall order of the reaction is m+n.
In the rate experiments it is important to make measurements at a constant temperature and to investigate only one variable at a time. Other concentrations must be kept constant
To find the order of reaction with respect to a reactant A, the rate of reaction is found at different concentrations of A.
This may be done in various ways: by drawing tangents at various points on the progress curve for the reacion (the gradient of the tangent is proportional to the rate of reaction for that value of [A]), by finding the initial rate of reaction for different reaction mixtures e.g. by drawing tangents to the progress curve for each reaction mixture at the point t=0, or by using a clock technique to find the reaction time for a small amount of reaction to take place.
A graph of the rate of reaction (or quantity that is proportional to the rate of reaction) is then plotted against [A]. If the plot is a straight line, which shows that the rate is proportional to [A], the reaction is first order with respect to A.
A horizontal straight line shows that the rate is independent of [A] and so the reaction is zero order with respect to A.

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Other orders give curved graphs. If the reaction is second order with respect to A, a plot of the rate against [A]squared is a straight line.
An alternative method of showing that a reaction is first order is to calculate the values of several half-lives for the reaction from the progress curve. If the values of the half-lives are euqal then the reaction is first order.
This method can only be used to check that a rection is first order.
The rate constant for a reaction at a particular temperature can be found by substituting values for the rate of reaction and values of [A] and [B] into the rate euqation - make sure that you used the correct units.
If you have been following the reaction by measuring a property such as pH, the rate of reaction in terms of this property must be converted to the rate of reaction in terms of concentration.

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