Initial rate method

The rate of a reaction decreases with time because the concentrations of reactants decrease as a reaction progresses. This poses a problem when we want to compare reactions under different conditions, e.g. to compare the reaction rates for different concentrations of HCl on CaCO3.

The diagram above shows the pressure of CO2 liberated over time for the reaction of CaCO3 with HCl at three different concentrations: A, B and C. Instead of arbitrarily choosing points on each curve to determine the gradients and hence the respective reaction rates (upper left graph), a basis of comparison must be established before finding the gradients. The initial rate of reaction (i.e. the gradient at t ≈ 0, just after the start of the reaction) is eventually chosen as the reference point (upper right graph), because the concentrations of HCl are approximately the same as that before the start of the respective reactions, especially for slow reactions. It is also chosen partly to minimise the effects of temperature (from exothermic or endothermic reactions) on the system when the reaction progresses. Furthermore, the initial rate of reaction method is useful for studying the forward reaction rate of a reversible reaction where the reverse reaction is negligible at the start. The initial rate method can be used to determine rate equations involving either a single or multiple reactants.

To illustrate the method, consider a constant volume reaction with the rate law:

R=k[A]^i\; \; \; \; \; \; \; \; 25

The experiment is carried out with four different initial concentrations of the reactant, A, with the data plotted in a concentration versus time graph (see diagram below).


R=\frac{change\, in\, concentration\, of \, reactants\, or\, products}{\, change\, in\, time}

the four gradients of the curves a, b, c and d are the rates of the respective reactions at t = 0, i.e. the initial rates. Taking the natural logarithm of both sides of eq25, we have

lnR=lnk+iln[A]\; \; or\; \; lnR_0=lnk+iln[A]_0\; \; \; \; \; \; \; \; 26

where R0 and [A]0 are the initial rate of reaction and initial concentration of A respectively. If we plot the natural logarithm of the initial reaction rates of the four curves against the natural logarithm of the respective initial concentrations of A, we get a straight line with gradient i and vertical intercept lnk. Therefore, the rate constant and the order of eq25, and hence the entire rate law, can be found.


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