Graphical Method of Order Determination

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First, the data of concentrations versus time is obtained by a suitable method. Then, the data is plotted as concentration versus time. From the resulting plot, the instantaneous rates are determined by drawing tangents to curve and then calculating their slopes. The reaction rate so obtained are plotted against concentrations raised to various powers. That is rates are plotted against [C]¹, [C]² and [C]³.. [C]ⁿ, n (n need not be integral numbers). From the nature of the plots, the order of the reaction can be judged. For a zero order reaction, the rate will not vary with concentration and the plot will be a line parallel to the concentration axis.

If the reaction displays any other order, then the plot of rate against concentration raised to the appropriate order will be linear which obeys the relation, y = mx. The slope m gives the rate constant k of the reaction.

Example 8:

Decomposition rates of N₂O₅ g at different values of concentrations of N₂O₅ as given in the data below:

These values are plotted as rate versus concentration in figure 6.7 and rate versus (concentration)² in the figure 6.8.

fig 6.7 - Rate of decomposition of [N₂O₅] versus concentration of [N₂O₅]

fig 6.8 - Rate of decomposition of [N₂O₅] versus concentration of [N₂O₅]²

It is seen that the rate is proportional to the concentration of N₂O₅ raised to the power one. Therefore, dinitrogen pentoxide decomposes in a first order manner. The value of the rate constant k, as evaluated from the data, is