0.5 Reaction rates  (Page 3/10)

We can estimate the rate of reaction at each time step as in , and these data are presented in as well. Again we see that the rate of reaction decreases as theconcentration of butadiene decreases. This suggests that the rate is given by an expression like . To test this, we calculate $\frac{\mathrm{Rate}}{\left[C_4{H}_6\right]}$ in for each time step. We note that this is not a constant, so does not describe the relationship between the rate of reaction and the concentration of butadiene.Instead we calculate $\frac{\mathrm{Rate}}{\left[C_4{H}_6\right]^2}$ in . We discover that this ratio is a constant throughout the reaction. Therefore, therelationship between the rate of the reaction and the concentration of the reactant in this case is given by

Observation 2: rate laws and the order of reaction

We would like to understand what determines the specific dependence of the reaction rate on concentration ineach reaction. In the first case considered above, the rate depends on the concentration of the reactant to the first power. We referto this as a first order reaction . In the second case above, the rate depends on the concentration of the reactant to the secondpower, so this is called a second order reaction . There are also third order reactions , and even zeroth order reactions whose rates do not depend on the amount of the reactant. We need more observations of rate laws fordifferent reactions.

The approach used in the previous section to determine a reaction's rate law is fairly clumsy and at thispoint difficult to apply. We consider here a more systematic approach. First, consider the decomposition of $N_2{O}_5\left(g\right)$ . $$2N_2{O}_5\left(g\right)\to 4N{O}_2\left(g\right)+O_2\left(g\right)$$ We can create an initial concentration of $N_2{O}_5$ in a flask and measure the rate at which the $N_2{O}_5$ first decomposes. We can then create a different initial concentration of $N_2{O}_5$ and measure the new rate at which the $N_2{O}_5$ decomposes. By comparing these rates, we can find the order of the decomposition reaction. The rate law for decomposition of $N_2{O}_5\left(g\right)$ is of the general form: