It would be very helpful to have the equation that governs the curves like the one above on the decomposition of sucrose. It is possible to obtain such equations, but the methods used to obtain the equations involve the use of differential and integral calculus. This is a very important equation. If we experimentally measure the concentration of reactant at some time, we can easily calculate the rate constant.
Many radioactive decays are first-order reactions.
The number 0.693 is the value of ln2. We can use these equations to obtain the order of the reaction and the rate constant. Review Questions Derive the equations for the half-lifes in the above table. Outline the methods that we now have for experimentally determining the orders and rate constants for chemical reactions. Work Exercise 15.9 on page 709.