At 25 °C, the initial rate of reaction is 3.1 × 10−3 mol dm−3 s−1 when the initial concentration of C is 0.48 mol dm−3 and the initial concentration of D is 0.23 mol dm−3 . Calculate a value for the rate constant at this T when rate = k [C][D].

The rate equation is given. So the first step is rearranging it to make the rate constant k the subject of the equation, by dividing both sides by [C][D]. k = (rate/[C][D]) now plug in the values given in the questions to find the numerical answer k = 3.1x10^-3/(0.48 x 0.23) = 2.8 x 10^-2 this is the numerical value correct to 2 significant figures ( be careful with the number of significant figures in the answer, if every value given in the question is given to 2 s.f., the result cannot be given accurately to more than 2 s.f.) now insert to the same equation corresponding units to find the units of the rate equation. k= mol dm^-3 s^-1/ (mol dm^-3 x mol dm^-3 )=mol^–1 dm³ s ^–1