# Math Help - expression for time?

1. ## expression for time?

The rate of reaction of an irreversible second order bimolecular reaction of species
A and B can be written as:

$-ra = C_{A0} \frac{dX_{A}}{dt} = k(C_{A0} - C_{A0}X_{A})(C_{B0} - C_{A0}X_{A})$

where $C_{A0}$ and $C_{B0}$ represent the initial concentration of reactants A and B respectively, k is the reaction rate constant and $X_{A}$ is the conversion of the limiting reactant A.

Find an expression for the conversion of A $(X_{A})$ in terms of time for the above reaction.

I thought of simply rearranging the formula to get it in terms of dxa/dt, since this is the change of the concentration of the reactant A with respect to time, however it is not the correct answer. Can someone please explain how to start this? I dont understand what I am being asked to do?

Thank you.

2. can someone tell me what is the integral of $\int \frac{dX_{A}}{dt}$ ? Does that give me 'time' ?