A + 2B => R

I assume XA refers to X_{A} - the conversion of A.

**This is the rate equation:** Rate = - d[A]/dt = K[A][ B ]^{2}

- d[A]/dt = - (d/dt)([A]_{0}(1 - X_{A}) = [A]_{0}dX_{A}/dt

From the stoichiometric ratio, [ B ]_{0}X_{B} = 2 [A]_{0}X_{A}

[ B ] = [ B ]_{0}(1 - X_{B})

K[ A ][ B ]^{2} = K[A]_{0}(1 - X_{A})([ B ]_{0}-[ B ]_{0}X_{B})^{2} = K[A]_{0}(1 - X_{A})([ B ]_{0} - 2[A]_{0}X_{A})^{2}

[A]_{0}dX_{A}/dt = K[A]_{0}(1 - X_{A})([ B ]_{0} - 2[A]_{0}X_{A})^{2}

dX_{A}/dt = K(1 - X_{A})([ B ]_{0} - 2[A]_{0}X_{A})^{2}

Solving the above ODE will yield the correct **reaction profile**.