In contrast to the situation of Exercise 40, experiments show that the reaction H2 + Br2 → 2HBr satisfies the rate law
D[HBr/dt] = k[H2][Br2]1/2
And so for this reaction the differential equation becomes
dx/dt = k(a -x)(b - x)1/2
Where x = [HBr] and a and b are initial concentrations of hydrogen and bromine.
(a) Find as a function of in the case where a = b. Use the fact that x(0) = 0.
(b) If a > b, find t as a function of x. [In performing the integration, make the substitution u = √b - x.]