This reaction was monitored as a function of time: ab --> a + b a plot of 1/[ab] versus time yields a straight line with slope of -0.055/m*s. a) what is the value of the rate constant (k) for this reaction t this temperature? b) write the rate law for the reaction. c) what is the half-life when the initial concentration is 0.55m? d) if the initial concentration of ab is 0.250m, and the reaction mixture initially contains no products, what are the concentrations of a and b after 75s?

A) Since the plot 1/[AB] vs time gives straight line, the order of the reaction with respect to A is second order:
rate constant, K = slope = 5.5 x 10⁻² M⁻¹S⁻¹

b) Rate law : Rate = k[AB]²

c) half life period of the 2nd order is inversely proportional to the initial concentration of the reactants 
t 1/2 = . 
t 1/2 = 

d) k = 5.5 x 10⁻² M⁻¹s⁻¹
Initial concentration of AB, [A₀] = 0.250 M
concentration of AB after 75 s = [A]
k = 
[A] = 0.123 M
Equation: AB → A + B
  concentration of AB after 75 s = 0.123 M
Amount of AB dissociated = 0.25 - 0.123 = 0.127 M
concentration of [A] produced = concentration of [B] produced = Amount of AB reacted = 0.127 M