For a reversible reaction R P , at constant temperature, both the forward and the backward reactions are first order elementary reactions with rate constants k_f and k_b , respectively. At time zero, the concentration of R is [ R ]₀ and the concentration of P is zero. At any given time, [ R ] and [ P ] are the concentrations of R and P , respectively. If k_b = 4k_f , the correct graphical representation of the reacti

Step-by-step solution

For the reversible first-order reaction R P , at equilibrium, the rate of the forward reaction equals the rate of the backward reaction. k_f [ R ]_ eq = k_b [ P ]_ eq Given k_b = 4k_f , we can substitute this into the equilibrium condition: k_f [ R ]_ eq = 4k_f [ P ]_ eq [ R ]_ eq = 4[ P ]_ eq From the conservation of mass, the total concentration remains constant at any time t : [ R ]_ eq + [ P ]_ eq = [ R ]₀ Substituting [ R ]_ eq = 4[ P ]_ eq into the mass balance equation gives: 4[ P ]_ eq + [ P ]_ eq = [ R ]₀