Sticking with the topic of sulfides, consider the kinetics of the following elem

Question

Sticking with the topic of sulfides, consider the kinetics of the following elementary reaction: H_2S HS^- + H^+ with rate constants k_f and k_b for the forward and back reactions, respectively. Write the overall rate equation for this reaction. If kf = 10^3 s^-1, and K_al = 107 M, what are the value and units of k_b? What are the "orders" of k_f and k_b? And what is the "order" of the overall rate equation? If the pH=7, what are the concentrations of H_2S and HS. if the [S]_T = 10^-4 M? What are the forward and reverse exchange rates at this pH and S_tau concentration at equilibrium? If a large amount of "marsh gas" (methane; CH_4) were to bubble out of the sediments, and thereby strip much of the gaseous H_2S out of the water, how long would the sulfide system take to return to equilibrium? If the pH of this water were to drop to 5, what would happen to the rates of the forward and back reactions? And what would happen to the relaxation time of the sulfide system?

Explanation / Answer

a) The rate for a reaction in a certain direction (foward or back) is proportional to the concentration of the reactants and a constant k. To write the rate of reaction for the compound H2S, both the foward reaction and the back must be considered. The total rate of reaction for H2S can be expressed as:

Total rate = rate of production - rate of consumption.

The rate of production in this case is the back reaction and the rate of consumption is the foward reaction. Hence, the total rate is:

d [H2S]/dt = k2 [HS-] [H+] - k1 [H2S], where [X] is the concentration of X at any time, usually expressed in mol/m3.

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