Question

Read the passage carefully and answer the questions that follow.

Dependence of the rate of reaction on the concentration of reactants, temperature, and other factors is the most general method for weeding out unsuitable reaction mechanisms. The term mechanism means all the individual collisional or elementary processes involving molecules (atoms, radicals, and ions included) that take place simultaneously or consecutively to produce the observed overall reaction. For example, when hydrogen gas reacts with bromine, the rate of the reaction was found to be proportional to the concentration of \[\ce{H2}\] and to the square root of the concentration of \[\ce{Br2}\]. Furthermore, the rate was inhibited by increasing the concentration of \[\ce{HBr}\] as the reaction proceeded. These observations are not consistent with a mechanism involving bimolecular collisions of a single molecule of each kind. The currently accepted mechanism is considerably more complicated, involving the dissociation of bromine molecules into atoms followed by reactions between atoms and molecules: It is clear from this example that the mechanism cannot be predicted from the overall stoichiometry.

1. Predict the expression for the rate of reaction and order for the following: 
   \[\ce{H2 + Br2 -> 2HBr}\]
   What are the units of rate constant for the above reaction?  
2. How will the rate of reaction be affected if the concentration of \[\ce{Br2}\] is tripled? 
                                               OR
   What change in the concentration of \[\ce{H2}\] will triple the rate of reaction?
3. Suppose a reaction between A and B was experimentally found to be first-order with respect to both A and B. So the rate equation is:
   Rate = k[A][B]
   Which of these two mechanisms is consistent with this experimental finding? Why?
   Mechanism 1
   \[\ce{A -> C + D (slow)}\]
   \[\ce{B + C -> E (fast)}\]
   Mechanism 2
   \[\ce{A + B -> C + D (slow)}\]
   \[\ce{C -> E (fast)}\]

Answer 1

a. Rate = k [H₂] [Br₂]^1/2

order = `3/2`

units of k = `("molL"^-1"s"^-1)/("mol"^(3//2)"L"^(-3//2)`

= mol^-1/2 L ^1/2 s^-1

b. Rate = k [H₂] [Br₂]^1/2 if conc of \[\ce{Br2}\] is tripled.

Rate’ = k [H₂] [3Br₂]^1/2

Rate’ = `sqrt3 k [H_2] [Br_2]^(1//2)`

Rate’ = `sqrt3  "Rate"`

OR

Rate = k [H₂] [Br₂]^1/2 if conc of \[\ce{Br2}\] is tripled.

Rate’ = 3 Rate = k [XH₂] [Br₂]^1/2

3 Rate = k [XH₂] [Br₂]^1/2

X = 3, the concentration of \[\ce{H2}\] is tripled.

c. The slowest step is the one that determines the rate. From mechanism 2, Rate = k [A] [B] while from mechanism 1, Rate = k [A]. Therefore, mechanism 2 is consistent with the experimental finding.