Question

For the following reaction: 2HI (g) ----> H2(g) + I2(g), the rate law is rate= k[HI]^2. You are starting with 1.0M HI. How long will the first half-life reaction be? (The professor adds: Note that since you don't know the value for the rate constant k, just leave it in your answers.)

Answer 1

Ans. Given,

            Initial [HI] = [A]₀ = 1.0 M

            The order of reaction = 2

At first half of reaction, Final [HI] = ½ x Initial [HI] = ½ x 1.0 M = 0.5 M

Using second order kinetics-

1/ [A] = kt + (1/ [A]₀)        - equation 1

Where, [A]0 = Initial concentration of X

[A] = Final concentration of X after time t

k = rate constant

t = time of reaction.

Putting the values in above equation-

            1/ 0.5 = kt + 1/1 = kt + 1

            Or, 2 – 1 = kt

            Or, t = 1/k

Therefore, required time to complete first-half reaction (i.e. half of reactant is consumed) = 1/k