Rate Constant for a Second Order Reaction

Question

Hydrogen iodide decomposes at 800 K via a second-order process to produce hydrogen and iodine according to the following chemical equation.

2 HI(g) → H2(g) I2(g)

At 800 K it takes 142 seconds for the initial concentration of HI to decrease from 6.75 × 10-2 mol dm-3 to 3.50 × 10-2 mol dm-3. What is the rate constant for the reaction at this temperature?

a. 1.95 × 103 dm3 mol -1s-1

b. 10.3 dm3 mol -1s-1

c. 9.69 × 10-2 dm3 mol -1s-1

d. 5.12 × 10-4 dm3 mol -1s-1

I'm lost on what equation i must use to solve this....

Answer 1

The equation to use is the integrated form of 2nd order rate law:

1/[HI] = kt + 1/[HI]o

Substituting,

1/(0.035 M) = k (142 s) + 1/(0.0675 M)

Solving for k,

k = 0.0968 /M*s, so the answer is c.