For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.

t (sec)	P(mm of Hg)
0	35.0
360	54.0
720	63.0

Calculate the rate constant.

When t = 0, the total partial pressure is P₀ = 35.0 mm of Hg

When time t = t, the total partial pressure is P_t = P₀ + p

P₀-p = P_t-2p, but by the above equation, we know p = P_t-P₀

Hence, P₀-p = P_t-2( P_t-P₀)

Thus, P₀-p = 2P₀ – P_t

We know that time

Where, k- rate constant

[R]_° -Initial concentration of reactant

[R]-Concentration of reactant at time ‘t’

Here concentration can be replaced by the corresponding partial pressures.

Hence, the equation becomes,

→ equation 1

At time t = 360 s, P_t = 54 mm of Hg and P₀ = 30 mm of Hg,

Substituting in equation 1,

⇒

⇒ k = 2.175 × 10^-3 s^-1

At time t = 720 s, P_t = 63 mm of Hg and P₀ = 30 mm of Hg,

Substituting in equation 1,

⇒

Thus, k = 2.235 × 10^-3 s^–1

Taking average, k = (2.235 × 10^-3 s^–1 + 2.175 × 10^-3 s^–1)/2

∴ k = 2.21 × 10^-3 s^–1.