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

Question 4.20:  For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.

Calculate the rate constant.
Answer
Let initial pressure = p_o
And pressure after time t = p_t
Amount of substance = a
Decomposed quantity = x
The decomposition of azoisopropane to hexane and nitrogen at 543 K is


In this problem we take pressure in place of concentration or quantity
Final pressure due to reactant = p_o - p = 2po - p_t
Plug the values from the table we get
When t = 360 sec
k₁ = 2.175 × 10⁻³ s⁻¹
When t = 720 sec

K₂= 2.235 × 10⁻³ sec⁻¹
Hence, the average value of rate constant is
To get average value add both values and divide by 2 we get
k = (k₁ +k₂)/2
After calculation we get
k= 2.21 × 10⁻³ sec⁻¹