Given:A→2B+2CBatch reactor Volume is constant Gas phase Isothermal t (min) 0 2 5 10 15 20To determine :The rate of the reaction equation Solution :The reaction equation is given as :A → 2B + 2CThe given reaction is of first order reaction.
Hence, the rate equation for the reaction is given by rate = k[A]^1k is the rate constant. For batch reactors, the volume remains constant. Hence, the rate of reaction is given as d[A]/dt = -k[A]^1
Since A is getting converted to B and C, therefore, the rate of formation of B and C would be
d[B]/dt = 2k[A]^1d[C]/dt = 2k[A]^1
As per the given data, we have t (min) and A (concentration).From the data, we can calculate the rate of reaction using the integrated rate equation for first-order reactions.
The integrated rate equation is given by ln[A]t/[A]0 = -kt where [A]0 is the initial concentration of A and [A]t is the concentration of A at time t.
The value of k can be calculated from the slope of the linear plot of ln[A]t/[A]0 versus time t .Using the given data, we have :
ln[A]t/[A]0 = -kt t(min)[A] (mol/L)ln[A]t/[A]0t(min).
The given data can be tabulated as follows :
t (min)A (mol/L)ln[A]t/[A]0-kt (min^-1)002.0000.0000.0000251.500-0.4051001.250-0.5082501.000-0.69310.750-0.91615.500-1.25220.250-2.302.
The plot of ln[A]t/[A]0 versus time t is shown below:
Slope of the linear plot = -k = 0.693/10= 0.0693 min^-1Rate of reaction = k[A]^1= 0.0693 × [A]^1 mol/L min^-1= 0.0693 mol L^-1 min^-1
Therefore, the rate of reaction equation is given by: d[A]/dt = -0.0693[A]^1d[B]/dt = 2 × 0.0693[A]^1d[C]/dt = 2 × 0.0693[A]^1