Write a differential equation describing a second order reaction – a reaction in
which the rate of depletion of the concentration of the reactants depends on the
square of reactants’ concentration. Solve this differential equation and hence find
an expression for the concentration of the reactants as a function of time.
Have you looked in your text for this. I think I have a freshman text that lists the integrated equation.
No, I can't find one for a second order reaction.
For the reaction
aA ==>products.
d[A]/adt = k[A]^2
To describe a second order reaction where the rate of depletion of the concentration of reactants depends on the square of the reactants' concentration, we can start by defining the concentration of the reactant as [A]. Let the reaction rate be k[A]^2, where k is the rate constant.
According to the law of mass action, the rate of reaction is proportional to the product of the reactant concentrations. Therefore, the differential equation for a second order reaction can be written as:
d[A]/dt = -k[A]^2
To solve this differential equation, we can separate the variables and integrate both sides. Rearranging the equation, we have:
1/[A]^2 d[A] = -k dt
Integrating both sides, we get:
∫ 1/[A]^2 d[A] = -∫ k dt
Simplifying the integrals:
-1/[A] = -kt + C
Where C is the constant of integration.
Now, we can solve for [A] as a function of time. Rearranging the equation, we get:
[A] = 1/(kt - C)
So, the expression for the concentration of the reactant as a function of time in a second order reaction is [A] = 1/(kt - C).