For a reaction with rate equation - dc/dt = kc2, Co and C are the concentration of the reactant at time zero and t respectively. If 10 minutes were required for C0 to becomes C0/2 the time required for Co to becomes C0/4 is ____ min. (Answer should be an integer).Correct answer is '30'. Can you explain this answer?

Question

Answer

Explanation:

Given, rate equation - dc/dt = kc2

Let's assume that the initial concentration of the reactant is Co.

It is given that it takes 10 minutes for Co to become Co/2.

This means that after 10 minutes, the concentration of the reactant will be Co/2.

Let's calculate the value of k using the given information.

At t=0, c=Co, and at t=10, c=Co/2.

Substituting these values in the rate equation, we get:

k = dc/dt * 1/c2 = (Co/2 - Co)/(10 * Co2) = -Co/20 * Co2

Now, let's find out the time required for Co to become Co/4.

Let's assume that it takes t minutes for Co to become Co/4.

At t=0, c=Co, and at t=t, c=Co/4.

Substituting these values in the rate equation and using the value of k that we just calculated, we get:

dc/dt = -Co/20 * Co2 * c2

Integrating both sides, we get:

-1/c = Co/20 * t + 1/c0

Substituting the values of c and c0, we get:

-4/Co = Co/20 * t + 1/Co

Solving for t, we get:

t = 30 minutes

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