What do you mean by zero order reaction? How the value of rate constant is determined? What is the relation between rate constant and half-life period?

Solution

When the rate of the reaction is independent of the concentration of the reactants, the reaction is known as zero order reaction. In zero order reaction, the concentration of reactant (R) remains unaltered during the course of reaction.

It means

rate = \frac{- d [R]}{dt} = k [R] ° = k

d (R) = - k dt

on integration of this equation, we get

[R] = - kt + constant

...(i)

Since

[R] = [R] °

where t = 0 (i.e., no product is formed at the beginning of the reaction), the constant must be zero.
Thus, [R]° = – K x 0 = constant
Constant = [R]°
Put the value of constant in eqn. (i), we get

[R] = – kt + [ R]° ...(ii)

When a plot is drawn between concentration of reactant (R) and time t, a straight line is obtained, slope of which gives the value of – k and intercept on y-axis is equal to the value of [R]°.
Alternatively, the value of k can be obtained from eqn. (i) by putting the value of concentration, [R] at any time t and initial concentration, [R]°.

Hence,

k = \frac{[R] ° - [R] t}{t}

Half life period is the time period to reduce the initial concentration of the reactant to half of its initial value.
Thus,

t_{1 / 2} = \frac{[R] - \frac{1}{2} [R] °}{k} = \frac{[R] °}{2 k}

Thus, the half life period is directly proportional to the initial concentration of the reactant, [R]° and inversely proportional to the rate constant k.

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For Daily Free Study Material Join wiredfaculty

Chemical Kinetics

What do you mean by zero order reaction? How the value of rate constant is determined? What is the relation between rate constant and half-life period?

Some More Questions From Chemical Kinetics Chapter

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

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