__Zeroth order reaction__

__Zeroth order reaction__

If the rate of reaction is independent of concentration of the reactant participating in the reaction then the reaction is called Zeroth order reaction.

A –> B

At time t = 0 concentration of A (reactant) is a and B (product) is 0. At time t = t the concentration of A (reactant) is (a-x) and that of B (product) is x.

-d[A]/dt = k_{0}[A]^{0} => dx/dt = k_{0}(a-x)^{0}

dx/dt = k_{0}

∫ _{0}^{x} dx =k_{0} ∫_{0}^{ x}dt

X = k_{0}t

** PROBLEM**. The decomposition of NH3on platinum surface is zero order reaction. What are the rates of production of N2and H2if k = 2.5 x 10-4mol-1L s-1?

** SOLUTION**. 2NH

_{3 }–> N

_{2}+ 3H

_{2}

Rate of zero order reaction

-1/2 (d[NH_{3}]/dt) = d[N_{2}]/dt = 1/3 (d[H_{2}]/dt)

-1/2 (d[NH_{3}]/dt) = d[N_{2}]/dt = 1/3 (d[H_{2}]/dt)= k = 2.5 x 10^{-4} mol L^{-1} s^{-1}

Rate of production of N_{2}

d[N_{2}]/dt = 2.5 x 10^{-4} mol L^{-1} s^{-1}

Rate of production of H_{2}

d[H_{2}]/dt = 3 x 2.5 x 10^{-4} mol L^{-1} s^{-1}

__First order reaction__

__First order reaction__

If the rate of reaction depends on the concentration of single reactant participating in chemical reaction raised to the first power then it is called a first order reaction.

A –> B

At time t = 0 concentration of A (reactant) is a and B (product) is 0. At time t = t the concentration of A (reactant) is (a-x) and that of B (product) is x.

-dx/dt ∝ (a-x) = dx/dt = k1(a-x)

∫ 0x dx/(a-x) = k1∫ 0t dt

dx/dt = k0(a-x)0

dx/dt = k0

∫0 x dx = k0∫ 0t dt

ln (a/a-x) = k1t => t = 1/ k1 ln (a/a-x) = 2.303/ k1 log (a/a-x)

k1 = 2.303 log (a/a-x)

** PROBLEM**. A first order reaction has a rate constant 1.15 10-3s-1. How long will 5 g of this reactant take to reduce to 3 g?

** SOLUTION**. From the question, we can write down the following information:

Initial amount = 5 g

Final concentration = 3 g

Rate constant = 1.15 10 – 3s – 1

We know that for a 1st order reaction,

t = (2.303/k)log[R0]/[R]

(2.303/1.15X10-3)log[5]/[3]

(2.303/1.15X10-3) X 0.2219 = 444.38 s = 444 s

__Second order reaction__

__Second order reaction__

A reaction with order equal to two is called a second order reaction.

r = k[A]^{2}

or r = k [A][B]

__Pseudo order reaction__

__Pseudo order reaction__

The reaction that appears to be an n^{th} order reaction but belongs to some different order is called Pseudo order reaction.

For example, a pseudo first order reaction is a chemical reaction between two reactants participating in a chemical reaction and therefore should be a second order reaction. But it resembles to be a first order reaction due to the presence of reactants in negligible quantity.

Let R` + R“ –> P

Rate = k[A]^{1}[B]^{1}

Order of reaction = 2.

Let us consider another reaction,

CH_{3}Br + OH^{−}→ CH_{3}OH+Br^{−}

Rate law for this reaction is

Rate = k [OH^{−}][CH_{3}Br]

Rate = k [OH^{−}][CH_{3}Br] = k(constant)[CH_{3}Br]=k′[CH_{3}Br]

As only the concentration of CH_{3}Br would change during the reaction, the rate would solely depend upon the changes in the CH_{3}Br reaction.