0

Guest

Courses New

Derive the rate kinetics of any second order reaction

Derive the rate kinetics of any second order reaction

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
 

A second-order reaction depends on the concentrations of one second-order reactant, or two first-order reactants.

For a second order reaction, its reaction rate is given by:

\ -\frac{d[A]}{dt} = 2k[B]^2 or \ -\frac{d[A]}{dt} = k[A][B] or \ -\frac{d[A]}{dt} = 2k[A]^2

In several popular kinetics books, the definition of the rate law for second-order reactions is -\frac{d[A]}{dt} = k[A]^2. Conflating the 2 inside the constant for the first, derivative, form will only make it required in the second, integrated form (presented below). The option of keeping the 2 out of the constant in the derivative form is considered more correct, as it is almost always used in peer-reviewed literature, tables of rate constants, and simulation software.[8]

The integrated second-order rate laws are respectively

\frac{1}{[A]} = \frac{1}{[A]_0} + kt

or

\frac{[A]}{[B]} = \frac{[A]_0}{[B]_0} e^{([A]_0 - [B]_0)kt}

[A]0 and [B]0 must be different to obtain that integrated equation.

The half-life equation for a second-order reaction dependent on one second-order reactant is \ t_ \frac{1}{2} = \frac{1}{k[A]_0}. For a second-order reaction half-lives progressively double.

Another way to present the above rate laws is to take the log of both sides: \ln{}r = \ln{}k + 2\ln\left[A\right]

Examples of a Second-order reaction
  • 2\mbox{NO}_2(g) \rightarrow \; 2\mbox{NO}(g) + \mbox{O}_2(g)
 
Regards
Arun

Think You Can Provide A Better Answer ?

Other Related Questions on Physical Chemistry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More