[slwJAMS]

i am doing a kenetic factor homework problem and i was givin the k, the t, and the initial concentration. i don't understand why my book changed the equation around the way they did.

origional 2nd order rate law equation:

 1  _  1 = kt
[A]   [A]₀

to solve for the ending concentration, my book swiched it around like this:

[A]= [A]₀
     1+[A]₀kt


why is the initial rate on both the top and the bottom? i'm puzzled.

[Rabn]

solve the original equation for [A]..what happens? It isn't magic, it's algebra.

[slwJAMS]

yeah i know. but the way i would rearrange it isnt that equation.

i would usually use the origional equation and solve it algebraically and i wasnt getting the same answer. if i were to rearrange it, this is how i would have done it:

[A]= 1/(kt + 1/[A]₀)

wait. now im getting the right answer. and i type it into my calculator step by step and not all at once. but what i'm still seeing is that initial concentration ([A]₀) not on the top and bottom like the equation that my book gave me.

[Rabn]

The first step in solving for [A] is to add (1/[A]₀) to the right side.  To get the equation in your book, give the term on the right side a common denominator and invert both sides.  That gives you the equation in the book.