The following reaction was monitored as a function of time: AB-->A+B A plot of 1/AB versus time yields a straight line with slope 5.5 * 10^-2 (M?s)^-1.

What is the half-life when the initial concentration is 0.58 M ?

If the initial concentration of AB is 0.240 M , and the reaction mixture initially contains no products, what are the concentrations of A and B after 80s ?

half-life = 31.3 s

0.123 M A, 0.123 M B

Explanation:

When they tell us that a graph of 1 /[AB] versus time yields a straight line, they are telling us that the reaction is first order repect to AB.

A first order rection has a form:

rate = - ΔA/Δt = - k[A]²

The integrated rate law for this equation from calculus is:

1/[A]t = kt+ 1/[A]₀

which we see is the equation of a line with slope k and y intercept 1/[A]₀

Therefore k = 5.5 10⁻² /Ms

The above equation can rewritten as:

1/ (1/2 [A]₀) = k t1/2 + 1/[A]₀

2/[A]₀ = k t1/2 + 1/[A]₀

and the half life will be given by:

t 1/2 =  1 / k[A]₀

t 1/2  = 1 / [( 5.5 x 10⁻² /Ms ) x 0.58 M]

t 1/2  = 31.3 s

For the second part we make use of the equation from above:

1/[A]t = kt+ 1/[A]₀

to determine [A]t, and from the stoichiometry of the reaction we will calculate how much of A and B has been produced.

1/[A]t =  ( 5.5 x 10⁻²/Ms) x 80s + 1/0.240 M

1/[A]t = 4.40 / M +  4.167 / M = 8.56 / M

⇒ [A]t = 0.117 M

If after 80 seconds we have 0.117 M of AB, this means  (0.240 - 0.117)  of AB reacted to produce 0.123 M of A and .123 M of B.

It maybe a bit confusing that we almost have half of our original concentration of AB, and from the first part we know the half-life was 31.3 s.

But, you have to realize that the half-life for second order reactions depend on the initial concentration ( different from first order ). Calculating the half life in this part with an original concentration of 0.240 M gives us a half-life of 75.8 s which makes sense with our result.

why do the isotopes of a particular element behave differently in nuclear reactions but the same in chemical reactions? chemical reactions involve changes to electrons in an atom; isotopes do not differ in electrons, and so they react the same way during chemical changes.

because of all the things that happen around the us, many people get into arguments which sadly could get physical, but we should actually make a change for that.