The reactant concentration in a first-order reaction was 7.60 x 10-2 m after 35.0 s and 5.50 x 10-3 m after 85.0 s. what is the rate constant for this reaction? [express or answer in units of s-1]

5.25*10^-2 s^-1

Explanation:

For a first order reaction the rate of reaction just depends on the concentration of one specie [B] and it’s expressed as  :

if we integrate between the initial concentration and the concentration at any time we get:

Solution:

(equation 1)

You can clear this equation to get a equation for [B] at any time but because we want to estimate k is easier to use this expression.  

In equation 1 we don’t know the value of [B]o so we can’t clear directly to get the value of K, but we know the concentration at two different times. With this information, we can get a system with two mathematical unknowns and two equations that we can solve.

Equations:

(1)

(2)

With  

From (1)  

Replacing this value for on (2) we get  

Organizing

With k equals to