# First Order Reaction calculation

• Attraction
In summary, the decomposition of AB is a first order reaction with a rate constant of 2.3 x 10^-7 s^-1 at 45oC. Using the equation ln[A]t = -kt x ln[A]0, and a initial concentration of 0.25 M, the concentration after 2.3 minutes can be calculated to be 0.25 M. The equation ln[AB]t = -2.3 x 10^-7 x 138 (seconds) + ln.25 was used to solve for the concentration of AB after 138 seconds, which is equivalent to 2.3 minutes. The final concentration of AB is 0.25 M.
Attraction

## Homework Statement

The decomposition of AB is first order with a k = 2.3 x 10-7 s-1 at 45oC. If the initial concentration is 0.25 M, the concentration after 2.3 min is:

## Homework Equations

ln[A]t = -kt x ln[A]0

## The Attempt at a Solution

I have subbed in the values I have but I am not getting the right answer. I am unable to solve the logarithmic equation and need help there but also need to know if my method is correct.

I have subbed in:

ln[A]t = -2.3 x 10-7 x 138 (seconds) x ln.25

I am getting :

ln[A]t = 4.4 x 10-5

My problem is that I cannot remember how to solve that equation for [A]t. It's been a while since i looked at logarithmic equations. I have done google searches for the past hour and tried a few things but can't solve it. I'm not sure if my method is even correct in the first place.

What is logarithm definition?

YES! I have figured it out. Sometimes I wonder if I have the aptitue to learn this chemistry stuff, but I am doing well so far and I am teaching myself so it's obviously not going to be easy all the way. Anyway.. this was where I left off last time.

ln[AB]t = -2.3 x 10-7 x 138 (seconds) + ln.25
= -1.386

ln[AB]138 = -1.386
[AB] = e-1.386 **This is the step that was killing me, simple logarithmic algebra)**

[AB] = .25M

Now, let's see how I get on with the rest of the problems!

## 1. What is a first order reaction?

A first order reaction is a type of chemical reaction in which the rate of the reaction is directly proportional to the concentration of a single reactant. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases.

## 2. How do you calculate the rate constant for a first order reaction?

The rate constant for a first order reaction can be calculated using the equation k = ln(A0/At)/t, where A0 is the initial concentration of the reactant, At is the concentration of the reactant at a specific time, and t is the time elapsed.

## 3. What is the half-life of a first order reaction?

The half-life of a first order reaction is the amount of time it takes for half of the initial concentration of the reactant to be consumed. It can be calculated using the equation t1/2 = ln(2)/k, where k is the rate constant.

## 4. How can the reaction rate be affected in a first order reaction?

The reaction rate in a first order reaction can be affected by changing the concentration of the reactant, changing the temperature, or adding a catalyst. Increasing the concentration of the reactant or the temperature will increase the reaction rate, while adding a catalyst will decrease the reaction rate.

## 5. Can a first order reaction ever reach completion?

No, a first order reaction can never reach completion. As the concentration of the reactant decreases, the rate of the reaction also decreases, meaning that there will always be some amount of reactant remaining. However, the reaction rate will become increasingly slower as the concentration of the reactant decreases, making it virtually undetectable after a certain amount of time.

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