# Half-life decomposition, find final concentration

• dolpho
In summary, the first order decomposition with a rate constant of 0.03 sec-1 resulted in 0.621 mol/L of the compound remaining after 39 seconds, starting with an initial concentration of 2.00 mol/L. The correct equation for first order reactions is ln(A) = -kt + ln(Ao). To solve for A, the antilogarithm must be taken, which is represented as e^ln(A).
dolpho

## Homework Statement

In a first order decomposition in which the rate constant is 0.03 sec-1, how much of the compound (in mol/L) is left after 39 sec, if there was 2.00 mol/L at the start?

I'm using a few equations and trying to plug it in but I don't know whether they are appropriate or not.

The answer is .621 but I'm not sure how to get there

## Homework Equations

Ln(A(initial) /A(final) = -kt

A(final) = -KT + A(initial)

## The Attempt at a Solution

I've tried plugging into these equations but haven't gotten the right answer yet. Are these the correct equations to use?

dolpho said:

## Homework Equations

Ln(A(initial) /A(final) = -kt

A(final) = -KT + A(initial)

They can't be both right at the same time - one is for the zeroth order reactions.

Which one is for first order reactions?

What is k?

Show details of what you did.

Borek said:
They can't be both right at the same time - one is for the zeroth order reactions.

Which one is for first order reactions?

What is k?

Show details of what you did.

I used the formula ln[A] = -kt + ln[A]o

Ao = unknown
Ao = 2 M
K = .03 sec^-1
t=39 seconds

Ln A = (-.03)(39 seconds) + Ln2
LnA = -.4767 which I can't take the natural log of. I think I'm doing something wrong in the equation but I'm really not sure what :|

dolpho said:
I used the formula ln[A] = -kt + ln[A]o

OK

Ao = unknown
Ao = 2 M

So it is an unknown with a known value? But let's assume it was just a typo.

LnA = -.4767 which I can't take the natural log of.

That's were your thinking got derailed. Why do you want to take a logarithm of logarithm and not an antilogarithm?

Borek said:
OK

So it is an unknown with a known value? But let's assume it was just a typo.

That's were your thinking got derailed. Why do you want to take a logarithm of logarithm and not an antilogarithm?

Yea to be honest logarithms have always been confusing to me. I found out how to get the answer but I used e^(-.4767)

Why would I use the Ln on the 2mol/l and then switch to e, even though the formula has LnA? I don't really get the concept of logs yet :|

Your problem is with math, not with the chemistry.

From the logarithm definitions, if b=ln(A), A=eb. You have calculated ln(A), so the value you are looking for is eln(A).

## 1. What is half-life decomposition?

Half-life decomposition is the process by which a substance breaks down into smaller, more stable components over time. It is a natural phenomenon that occurs in many chemical and radioactive substances.

## 2. How is the half-life of a substance calculated?

The half-life of a substance can be calculated by measuring the time it takes for half of the original amount of the substance to decay. This time period is constant for each substance and can be used to determine the rate of decay.

## 3. What factors can affect the half-life of a substance?

The half-life of a substance can be affected by various factors such as temperature, pressure, and the presence of other chemicals. Environmental conditions and the physical and chemical properties of the substance can also play a role in determining its half-life.

## 4. How can the final concentration of a substance be determined using half-life decomposition?

The final concentration of a substance can be determined by using the half-life of the substance and the initial concentration. By knowing the rate of decay and the amount of time that has passed, the final concentration can be calculated using mathematical equations.

## 5. Are there any practical applications of half-life decomposition?

Yes, half-life decomposition has many practical applications in fields such as medicine, environmental science, and nuclear energy. It is used to determine the shelf life of medications, track the movement of pollutants in the environment, and control the release of energy in nuclear reactions, among other uses.

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