# First Order Decomposition -> % of compound. Please help

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In summary, the constant for a first order decomposition is 0.00313 sec-1. After 7.17 minutes, the percentage of the compound that has decomposed can be found using the equation rate = ln[A]o - ln[A]t = kt.
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## Homework Statement

In a first order decomposition, the constant is 0.00313 sec-1. What percentage of the compound has decomposed after 7.17 minutes?

## Homework Equations

rate = ln[A]o - ln[A]t = kt

## The Attempt at a Solution

I feel bad because I have no idea how to solve this problem. My 1st test is soon to come, please help me!

Oh, please ignore this message because I got the answer already. After talking with my friend for awhile, I finally understand how to work this problem out. I am sorry if I ever bother you.

First, let's define some terms. First order decomposition refers to a chemical reaction in which the rate of decomposition is directly proportional to the concentration of the compound. The constant, k, is known as the rate constant and is specific to the particular reaction being studied. In this case, the rate constant is 0.00313 sec-1.

To solve this problem, we can use the first order decomposition equation:

rate = ln[A]o - ln[A]t = kt

Where [A]o is the initial concentration of the compound and [A]t is the concentration at time t. We can rearrange this equation to solve for [A]t:

[A]t = [A]o * e^(-kt)

Now, we can plug in the values given in the problem. We know that the initial concentration, [A]o, is 100% or 1. So, we have:

[A]t = 1 * e^(-0.00313*7.17*60)

[A]t = 0.931 or 93.1%

Therefore, after 7.17 minutes, approximately 93.1% of the compound has decomposed. I hope this helps! Remember, practice makes perfect, so keep studying and good luck on your test!

## 1. What is first order decomposition?

First order decomposition refers to a chemical reaction in which a compound breaks down into simpler substances at a constant rate. This type of reaction is often characterized by a half-life, which is the time it takes for half of the original compound to decompose.

## 2. How is the percentage of compound determined during first order decomposition?

The percentage of compound remaining during first order decomposition can be calculated using the following equation: [A]t = [A]0 * e^(-kt), where [A]t is the concentration of the compound at a given time, [A]0 is the initial concentration, k is the reaction rate constant, and t is the time elapsed.

## 3. What factors can affect the rate of first order decomposition?

The rate of first order decomposition can be influenced by factors such as temperature, concentration of the reactants, presence of catalysts, and the nature of the compound being decomposed. Higher temperatures and higher concentrations generally result in faster decomposition, while the presence of a catalyst can increase the rate of the reaction.

## 4. How does first order decomposition differ from other types of chemical reactions?

First order decomposition is a type of unimolecular reaction, meaning it involves the decomposition of a single molecule. Other types of reactions include bimolecular reactions, which involve the collision of two molecules, and termolecular reactions, which involve three molecules.

## 5. What are some real-life applications of first order decomposition?

First order decomposition is commonly used to model the decay of radioactive substances, as well as the breakdown of drugs and other compounds in biological systems. It also has practical applications in industries such as food preservation and waste management.

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