First Order Decomposition -> % of compound. Please help

[lucky_star]

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

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!

 

[lucky_star]

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.

 

[Blueshift5]

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!