How Do You Calculate the Rate Constant for a First Order Reaction?

[helpimstuck]

I have a first order reaction that after 35 minutes 33.8% of the reactant remains, i am trying to find out the rate constant k from these two figures but i am rubbish at physical chemisty can anyone point me in the wright direction please?

 

[GCT]

use the half life equation...

 

[Blueshift5]

First of all, don't worry, physical chemistry can be challenging for many people. Let's break down the information we have and use the first order reaction equation to find the rate constant.

We know that the reaction is first order, which means the rate of the reaction is directly proportional to the concentration of the reactant. This can be expressed as:

Rate = k[A]

Where k is the rate constant and [A] is the concentration of the reactant.

We also know that after 35 minutes, 33.8% of the reactant remains. This means that 66.2% of the reactant has been consumed, or in other words, the concentration has decreased by a factor of 0.662.

Now, we can plug in these values into the first order reaction equation:

Rate = k[A]
0.662[A0] = k[A0]

Where [A0] is the initial concentration of the reactant.

We can simplify this equation to:

0.662 = e^(-kt)

Where t is the time in minutes.

To solve for k, we can take the natural logarithm of both sides:

ln(0.662) = -kt
k = -ln(0.662) / t

Substituting the given time of 35 minutes, we get:

k = -ln(0.662) / 35 minutes = 0.0054 minutes^-1

So the rate constant for this first order reaction is 0.0054 minutes^-1. I hope this helps guide you in the right direction. Remember, practice makes perfect, so keep working on those physical chemistry problems!