Kinetics Homework Help: N2O5 Decomposition @ 70°C

[youxcrushxme]

Hi everyone

I need some help with this problem -

The first order rate constant for the decomposition of N2O5 at 70 degrees celsius is 6.82x10-3 s-1

2N2O5 -> 4NO2 +O2

Suppose we start with 25 mmol of N2O5 in a volume of 2L. How many mmol of N2O5 will remain after 2.5 min?

I'm not sure about what formula I should be using for this. Any help would be appreciated :)

 

[gradeaswimr]

http://www2.wwnorton.com/college/chemistry/gilbert/concepts/chapter14/ch14_3.htm#2

 

[Blueshift5]

Hello,

The formula you should use for this problem is the first-order rate law, which is expressed as:

A = A0 * e^-kt

Where A is the amount of N2O5 remaining at time t, A0 is the initial amount of N2O5, e is the base of natural logarithm, k is the rate constant, and t is the time in seconds.

To solve this problem, we first need to convert 2.5 minutes to seconds, which is 150 seconds. Then, we can plug in the values we know:

A = ? (amount of N2O5 remaining after 2.5 min)
A0 = 25 mmol
k = 6.82x10^-3 s^-1
t = 150 seconds

Now, we can solve for A by rearranging the equation:

A = A0 * e^-kt
A = 25 mmol * e^-(6.82x10^-3 s^-1 * 150 seconds)
A = 25 mmol * e^-1.023
A = 25 mmol * 0.360
A = 9.00 mmol

Therefore, after 2.5 minutes, there will be 9.00 mmol of N2O5 remaining in the 2L volume. I hope this helps! Let me know if you have any further questions.