At 100 degrees C , a certain substance undergoes second-order decomposition with a half-life of 26 minutes.

If the initial concentration of the substance is 3.9×10−2M , what is the value of the rate constant at 100degrees C?

So I put in (1560seconds) 1/2 = 1/ k (3.9×10−2M) and end up getting 2.5x10^-5

What am I doing wrong? :[

1560=1/k*3.9E-2

k=1/(1560*3.9E-2)=1/60.84=1.64E-2

I don't think you calculated with Ao in the denominator.

You are most correct, I did not.

Thank you so much.

To solve this problem, you need to use the second-order rate equation and the concept of half-life. Let's break down the steps to find the correct value for the rate constant.

1. First, recognize that the second-order reaction follows the rate equation: rate = k[A]^2. Here, [A] represents the concentration of the substance.

2. You are given the half-life (t1/2) of the reaction, which is 26 minutes or 1560 seconds. The half-life equation for a second-order reaction is: t1/2 = 1 / (k[A]0), where [A]0 is the initial concentration of the substance.

3. Rearrange the half-life equation to solve for k: k = 1 / (t1/2 x [A]0). You will plug in the values for t1/2 (1560 seconds) and [A]0 (3.9×10^−2 M) to find the rate constant k.

Let's do the calculations:
k = 1 / (1560 s x 3.9×10^-2 M)
= 1 / (6.084 × 10^4 s^-1 × M)
≈ 1.6417 × 10^-5 M^-1 s^-1

So, the correct value for the rate constant at 100 degrees C is approximately 1.6417 × 10^-5 M^-1 s^-1.

It looks like you missed the factor of concentration [A], which is squared in the rate equation, when you calculated the rate constant. Make sure to include all the variables correctly to get the accurate result.