Hi, I was wondering if you could possibly help me with this chem question.

For the relatively slow decomposition of NOCL into NO and Cl2 according to the reaction below, it is known that the reaction is second order w/ respect to NOCl and that after 23.4 minutes that 75% of NOCl is decomposed when the initial concentration of NOCl is 0.0732 M. How long (in minutes) would it take until 35.8% of the NOCl has decayed?

2 NOCl ---> 2 NO + Cl2

i think i have to use the integrated law but other than that how would i work this out? Thank you.

1/[A]=(kt + 1)/A null

For a second order reaction, the equation is

(1/A) - (1/Ao) = akt
I think you have Ao, A, a, and t (23.4 min) so you can solve for k (at 75% decomposition).
Then use k in the revised equation. You will have k, A, Ao (for 35.8% decomposition) and a, and you can solve for t. Check my thinking.

To solve this question, you are correct that you need to use the integrated rate law. The integrated rate law for a second-order reaction is:

1/[A] = kt + 1/[A]₀

Where [A] is the concentration of the reactant at a given time, [A]₀ is the initial concentration, k is the rate constant, and t is the time.

In this case, you are given that the reaction is second order with respect to NOCl, so the integrated rate law becomes:

1/[NOCl] = kt + 1/[NOCl]₀

You are also given that after 23.4 minutes, 75% of NOCl is decomposed, which means that only 25% (100% - 75% = 25%) is remaining. Therefore, [NOCl] = 0.25 * [NOCl]₀.

To find the rate constant (k), you can rearrange the equation as follows:

1/0.25[NOCl]₀ = k(23.4 minutes) + 1/[NOCl]₀

Simplifying, you get:

4/[NOCl]₀ = k(23.4 minutes) + 1/[NOCl]₀

Now, you can solve for the rate constant (k) using the given initial concentration ([NOCl]₀) and the time (23.4 minutes).

Once you have the value of the rate constant (k), you can use it in the integrated rate law to find the time needed for 35.8% (100% - 35.8% = 64.2%) of NOCl to decompose.

1/[NOCl] = k * t + 1/[NOCl]₀

Plug in the known values, with [NOCl] = 0.642 * [NOCl]₀ (since 35.8% remains), and solve for t.

This will give you the time (in minutes) until 35.8% of the NOCl has decayed.

Remember to keep track of units and adjust them accordingly during calculations.