CHEMISTRY COMMUNITY

The decomposition of SO2Cl2 has a rate constant of 1.42x10^-4 s^-1 at a certain temperature and has a half
life which is independent of the initial concentration.

(a) How long will it take for the concentration of SO2Cl2 to decrease to 25% of its initial concentration?

t1/2= 0.693/k
so then 0.693/1.42x10^-4 s^-1 =4.88x10^-3 s^-1

(b) How long will it take for the concentration of SO2Cl2 to decrease to 25% of its initial concentration?

- why is it that for 25% of the initial concentration you take 2 half lives? Wouldn't two half lives equal the full reaction? thus decreasing the concentration to 0? Could someone help me sharpen this concept?

how does it change for 50%, 25%, 12:5%? Thank you so much!

Hey there it seems that you are confused about half life.
You just need to apply some math. Half life means that after that amount of time, the initial value will decrease by half. It's like cutting a cookie in half. After one half life, you have half a cookie. After the second half life, you have one fourth of a cookie since you cut the remaining half in half. Do you see it now? So each half life divides the product in half each time. So you go from 100% to 50, 25, and 12.5 and so on and so forth.

Because .25=1/4. 1/4=(1/2)^2. Therefore, to find the "fourth life" you just multiply the half life by 2.

thanks!

Multiplying the half life by 2 to get a "fourth life" would only work with a first order reaction though right?