Heyy, okay I have this chemistry assingmnet and its on kinetics, and I got every single one except this one question and I've been trying for over an hour. I know that I'm probably jus tmissing something but everything I've tried doesnt work. Any help is greatly apprecaited. The question is:
A compound decomposes via a first-order reaction. After a period of 932 minutes at 25°C, 25.6% of the compound was found to have decomposed. If 78.2 g of the compound was originally present, what mass would remain after a further 932 minutes?
Thanks in advance
If 25.6% decomposes in the first 932 minutes, I think 25.6% more will decompose in the next 932 minutes. Check my thinking. That would mean 78.2 - 25.6% - 25.6% = about 43 grams.
To confirm that
ln(No/N)=kt
Plug in No = 78.2
N= 78.2 - 25.6% = 58.18
solve for k
t = 932 min.
THEN use the same formula and plug in No = 58.18
solve for N
you know k
t = 932 min.
Should give the same about 43 g.
Let me know if you have problems with this.
Ahhh, see I was thinking the same thing but I was making it more complicated trying to use the equations, and when I did solve for K I seemed to have divded instead of subtracted...that will do it. Thanks alot!
You're welcome! I'm glad I could help.
It's easy to make small mistakes when solving problems, especially when dealing with equations. It's important to carefully read the question and understand what information is given and what is being asked for.
In this case, you correctly identified that it is a first-order reaction and that 25.6% of the compound decomposes in the first 932 minutes. The idea that an additional 25.6% would decompose in the next 932 minutes is also correct.
To find the amount that remains after a further 932 minutes, you subtract the decomposed amount (25.6%) from the initial amount (78.2 g). So, 78.2 g - 25.6% - 25.6% = 78.2 g - 2 * 25.6% = 78.2 g - 51.2% = 78.2 g - 0.512 * 78.2 g = 78.2 g - 40.06 g ≈ 38.14 g.
To confirm this result, you can use the first-order reaction kinetics formula: ln(No/N) = kt, where No is the initial amount, N is the amount remaining, k is the rate constant, and t is the time.
Using the initial amount No = 78.2 g and the decomposed amount N = 58.18 g (calculated earlier), you can solve for k. Plug in these values and the time t = 932 minutes into the equation, and solve for k.
Once you have the value of k, you can use the same formula to find the amount remaining after the second 932 minutes. This time, use the value of N = 58.18 g, the calculated value of k, and the time t = 932 minutes.
Both calculations should give you approximately 38.14 g, confirming your earlier result.
Remember to double-check your work and ensure that you're using the correct calculations and formulas. Good luck with your assignment!