[Kinetics] Using Rate as a Conversion Factor

[brbrett]

Homework Statement

Certain pollutants encourage the following decomposition of ozone: 2O ₃(g) -> 3O ₂(g), at a rate of 6.5 x 10^-4 M O ₃/s. How many molecules of O2 gas are formed in each litre of atmosphere every day by this process? (As this problem provides a rate in units of mol/L/s and requires molecules/L as an answer, we can simply leave the unit "L" in the denominator the entire time.)

Homework Equations

Stoichiometry, mole conversions, Mole concentration (molarity)

The Attempt at a Solution

2O ₃(g) -> 3O ₂(g)
6.5 E 23 * 3/2 = 0.000975molO₂
0.000975moleO₂/s * 6.02*1023/1mol * 86400/day = 5.071248 E 25
This answer is not correct according to my book. The book says the answer is 5.1 * 1025 molecules/L. Not sure why they didn't mention days in the answer, considering how that is part of the question.

I appreciate any help! I only just started learning this, and may have forgotten something regarding stoichiometry since I haven't done it for a couple of months. Please avoid telling the steps, since I want to understand it~

 

[Dr Uma Sharma]

Homework Statement

How many molecules of O2 gas are formed in each litre of atmosphere every day by this process? (As this problem provides a rate in units of mol/L/s and requires molecules/L as an answer, we can simply leave the unit "L" in the denominator the entire time.)

The Attempt at a Solution

2O ₃(g) -> 3O ₂(g)
6.5 E 23 * 3/2 = 0.000975molO₂
0.000975moleO₂/s * 6.02*1023/1mol * 86400/day = 5.071248 E 25
This answer is not correct according to my book. The book says the answer is 5.1 * 1025 molecules/L. Not sure why they didn't mention days in the answer, considering how that is part of the question.
~

so I think the problem is with the units only? numerically your answer is same as the answer given in the book .Your attempt is also right ..
First you calculated the moles of O2 released per L in one second.Then you converted it for per day.You can drop the unit of time ..because they are asking in one day how many molecules of gas is released per L ...in the book answer provided is in molecules /L in one day.

 

[brbrett]

I did think I was right. Just looked, and it seems there is a typo in the book. It says 5.1 x 1025, but if you change it to 5.1 x 10^25, it matches my answer (or close enough anyways). Gotta love it when textbook answers aren't proofread... >.>

 

[Dr Uma Sharma]

some how I thought it as a typo error on this forum ...I thought you are asking why they did not use per day in the unit.

 

[Mark44]

I did think I was right. Just looked, and it seems there is a typo in the book. It says 5.1 x 1025, but if you change it to 5.1 x 10^25, it matches my answer (or close enough anyways). Gotta love it when textbook answers aren't proofread... >.>

I'm almost certain that the 5.1 x 1025 in your book is a typo. Their answer is a bit over 5000, and I doubt anyone would write that number as 5.1 x 1025. 5.1 x 10²⁵ makes sense to me.

Lots of science and math books have incorrect answers, especially the more advanced ones. I've seen books that had the text formatted in one edition, but in a later edition, someone dropped the ball on formatting.