[Kinetics] Using Rate as a Conversion Factor

In summary: So the answer might be 5.1 x 1025 in one edition, and 5.1 x 1025 in another. There's no way to know for sure.
  • #1
brbrett
35
0

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~
 
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  • #2
brbrett said:

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.
 
  • #3
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... >.>
 
  • #4
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.
 
  • #5
brbrett said:
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.
 

FAQ: [Kinetics] Using Rate as a Conversion Factor

What is kinetics and why is it important in science?

Kinetics is the study of the rates of chemical reactions. It is important in science because it helps us understand how fast a reaction occurs and how different factors, such as temperature and concentration, affect the rate of a reaction.

What is rate and how is it used as a conversion factor in kinetics?

Rate is the measure of how fast a reaction occurs. In kinetics, rate is used as a conversion factor to convert the change in concentration of a reactant or product to the amount of time it takes for that change to occur. This allows us to quantitatively measure the speed of a reaction.

How do you calculate the rate of a reaction using rate as a conversion factor?

The rate of a reaction can be calculated by dividing the change in concentration of a reactant or product by the time it took for that change to occur. This is represented by the equation: rate = ∆[A]/∆t, where ∆[A] is the change in concentration and ∆t is the change in time.

What factors can affect the rate of a reaction?

The rate of a reaction can be affected by several factors, including temperature, concentration of reactants, surface area, and the presence of a catalyst. These factors can either increase or decrease the rate of a reaction.

How is rate used to determine the order of a reaction?

The rate of a reaction is directly related to the concentration of reactants. By measuring the rate of a reaction at different concentrations, the order of the reaction can be determined. The order of a reaction is the power to which the concentration of a reactant is raised in the rate equation.

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