Questions 2013-03-03

Email questions...

"I am having trouble with determining orders of reactions.  I am pretty confused on the entire concept of them.  I am confused on questions like 3-5 on the practice tests.  I also don't understand what it means when the reaction increases by factors."
Some of this confusion may be a result of unfamiliar terminology. First, remember that for our class at this point, the only orders we are going to use are 0, 1, & 2. We determine those orders by changing the concentration of one reagent and seeing how the observed initial rate of the reaction changes. If we double the concentration of "A" {that's changing it by a factor of 2}, the observed initial rate of the reaction will either be unchanged {change by a factor of 2⁰} if the reaction is zero-order with respect to "A", or it will double {change by a factor of 2¹} if the reaction is first-order w.r.t. "A", or it will quadruple {change by a factor of 2²} if the reaction is second-order w.r.t. "A". Textbooks tend to really like just doubling concentrations, but there's nothing magic about multiplying by 2. You could determine the orders of a reaction by dividing the concentrations by 2 {this is also a change by a factor of 2, it's just dividing instead of multiplying}, or multiplying/dividing the concentrations by a factor of 3 or 4 or 72, it should all work the same way.

"I was looking at last spring's old chem exam 2a and for problem number 27 I got a different answer. I believe I did the math right but maybe I didn't. To get t, I did:  ln(1.03)-ln(1.67)/(-3.63x10^-2) and my answer was 14.2 and not 13.3 like you got."
This is a good calculator warning. Most importantly, when you are answering exam questions, show your work clearly and as completely as possible. If you have a calculation clearly set up correctly and just make a math/calculator error, you won't lose as many points as if you don't have your equation clearly set up. For this specific question, be sure to use parentheses on your calculator to make sure the math is being done in the order you intend. In the absence of parentheses, your calculator will evaluate multiplication/division before addition/subtraction, so if I put in the implied parentheses:
ln(1.03) - {ln(1.67)/(-3.63x10^-2)} = 14.2
But we really want that to be:

{ln(1.03) - ln(1.67)} / (-3.63x10^-2) = 13.3

By the way, if you see something on a posted answer key that seems incorrect, please let me know. I think I have everything done correctly on the keys, but there definitely could be some mistakes.

Lab questions...

A couple email questions about lab reports that are due this week...

"Could you give more specifics on how to write the introduction for the lab report. "
The Lab Report Format sheet has been updated on my website to include a bit about Introductions (http://www.drbodwin.com/teaching/genchemlab/labrep2013a.pdf).

The Introduction eases your reader into the content of the lab report. Some instructors and some disciplines don't use Introductions in their lab reports, I like them because they give me an indication of your understanding of the theory behind the experiment rather than just the (sometimes robotic) procedure you performed.

"I am a little confused how to report my final K value.  I got an answer of 176.  Using range over 2, I calculated my error as 57.  Does this mean I should report my K value as 170 +/- 50 because we should only have one sig fig in our error?  I'm also running in to the same problem for my "El".  For example, one of my average El's was 4528.5 +/- 130. My understanding then, is I should report that as 4500 +/- 100?  Also, should I show the work of how I got my original and then round because of significant figures?"
Good attempt at error, you're very close. For the K value, you're good except for the rounding... 57 should round to 60. Your "error digit" here is in the "tens" digit, so you should round your result to the "tens" digit, 176 should round to 180. The result you should report is 180 +/- 60.
Your result for the Beer's Law constant is a good example of an exception to the "rules" we used for the error on K. Let's look at the error part first... your range-over-2 error was 130... for the sake of this discussion, let's say it was really 131.8274 when it displayed on your calculator. We want to round the error to a single digit EXCEPT when that digit is "1". Why is that? Well, every time you round any number, you are accepting or introducing some error in that reported value. When we round a calculated error, we are introducing error into our error. Yikes, this could get out of control! As an example, let's look at 2 cases:
Case 1: You have calculated an error of 944. Rounding that to a single digit (sig fig) gives you 900. You've essentially thrown away 44 out of 944, that's a little under 5%, and we can probably live with that.
Case 2: You have calculated an error of 144. Rounding that to a single digit (sig fig) gives you 100. Now you've thrown away 44 out of 144, that's over 30%. Not good.
So the "rule" for rounding error is "Always round error to a single digit (sig fig), unless that single digit is "1", in which case you should keep two digits (sig figs) of error." Looking back at Case 2, if we round our calculated error of 144 to two digits, we get a rounded error of 140. We've still thrown away 4 out of 144, but that's under 3%, so I think we can live with it. Depending upon the exact values of the numbers and the type of numbers they are, many scientists will advocate for keeping two digits of error if the first digit is "1" or "2"... If you work through a series similar to Case 1 & 2 for values 244, 344, 444, 544, 644, 744, 844 you'll see that the whole idea of "error on error" can be very interesting and can certainly lead to debate... For our purposes in Gen Chem, I think we can stick with "Always round error to a single digit (sig fig), unless that single digit is "1", in which case you should keep two digits (sig figs) of error."
Getting back to your original question, the error in {el} should be rounded to 130, and the reported value should be rounded to the same place the error is rounded, in this case, the "tens" digit again, so this should be reported as 4530+/-130. You ARE planning to include units on that number, right? As for the "show your work" part of your question, the answer is pretty much always yes, although for common (and hopefully trivial) things like taking an average or adding up a series of numbers, you can just say "the average is XXXX" or "the total is XXXXX". Show a sample of how you calculated one of the {el} values (with an appropriate number of sig figs, but don't worry too much about rounding at that point) and then you can report "Average {el} = 4530+/-130". Remember, it's always better to show a little too much detail of your calculation than not enough... When in doubt, show it.
Error (or uncertainty, or variability) is an important tool in our understanding of the experiments we do and it takes practice. Gen Chem is a good place to start practicing. With practice, error becomes very natural and automatic and you'll find that you start estimating error and including error without even thinking about it.

Other questions, let me know...