Analysis of Iron Ore - question

Question from email:

I'm working on the hand in right now and I'm just a little stuck on the % Fe question. I have all of the molarities calculated out. Do I simply take the molarity of the samples and divide them by .100 L for the moles and then go to grams to percent? My percentages just seem so small. I'm getting numbers such as .22% Fe. Or do I use the .050 L instead of .100.

If you break this calculation down into its parts, it's not quite as intimidating as it might seem.
Step 1 - Using your Beer's Law plots, calculate the iron concentration in the orange solutions you made in the second week of lab.
Step 2 - How did you make those orange solutions? You should have made them from 1.00mL of the yellow iron solution you made by dissolving your iron ore sample (red powder) in acid. You can use C₁V₁=C₂V₂ to determine the concentration of iron in the yellow solution.
Step 3 - Once you know the concentration (moles of iron per liter of solution) of the yellow iron solution, you can calculate how many moles of iron are present in that solution. You made 100.0mL of the yellow solution from your red iron ore sample.
Step 4 - If you know how many moles of iron were present in the yellow iron solution, you know how many moles of iron were present in the red iron ore powder. {Hint: they just might be the same...}
Step 5 - You know how many moles of iron were present in the red iron ore sample, using the Periodic Table you can calculate how many grams of iron were in the red iron ore sample.
Step 6 - If you know how many grams of iron were present in the red iron ore sample, and you know the total mass of the red iron or sample, then you should be able to calculate the percent (by mass) of iron that was present in the red iron ore sample.

For the iron ore samples you all analyzed, the percent iron could have been as low as 9-11% or as high as 33-35%. If you get something lower than 9% or higher than 35%, double check your calculations.

Iron Ore assignment

A couple notes on the Iron Ore hand-ins I've seen so far...

1. Include your Beer's Law plot(s). Your entire data analysis depends upon the Beer's Law plot(s) you made (probably in MSExcel) from the data you collected during the first week of the experiment. If you do not include your Beer's Law plot(s) {Absorbance vs. concentration}, you will not earn many points on this assignment.

2. Explain your answers. The answer to a question is (almost) never just "yes" or "no". Explain why "yes" or "no" is the correct answer. Does the sun come up in the east? Yes, because the rotation of the Earth causes the sun to be visible first in the direction humans have defined as "east".

3. Show calculations. This is related to #2. When you "show" calculations, it is helpful to include a little bit of explanation, not just a sea of numbers that appear to be scattered across the page. Similarly, DO NOT SHOW YOUR CALCULATIONS IN PARAGRAPH FORM! If you're looking for an example of "show calculations", check out some of the exam answer keys I have posted on my website {like http://www.drbodwin.com/teaching/exams/c210ke2ak.pdf}. 

This week's assignment...

I just looked over the assignments that have been handed in so far, and I have a couple additional notes:

1. For each combination that reacted during the first week of the experiment, write a balanced chemical equation.  For reactions that formed complex ions, you can just note that the product of the reaction is “complex ion”.  Organize your reactions clearly in the order they appear in the lab manual, starting with all the reactions involving Ni(NO₃)₂(aq), then all the reactions involving Pb(NO₃)₂(aq), etc.
>>If a combination did not react, you do not have to write a reaction. You can write "full formula/molecular equations" or net ionic equations, it's your choice for this experiment.
>>DO NOT WRITE YOUR CHEMICAL EQUATIONS AS ONE BIG PARAGRAPH!! The point of organizing them is to make them easier for you to write them all and for me to follow/read/grade them. If you write them as a massive block of text, I will not read them, and you probably won't earn many points. One equation per line, with appropriate subscripts and/or superscripts, state labels, parentheses, etc.
>>"in the order they appear in the lab manual" is not a joke or a suggestion. If you do not organize your chemical equations in the correct order, I will not spend much time hunting through your randomly-ordered equations to try to find them all. I will assume they are not there and you probably won't earn many points.

2. Identify the contents of each of your unknowns with a brief explanation.  For example, “Unknown M4 contained phosphoric acid because it generated heat when reacting with bases and formed a precipitate with transition metal ions.”
>>Each set of unknowns had a letter AND a number associated with each sample. If you do not identify each unknown with a letter AND a number, it is wrong.

If you've already handed in an assignment and would like to fix some of these problems (that would be a really good idea...), you can turn in a revised assignment. If you choose to turn in a revised assignment, you must very clearly and obviously write or type "PLEASE GRADE THIS ASSIGNMENT AND DISCARD THE PREVIOUS ONE" on your assignment (you might even want to use a highlighter...). If you do not clearly and obviously indicate that you want the "new" assignment graded, I will grade the first assignment that was submitted.

Improving your scores

A few people have express concern over their scores on hand-in assignments for lab. There's definitely room for improvement, but a single low score will not have that much impact on your grade, so keep at it. There are a couple general pointers that I've been giving students to help improve your hand-in scores:

1. Make sure you're answering the questions. I lot of people have been losing points because they're not really answering the question that's being asked, or they're answering part of it without really exploring WHY the answer they're giving is correct. Most of the questions on the hand-ins require a bit of explanation, make sure you're explaining your answers, not just describing an observation. If your answer takes up fewer lines of text than the question, you're probably not answering the question completely. That doesn't mean I want everyone to write a book to answer each question, but you should be trying to answer the whole question.
2. Don't lose points for mechanical reasons. Lots of people are "forgetting" to include graphs or data tables, or just showing a result without showing the calculations that went into that result. {No, your Lab Assistant did not tell you to turn your only copy of the graph in with your carbons...} Assignments must be typed (including formulas, equations, calculations, etc.), if you hand-write your assignment you'll probably get a zero. Circle or highlight your section/lab assistant so I can keep track of different piles of assignments or you'll lose 5 points. Assignments are due at very specific times listed in the course syllabus, repeated late or missing assignments will cost you a LOT of points and you'll very quickly fair the course. Grammar and spelling are important even though this isn't an English class; if your answer is very clear and easy to understand, it's easier to grade.
3. Take advantage of your time in lab. Many students finish the "wet" part of the experiment and then run out the door. If you finish early, make sure that you take a look at the hand-in assignment and discuss the questions and answers with your partner before you leave. If you're not sure about a question, ask.
4. Take advantage of your lab instructor(s). If you're working on a hand-in and you're not sure about what a question is asking or how to interpret your data, ask your instructor. This is more effective if you have a question that shows you put some thought into it, like "I started trying to analyze my data by calculating how many moles of each substance were used in each reaction, and then I calculated the mole fraction. What's the next step?", rather than "I don't understand how to do any of this. Where should I start?"
5. This is similar to #3... Start your assignment early so you have time to ask questions if necessary. If you wait until Tuesday night to work on an assignment that's due at noon on Wednesday, you'll never be able to ask a question and expect to get an answer in time to turn in the assignment on time.

Those are probably the big ones. If everyone did those things, everyone would be getting MUCH better scores on hand-in assignments. Something that students don't often know... It is MUCH MUCH MUCH easier to grade assignments that are correct! I don't ask questions with the intention to be sneaky, or tricky. It's not my goal to see how many points I can take away. I would be giggling with glee if everyone handed in assignments that were mostly (or totally) correct and complete. I really do want you to succeed, but that does not mean that I'm going to give you points or grades that you don't earn by doing the assignments and thinking about the questions you are answering.

"Show your work" and "Explain"

In every field and for every instructor, there are certain instructions and questions that may not be explicitly stated, but are always implied. The two that I see people having the most consistent problems with are:
1. "Show your work" - If you are doing a calculation, you must ALWAYS show your work. If a question asks you to calculate the concentration of a solution, the answer is never just "1.18M". Show how you got to that number. You're doing it anyway, you should show it. If you're not doing it, then you're either "borrowing" an answer from someone else or guessing. Show your work. Sometimes, the way the question is worded might make it seem like you don't have to show your work ("What is the concentration of solution A?"), but you still need to show your work. The only real exception to "show your work" is for exceptionally trivial calculation, like adding up a molar mass (although you still should include the correctly balanced formula for anything you're adding up a molar mass for) or taking an average (if you really want to show the steps in taking an average, that's OK, but "average" is a standard enough operation that I don't require you to show your work). How do you decide if something is trivial or common enough that you don't have to show your work? One quick way to check is if the units have to be changed or transformed during the calculation. If the units change, show your work. When in doubt, show your work. If you're not sure, show your work. Even if you're really brilliant, show your work.
1a. "Show your work" = "Show your units" - This is another one that should be implied... In chemistry, there are a couple quantities that are unitless (pH, equilibrium constants), but the VAST majority of numbers should include units. If you do not show your units, you have not shown your work. Always show units on every number that has them. THE ONLY EXCEPTION is in tabulated data where the units can (and often should) be included in the column heading of the table rather than on each individual number.
2. "Explain" - If science was only used to answer the "what" aspects of our daily lives, it would be pretty boring. Science answers the "what" AND the "why". The "why" is always implied. This is the text analog of "show your work". I do not tend to ask questions that I feel can be answered in 1 word or a short phrase. I want to see an explanation of why the answer you gave makes sense in relation to the data you have collected. This does not mean that you have to write a page and a half to answer every question, but it does mean that a sentence or two (or more) is probably required. Support your answers with meaningful data or other explanations, it makes for a much clearer answer.

Aluminum + HCl experiment assignment

A few people have asked questions that lead me to believe that there may be a little confusion about the assignment that is due for "The Reaction of Aluminum with a Strong Acid".
This semester in Gen Chem Lab I, you will not have to write a full lab report for any of the experiments. Each experiment will have a hand-in assignment provided in MSWord format with questions that you will have to answer. {All answers and calculations must be typed. No exceptions.} For a number of these assignments, there will be a part of a full lab report included as one of the questions, but you will not have to do all the parts of a formal lab report for any single experiment.
The questions that are included in the lab procedure (either inserted in the experiment or at the end of the procedure) do not have to be included or handed in separately, the only things that have to be turned in are your carbons and the hand-in assignment. The questions in the experimental procedure are often similar to the questions on the hand-in, so it's a good idea to jot down some answers to the questions in the procedure while you're in lab, but these do not have to be turned in separately.
To help with some of the questions that might come up, I've posted "Features of a Sample Lab Report Format" (http://www.drbodwin.com/teaching/genchemlab/labrep01.pdf) so you can see what each part of a lab report looks like when you need it. A couple questions or problems that come up are...

Drawing the experimental setup - A drawing can be helpful for complex setups that are difficult to describe well with words. A drawing is a waste of space if the setup can be described effectively and concisely with words. For example: "The test tube was filled approximately half full with the mysterious blue liquid, see figure 1."

Figure 1: A half full test tube

Hopefully this is ridiculous enough to make my point... Is the figure really needed to clearly communicate what a test tube half full of blue liquid looks like? Um, no. The same is true for your "Experimental" section when you eventually have to write one. Don't draw trivial things unless your intent is to be trivial, which should never be your intent in a lab report.

Can I hand draw/write in by hand? - This question often comes up regarding drawing experimental setups and showing sample calculations. The quick answer is... no. Why not? There are a few reasons, but the most important one is for your own reference. If you just leave a big blank space for a hand-drawn experimental setup and then "the dog ate my homework" happens before you turn it in, you have to redraw everything rather than just re-print. Similarly, if later in the semester or year you want to look back at an experiment but you can't find the paper copy that you turned in, opening up the computer file and seeing a big blank box isn't too helpful. This is even more important with calculations, if you write out 2 pages of carefully thought out sample calculations and then spill your coffee (or juice or lasagne) on them, you'll have to re-think and re-write 2 pages of calculations. Just do everything electronically in the first place and at least 4 things will happen: 1) you'll have nice looking assignments; 2) you'll actually catch a few errors you might have missed; 3) you'll never have to re-write a page that gets lost or destroyed; 4) with a little practice, you'll get good at doing all these things electronically. Speaking of calculations...

Do I have to use one of those equation editor thingies or can I just use tabs and spaces to type my sample calculations? - Use an equation editor. They're not that hard to use (with a little practice) and they can make really nice looking equations. If the sample calculation you're trying to show is very simple, it's OK to just type it in-line, for example:

7.3 + 2.9 + 14.82 + 1.4 = 26.4

There's no reason to use an equation editor for that one, it's perfectly clear and clean typed in-line. On the other hand...

(2.635g Cu)(1 mole Cu / 63.546g Cu)(4 moles NH₃ / 1 mole Cu)(1L NH₃(aq) / 2.83 moles NH₃) = 0.0586L NH₃(aq)

Looks horrible and is hard to follow when typed in-line, it would look much better if an equation editor was used:

There are a couple good equation editor options. MSWord has at least one (sometimes 2) built in, Open Office has a good one built in, and the Daum Equation Editor (I got it in the Chrome web store...) also does a good job. As with any software, practice makes these things easier to use.

Good luck and let me know if there are any other questions.

Posting and removing info

A few people have had some questions about info that's posted in D2L, so...

Removing files - The hand-in files will not be removed from D2L before lab. It would usually be a good idea for you to download and read over the hand-in before your lab, but it will be available. I do remove the experimental procedures for 2 reasons:
1. To encourage everyone to read over the experimental procedure before coming to lab, and maybe even take a couple notes on it when you're watching the pre-lab video
2. To discourage people from printing out the experimental procedure over and over and over again. Poor little trees died to make all that paper, I always feel bad when I throw piles of excess printouts in the recycle bins...

Files not opening - D2L is a very helpful system, but sometimes it gets a little grumpy. With the exception of the quizzes, everything that's in D2L is just a link to something that's on my webpage (http://www.drbodwin.com/teaching/genchemlab.php). If a D2L link isn't working, pop over to my webpage and you should be able to find it there. If there's a broken link on my webpage, let me know so I can fix it.

Those were the two big questions that people have had. If there are others, let me know. Good luck in lab this week.

Still some confusion...

Hmm, I think a few people are still confused about what is due this week. Let me try to be very clear so that we all (hopefully) get the same message:

The assignment that is due this week by Wednesday at noon is:
http://www.drbodwin.com/teaching/genchemlab/c150L2012d01DandE1hi1.docx
It's a MSWord document. It needs to be typed. It should be printed and turned in to the assignment box for your lab section located outside HA103. Make sure you indicate your section/room/Lab Assistant. This is the hand-in assignment that is based upon the Data and Error activity we did in lab last week. You do not have to turn in anything else, your lab notebook carbons were turned in before you left lab last week.

There is also a pre-lab quiz due by Wednesday noon. It covers the MSExcel activity that we will be doing this week in lab as well as the safety info you should be looking at.
http://www.drbodwin.com/teaching/genchemlab/c150L2012d02excel1.pdf
http://www.drbodwin.com/teaching/genchemlab/safetyslides01a.pdf
http://www.drbodwin.com/teaching/genchemlab/safetyslides02a.pdf

OK, that might have sounded a little blunt. I wasn't trying to sound grumpy, I just wanted to be as clear as possible to (again, hopefully) avoid any confusion. I know these first couple weeks of lab can be a little busy because we're doing a bunch of different things to get caught up on safety and general lab issues, next week we'll be starting our first "wet" experiment. And yes, it will have the potential to get very wet!

First Lab

CHEM 150L labs will start this week. There have been a few questions, I'll try to answer all of them here:

1. Pre-lab Quiz - As of this morning, there are quite a few people who have not taken the pre-lab quiz. This first quiz is largely on the syllabus and the first week's Data and Error activity. Read these, have them handy, and make sure you take the quiz. Read over the part of the syllabus that describes pre-lab quizzes and the results of not taking them. Skipping quizzes will have a very quick and very negative impact on your grade.

2. A number of people have asked about what to bring to lab. I've moved/copied a couple of things into the "Week 1" content section in D2L that should help... You should print out this week's activity ("Data and Error"), the "Safety Map", and the two "Video Guides". Make sure you print these out BEFORE LAB. To discourage repeated and excessive printing, these links will not be available after NOON WEDNESDAYS. Also, bring your "carbon copy" lab notebook to lab with youand a pen.

2a. If you're a eBook/eReader user, feel free to use electronic versions of the lab procedures on your personal devices. If you choose to use a tablet or eReader in lab, be careful, there are numerous opportunities to spill things that will turn your device into an expensive paperweight.

2b. If you choose to print procedures out on paper, I would encourage you double-side or use 2-pages-per-sheet format.

3. Watch the "Safety Tour (video)". It goes over some of the safety features and/or equipment in the labs you will be in.

4. IF YOU ARE IN DR. MARASINGHE'S CLASS (Wed 2:30pm or Thurs 3:00pm), your class will meet in SL118 to begin class before moving up to the labs (SL302 and SL306)

5. IF YOU ARE IN DR. PROVOST'S CLASS (Thurs 9:00am) OR DR. EDVENSON'S CLASS (Thurs noon), your class will meet in the hallway outside of SL302 and SL306 for a minute before going directly into the labs.

6. Proper Lab Attire - There will be more details on this during some of the safety discussions that we have during the first couple weeks in lab, but there are a couple things to remember: 1) Open-toed shoes are not allowed in lab. The best option for safe lab footwear is probably something like leather (durable and liquids don't soak through), but as long as your footwear is closed-toe it should be OK. 2) Lab coats or aprons are not required, but you are welcome to wear them if you choose.

If there are other questions, let me know. Have a great first week in lab!

CHEM 150L - Fall 2012

Lab info is posted in D2L including your first quiz. Lab will not meet this week, but you should read the syllabus and the activity that we're going to be doing next week before you do the quiz. Good luck and welcome to Fall 2012!

Summer 2012 grades posted

Hmm, not sure I need to say more than what's in the title of the post. I submitted grades to the eServices system, they'll be visible to you whenever all the correct electrons flow through all the correct wires to make the interwebs update to display your grades.

I hope everyone had a useful class this summer, let me know if you have any questions and enjoy the rest of your summer.

Corrections to Exam 4 key

Typing up the key late at night was not a good idea... There were a number of errors on page 4 of the Exam 4 key that I posted this morning. If you already looked at the key or printed it out, throw away page 4 and go get a fresh version. Sorry about that. http://www.drbodwin.com/teaching/exams/c210pe4ak.pdf

Exams posted

All the exams we've taken for the summer 2012 class and their keys are posted on my web page, both on the "General Chemistry" page (http://www.drbodwin.com/teaching/genchem.php) and in the "Exam Archive" (http://www.drbodwin.com/teaching/examarchive.php). Let me know if you have questions.

Redox reactions

We looked at a few redox reactions today in class, some of you wanted the solutions posted. Enjoy.

For each pair of half cells, write the balanced spontaneous (standard) reaction and calculate the spontaneous (standard) cell voltage. {Actually, you'd do the secondpart of that process before you could do the first part}

Cu⁺¹|Cu (E⁰_red= +0.521V) and Fe³⁺|Fe²⁺(E⁰_red= +0.771V)

Cu half must be reversed to be the oxidation half rxn

E⁰_cell = E⁰_red+ E⁰_ox = 0.771V + (-0.521V) = +0.250V

Cu(s) ⇄ Cu⁺¹(aq) + 1e^⊖(aq)

1e^⊖ + Fe³⁺(aq) ⇄ Fe²⁺(aq)

------------------------------------------------------------------

Cu(s) + Fe³⁺(aq) ⇄ Fe²⁺(aq) + Cu⁺¹(aq)

BrO₃^-1|Br₂(E⁰_red= +1.478V) and Pt²⁺|Pt (E⁰_red= +1.188V)

Pt half must be reverse to be the oxidation half rxn

E⁰_cell = E⁰_red+ E⁰_ox = 1.478V + (-1.188V) = +0.290V

5 { Pt(s) ⇄ Pt⁺²(aq) + 2e^⊖(aq) }

12 H^⊕(aq) + 10e^⊖(aq) + 2 BrO₃^-1(aq) ⇄ Br₂(l) + 6 H₂O(l)

------------------------------------------------------------------

12 H^⊕(aq) + 5 Pt(s) + 2 BrO₃^-1(aq) ⇄ Br₂(l) + 5 Pt⁺²(aq) + 6 H₂O(l)

Cr⁺²|Cr (E⁰_red= -0.403V) and Pb⁺⁴|Pb⁺²(E⁰_red= +1.69V)

Cr half must be reverse to be the oxidation half rxn

E⁰_cell = E⁰_red+ E⁰_ox = 1.69V + (0.403V) = +2.09V

Cr(s) ⇄ Cr⁺²(aq) + 2e^⊖(aq)

2e^⊖ + Pb⁺⁴(aq) ⇄ Pb⁺²(aq)

------------------------------------------------------------------

Cr(s) + Pb⁺⁴(aq) ⇄ Pb²⁺(aq) + Cr⁺²(aq)

TeO₂|Te (E⁰_red= +0.604V) and Se|H₂Se (E⁰_red= -0.115V)

Se half must be reverse to be the oxidation half rxn

E⁰_cell = E⁰_red+ E⁰_ox = 0.604V + (0.115V) = +0.719V

2 { H₂Se(aq) ⇄ Se(s) + 2e^⊖(aq) + 2 H^⊕(aq) }

4 H^⊕(aq) + 4e^⊖ + TeO₂(s) ⇄ Te(s) + 2 H₂O(l)

------------------------------------------------------------------

4 H^⊕(aq) + 2 H₂Se(aq) + TeO₂(s) ⇄ Te(s) + 2 Se(s) + 4 H^⊕(aq) + 2 H₂O(l)

2 H₂Se(aq) + TeO₂(s) ⇄ Te(s) + 2 Se(s) + 2 H₂O(l)

MnO₄^-1|Mn⁺²(E⁰_red= +1.23V) and ClO₄^-1|ClO₃^-1(E⁰_red= +1.201V)

Cl half must be reverse to be the oxidation half rxn

E⁰_cell = E⁰_red+ E⁰_ox = 1.23V + (-1.201V) = +0.03V

5 { H₂O(l) + ClO₃^-1(aq) ⇄ ClO₄^-1(aq) + 2e^⊖(aq) + 2 H^⊕(aq) }

2 { 8 H^⊕(aq) + 5e^⊖ + MnO₄^-1(aq) ⇄ Mn²⁺(aq) + 4 H₂O(l) }

------------------------------------------------------------------

616H^⊕(aq) + 5 H₂O(l) + 2 MnO₄^-1(aq) + 5 ClO₃^-1(aq) ⇄ 5 ClO₄^-1(aq) + 2 Mn²⁺(aq) + 38H₂O(l) + 10 H^⊕(aq)

6 H^⊕(aq) + 5 H₂O(l) + 2 MnO₄^-1(aq) + 5 ClO₃^-1(aq) ⇄ 5 ClO₄^-1(aq) + 2 Mn²⁺(aq) + 3 H₂O(l)

Titrations are AWESOME!!

We looked at titrations today. Remember, titrations are just stoichiometry problems applied to a specific system/type of problem, they're not completely new information, approach them the same way you would approach any other stoichiometry problem:

1. Write a balanced chemical equation

2. Convert whatever you know the most about to moles

3. Using the mole ratio from the balanced chemical equation, convert moles of what you know to moles of what you're looking for

4. Convert moles of what you're looking for into whatever you want to know about it (grams, volume, concentration, etc.)

5. Check that your answer is reasonable (if possible)

On to today's problems...

30.00mL of 0.713M HNO₂(aq) is titrated to the equivalence point with 28.43mL of NaOH(aq) of an unknown concentration. What is the concentration of the NaOH(aq) stock solution? What was the pH of the HNO₂(aq) solution before the titration begins? What is the pH at the equivalence point? {K_a(HNO₂) = 4.0x10^-4}

HNO₂(aq) + NaOH(aq) ⇄ H₂O(l) + NaNO₂(aq)

(0.03000L HNO₂(aq)) (0.713M HNO₂(aq)) = 0.02139mols HNO₂

(0.02139mols HNO₂) (1mol NaOH / 1mol HNO₂) = 0.02139mols NaOH

(0.02139mols NaOH) / (0.02843L NaOH(aq)) = 0.752M NaOH(aq)

NaOH(aq) should be slightly more concentrated than HNO₂(aq), so this answer is reasonable

Before the titration begins, this is an aqueous solution of a weak acid, so we can calculate the pH using a K_a-type approach. Setting up a table...

	HNO2(aq) +	H2O(l) ⇄	H3O+(aq) +	NO2-1(aq)
[ ]initial	0.713M	XXXX	0	0
Δ[ ]	- x	XXXX	+ x	+ x
[ ]equilibrium	(0.713 – x) M	XXXX	x M	x M

Assuming that “x” is much less than 0.713, the K_a expression simplifies to:

K_a = (x)(x) / (0.713) = 4.0x10^-4

x = 0.01689 = [H₃O⁺]

pH = -log[H₃O⁺] = -log(0.01689) = 1.77

At the equivalence point, all of the HNO₂(aq) that was originally in the reaction has reacted with OH^-1(aq) to form nitrite ions, NO₂^-1(aq). The titration started with:

(0.03000L HNO₂(aq)) (0.713M HNO₂(aq)) = 0.02139mols HNO₂

So at the equivalence point we have a solution that contains 0.02139mols of NO₂^-1(aq) in (30.00mL + 28.43mL = 58.43mL) of solution. The concentration of NO₂^-1(aq) at the equivalence point is:

(0.02139mols of NO₂^-1(aq)) / (0.05843L) = 0.3659M NO₂^-1(aq)

This can now be plugged in to a K_b-type equilibrium to solve...

	NO2-1(aq) +	H2O(l) ⇄	OH-1(aq) +	HNO2(aq)
[ ]initial	0.3659M	XXXX	0	0
Δ[ ]	- x	XXXX	+ x	+ x
[ ]equilibrium	(0.3659 – x) M	XXXX	x M	x M

Assuming that “x” is much less than 0.3659, the K_b expression simplifies to:

K_b = (x)(x) / (0.3659) = 2.5x10^-11

x = 3.02x10^-6 = [OH^-1]

pOH = -log[OH^-1] = -log(3.02x10^-6) = 5.519

pH = 14 – 5.519 = 8.48

15.00mL of sulfurous acid of unknown concentration is titrated to the second equivalence point with 23.18mL of 0.332M NaOH(aq). What is the concentration of the sulfurous acid stock solution?

H₂SO₃(aq) + 2 NaOH(aq) ⇄ H₂O(l) + Na₂SO₃(aq)

(0.02318L NaOH(aq)) (0.332M NaOH(aq)) = 7.696x10^-3mols NaOH

(7.696x10^-3mols NaOH) (1mol H₂SO₃/ 2mol NaOH) = 3.848x10^-3mols H₂SO₃

(3.848x10^-3mols H₂SO₃) / (0.01500L H₂SO₃(aq)) = 0.257M H₂SO₃(aq)

NaOH(aq) should be slightly more concentrated than H₂SO₃(aq), so this answer is reasonable

I'll be in tomorrow morning, let me know if you have any questions.

Crunching through K_a problems...

4. What is the expected pH of a 2.49M solution of acetic acid {K_a= 1.8x10^-5}? What is the expected pH when 100.0mL of this solution is combined with 100.0mL of water? Assume volumes are additive.

This is a K_a-type equilibrium problem, organize the information using a table.

	HC2H3O2(aq) +	H2O(l) ⇄	H3O+(aq) +	C2H3O2-1(aq)
[ ]initial	2.49 M	XXXX	0 M	0 M
Δ[ ]	- x	XXXX	+ x	+ x
[ ]equilibrium	(2.49 – x) M	XXXX	x M	x M

Assume “x” is much smaller than 2.49, plug in to the equilibrium constant expression...

x = 6.69x10^-3 = [H₃O⁺¹]

Assumption is good.

pH = -log[H₃O⁺¹] = -log(6.69x10^-3) = 2.174

For the second part, the set-up is the same, the only difference is that the initial concentration of acetic acid has been diluted. Calculating the dilution...

C₁V₁= C₂V₂

(2.49M)(100.0mL) = C₂(200.0mL)

C₂= 1.245M

Plug in and solve the same way:

x = 4.73x10^-3 = [H₃O⁺¹]

Assumption is still good.

pH = -log[H₃O⁺¹] = -log(4.73x10^-3) = 2.325

5. A 1.83M solution of a weak, monoprotic acid {HA(aq)} has a pH of 3.48. What is the K_a of this acid?

We can approach this as a K_a-type equilibrium problem as well, organize the information using a table.

	HA(aq) +	H2O(l) ⇄	H3O+(aq) +	A-1(aq)
[ ]initial	1.83 M	XXXX	0 M	0 M
Δ[ ]	- x	XXXX	+ x	+ x
[ ]equilibrium	(1.83 – x) M	XXXX	x M	x M

In this case, we are given a pH, which gives us a way to calculate [H₃O⁺], which gives us “x”...

[H₃O⁺] = 10^-pH = 10^-3.48 = 3.3113x10^-4 (Assumption is good.)

K_a= (3.3113x10^-4)(3.3113x10^-4) / (1.83) = 5.99x10^-8

6. You have combined 100.0mL of 2.84M hydrofluoric acid {K_a = 6.8x10^-4} and 100.0mL of 2.19M fluoride ions. What is the expected pH of the resulting solution? Assume volumes are additive.

Again, we can approach this as a K_a-type equilibrium problem (Noticing a pattern here?), organize the information using a table.

	HF(aq) +	H2O(l) ⇄	H3O+(aq) +	F-1(aq)
[ ]initial	1.42 M	XXXX	0 M	1.095 M
Δ[ ]	- x	XXXX	+ x	+ x
[ ]equilibrium	(1.42 – x) M	XXXX	x M	(1.095 + x) M

A couple little adjustments in this case... the original concentrations given in the problem have to be diluted to get the “initial” concentrations in the table. The other key difference here is that we're starting out with a mixture of reactants and products. That might clutter up the math a little bit, but it doesn't really change the way we approach the problem. To simplify things, let's assume that “x” is small compared to both 1.42 and 1.095. Then the K_a expression is:

6.8x10^-4= (x)(1.095) / (1.42)

x = 8.818x10^-4

Assumption is good.

pH = -log[H₃O⁺¹] = -log(8.818x10^-4) = 3.055

Problem 3 (2012-07-09)

14.78g PCl₅(g) and 10.15g O₂(g) are combined in a 1.500L vessel and reach equilibrium with POCl₃(g) and ClO(g). If K = 8.53x10^-9, find all equilibrium concentrations.

	2 PCl5(g) +	3 O2(g) ⇄	2 POCl3(g) +	4 ClO(g)
[ ]initial	(14.78g / 208.239g/mol) / 1.500L = 0.047317M	(10.15g / 31.998g/mol) / 1.500L = 0.21147M	0 M	0 M
Δ [ ]	– 2x M	– 3x	+ 2x	+ 4x M
[ ]equilibrium	(0.047317 – 2x) M	(0.21147 – 3x) M	2x M	4x M

Plugging in to the equilibrium constant expression...

Solving this directly would be rough, so let's try a simplifying approximation. Since the equilibrium is quite reactant-favored, we can assume that 2x is small compared to 0.047317 and 3x is small compared to 0.21147. We need to check this later, but that will simplify the equilibrium constant expression to:

x⁶ = 1.76376x10^-16

x = 0.002368

BEFORE WE GO ANY FARTHER, CHECK THE ASSUMPTION WE MADE!! 2x = 0.0047, this is (0.0047/0.047317)*100 = 9.9%. This is a little too high for this assumption to work well. Oops. Don't worry, I don't expect anyone to solve a 6^th order polynomial on an exam, these numbers are a little off because I made this problem up during class. For numbers that work, try using K = 8.53x10^-12. , then x = 7.489x10^-4 and the assumption is OK. If you'd like to know how to solve the original problem, you could use the method of successive approximations, this was how I had to treat these problems when I was an undergrad taking Gen Chem.

Exam tomorrow, if you have questions let me know, I should be online until at least 7 or 8pm tonight.

Exam 1 and Key posted

Exam 1a and the key are posted at http://www.drbodwin.com/teaching/genchem.php, also linked in the exam archive.  


Enjoy the lovely weekend.

Second in-class problem from 2012-07-05

1.92M NF₃(g) + 1.63M O₂(g) → NOF₃(g) K_eq=1.74x10⁹, find all [ ]_eq

	2 NF3(g) +	O2(g) ⇄	2 NOF3(g)
[ ]initial	1.92 M	1.63 M	0 M
Δ [ ]	- 2x M	- x M	+ 2x M
[ ]equilibrium	(1.92 – 2x) M	(1.63 – 2x) M	2x M

Plugging in to the equilibrium constant expression, this would get ugly pretty quickly. Let's try to simplify it with an approximation. Since K_eqis quite product-favored, we can probably assume that the limiting reagent is essentially used up to form (almost) the theoretical yield of product. From the balanced chemical equation, we need 2 NF₃(g) for each O₂(g), but we didn't start with twice as much NF₃(g), so that must be the limiting reactant. For every mole of NF₃(g) that reacts, 1 mol of NOF₃(g) is formed, so the equilibrium concentration of NOF₃(g) will be (just a tiny bit less than) 1.92M. To make (just a tiny bit less than) 1.92M NOF₃(g), we need halfthat amount of O₂(g), so to reach equilibrium we will consume (very close to) 0.96M O₂(g), leaving (1.63M – 0.96M = 0.67M) of O₂(g) at equilibrium.

{NOTE: If you prefer, you could explicitly calculate this out using our standard 4-step process for limiting reactants/theoretical yields by assuming a volume. I'd assume 1L to make the calculations easier.}

We can now start with a fresh table to organize our information...

	2 NF3(g) +	O2(g) ⇄	2 NOF3(g)
[ ]equilibrium	“a tiny bit”	0.67 M	1.92 M

Now we can plug into the equilibrium constant expression:

Solving, “a tiny bit” = 5.62x10^-5M. Make sure you always CHECK YOUR ASSUMPTIONS! In this case, yes, 5.62x10^-5 is indeed very small compared to 1.92, so the assumption is valid. One of the nice things about equilibrium problems is that you can always plug your results back in to the equilibrium constant expression and see if you get an answer that's close to what's given in the problem. In this case...

(1.92)² / {5.62x10^-5)²(0.67) = 1.742x10⁹

So...

[NF₃]_eq= 5.62x10^-5 M

[O₂]_eq= 0.67M

[NOF₃]_eq= 1.92M

First in-class problem from 2012-07-05

2.63M NOCl₂(g) → NO(g) + Cl₂(g) K=0.118, find all [ ]_eq

	NOCl2(g) ⇄	NO(g) +	Cl2(g)
[ ]initial	2.63 M	0 M	0 M
Δ [ ]	- x M	+ x M	+ x M
[ ]equilibrium	(2.63 – x) M	x M	x M

Plugging in to the equilibrium constant expression...

Because the value of K is not exceptionally large or exceptionally small, this one will probably require working through the quadratic. Breaking it down in steps...

(x)(x) = 0.118(2.63-x)

x² = 0.31034 – 0.118x

x² + 0.118x + (-0.31034) = 0

Plugging in to the quadratic formula:

NOTE: The other root is negative, it doesn't work in this problem.

[NOCl₂]_eq= 2.63 – 0.50 = 2.13M

[NO]_eq = x = 0.501M

[Cl₂]_eq= x = 0.501M