[jennatbee]

Hello!
I've never posted here (or any forum, for that matter) so forgive me if I do something wrong or against "netiquette."
I recently took an exam in my analytical chemistry class and am confused about several of the problems I got wrong. Unfortunately, my professor is not very approachable or helpful. (In fact he said if we come to him for a regrade he'll take more points off than he gives back). 
I admit I'm also suspicious of a few of his answers on the key, so I'm hoping you all here can help me either understand it. 

I know this is long so I'm hoping to break it up so it's easy to follow.  If you can answer even just one part of the my post (one question below) I would greatly appreciate it!!

First question:
1) Shown below is a separation of a mixture of two components.  The separation achieved a resolution of 1.5 and the two retention times were 100 and 112, as shown. 

(Here he showed an image.. I have a screenshot because it's from the ebook, but I can't figure out how to a add it.  It is very simple, two peaks and it says resolution = 1.50.  Shows 6sigma between the peaks.  Then he added to retention times, 100 and 112 sec.)

How many plates were achieved in this separation?

--I understood that resolution = delta tr / wav so I found that the average width (wav) = 8 sec.  I became stuck on the exam because I couldn't remember any equations that relate average width to something useful for number of plates.  My professor used w = 4sigma to find sigma then used that in N =tr^2/sigma^2.
I had not seen any problem that does this before, so my question is: can you use an average width in place of width to find number of plates for the separation?  His key also lists two answers because he used each retention time and said either is correct. 
I still have a final in this course so if this is OK I do need to know for that.


2) Suppose the separation (same as question 1) is an example of gas chromatography.  What is the effect on the separation's number of plates of increasing the size of particles on which the stationary phase is coated? (a) N increases (b) N decreases (c) no change.  Why? Explain with equation. 

--He said to assume gas chromatography questions are referring to open-tubular columns since it is more common than packed.  I understood "particles on which the stationary phase is coated" to be referring to SCOT (support-coated open tubular) in which the stationary phase is a liquid film over the support particles, which are NOT stationary phase.  Here was the answer I put:

"(c) no change.  H = A + B/ux + Cux (Van Deemter)  No change because particle size affects the A term for a packed column but this is an open-tubular column.  Thickness of film coated on the particles would affect N and resolution, not particle size." 

Can anyone explain to me where I went wrong in my reasoning and how particle size would affect resolution in this question?  I could not find any reference to affect of particle size for GC unless the particle is the stationary phase, not when a stationary phase is coated on it (as in this question). 

3)Suppose the separation (same as question 1) is an example of gas chromatography.  What is the effect on the separation's number of plates increasing the carrier gas flow rate? (a) N increases (b) N decreases (c) no change.  Why? Explain with equation.

"None of the above.  H = A + B/ux + Cux  This would have _opposing_ effects, which can be seen in the van Deemter equation.  Ux is linear flow rate.  If it is increased, H will be increased by Cux which decreases N (N=L/H).  However, if Ux is increased it will also decrease the B/ux term which decreases H and increases N."

--Prof actually said no one in the class got full credit on this.  His answer was:

"(a) increases _and_ (b) decreases.  Depends on where you are on the van Deemter plot (H vs. U).  H can go up or down, N can go up or down."

I must say, I think my answer explains why the plot is shaped that way... please let me know if you see something different in my answer vs. his or I overlooked something.

Finally..
4) Using van Deemter equation, explain why longitudinal diffusion is a more serious problem in GC than LC.

My response:
"H = A + B/ux + Cux   The A term deals with multiple paths and particle size but in open-tubular GC, this term is irrelevant and the equation becomes H = B/ux + Cux.  Longitudinal diffusion is the B terms nd it contributed to plate height, H, more than it does in the packed LC van Deemter equation.  Plate height is inversely related to resolution, so when B affects GC more than LC, it negatively affects resolution in GC more than LC."

I was not very confident of this response, because it is just mathematical and less conceptual, so I know I need help on this one!



Again, I don't expect any one person to take the time to answer these.  I didn't know if they should be four separate topics or all on one, since they are all about chromatography and van Deemter.  I'd be happy to split them if that's what I should do.
Thank you in advance for any advice or explanation you can give me!!!!

[Pradeep]

Ohh My god! Can't you shorten the problem?

[jennatbee]

Shorter version below!  Here are just the 4 questions.  The rules for posting said "show that you attempted the problem" so I wanted to include that, as well as the answers my professor provided.  These are the questions though.  Thank you. 

1) Shown below is a separation of a mixture of two components.  The separation achieved a resolution of 1.5 and the two retention times were 100 and 112, as shown. 

(Here he showed an image.. It was very simple, two peaks and it says resolution = 1.50.  Shows 6sigma between the peaks.  Then he added to retention times, 100 and 112 sec.)

How many plates were achieved in this separation?


2) Suppose the separation (same as question 1) is an example of gas chromatography.  What is the effect on the separation's number of plates of increasing the size of particles on which the stationary phase is coated? (a) N increases (b) N decreases (c) no change.  Why? Explain with equation. 


3)Suppose the separation (same as question 1) is an example of gas chromatography.  What is the effect on the separation's number of plates increasing the carrier gas flow rate? (a) N increases (b) N decreases (c) no change.  Why? Explain with equation.


4) Using van Deemter equation, explain why longitudinal diffusion is a more serious problem in GC than LC.

[jennatbee]

Is there a way to edit or delete my post so I can make 4 separate posts with these questions? 

[Arkcon]

That's not necessary, there's no need for 4 separate threads covering essentially the same question.   We're sorry we're slow to get to you, but you posted on a weekend, and your question is very specific -- not everyone calculates separation efficiency every time they run a chromatograph.  You have a lot of information, so its hard to know -- what you're missing, what hints we can give to help you without doing it all for you.

Lets start with number 1.  Do you have the formula for plates?  From your text book or calls notes?  I could look it up in my reference, but maybe that's not the formula you need -- you seem to imply you have a formula, but maybe in different units?  Maybe you have to convert some of your given data before you can use it in your formula?  Something like that?  And if you have the image as a common image format, the + Additional Options... button below will allow you to attach it to a post.

[jennatbee]

Great!  No problem, I just started to wonder if I broke the rules by putting too many questions in the same post! 
The image is attached (not much to it). 
I first used the formula Resolution = delta t_r / w_av
w_av = 8 sec
The other equations i have to work with are
N = 16t_r² / w²
and
w=4sigma
I got stuck here because I didn't think it made sense to use w_av in place of w in w=4sigma. 
Keep in mind, I'm posting this because I suspect my professor made an error on the exam key.. but I'm not sure.  So it's possible it's not solvable with the given information.
Thanks so much for taking the time to read!

[Arkcon]

And what formula for theoretical plates are you supposed to use?  This is important, because in part 2, you're supposed to compare the result to gas chromatography particle size.

[jennatbee]

We did have several theoretical plate equations to memorize, but this is the one I first thought of.  The one my professor used on the key is N = t_r² / sigma²
Where sigma was 2 from w = 4sigma

[Arkcon]

See, in my reference; Snyder, Dolan and Jupile, gives the formula for theoretical plates as N=16(t_r/W_h)² or N=5.54(t_r/W_b)²) -- where t_r is retention time of the peak you're using, and W_b is the width at baseline and W_h is the width at half height.  I wouldn't use sigma as width, or to compute width.  If you Google for theoretical plates, you'll see these formulas again, but not yours.  In theory, both formulas give the same answer.  In practice, we use the width at half height, to avoid baseline issues.

*EDIT* correct typo, thanks jennatbee:

[jennatbee]

Ok, that is in line with my thinking.  However with the original data given in the problem, I don't think these equations are useful.  You are only given two retention times (100 and 112), resolution (1.50), and 6sigma between the two peaks.  Is there any way to solve this problem (asking for N, number of theoretical plates) with the given data? 
Even if I use the equation:
N=16(t_r/W_b)²
I still don't have a way of finding out either baseline width (w_b), do I?
I only have the average width, calculated from:
Resolution = delta t_r/ w_av
If I use w_av, would I use an average t_r or something?  This just doesn't seem right. 

Note: I believe the equation you listed N=5.54(t_r/W_b)²) should actually be w_h, as you indicated in the next line. Just in case someone else is following along here. 

[Arkcon]

Unfortunately, I can't help you there.  My reference gives a formula for resolution, R_s = (t_R2-t_R1)/0.5 (w_b2+w_b1) but I don't know how you're going to get width at baseline for both peaks from resolution using that formula.  My reference is from a training class, so it doesn't have an index, so I can't look up the formula for sigma, so I can't see if that will help.

Your instructor clearly wants you to derive these formulas yourself, and seems to be using derived formulas that are different than what you'll find in the internet or training courses.  You'll have to try to pull you class notes together, or directly ask your instructor where we've gone wrong.

[JGK]

See, in my reference; Snyder, Dolan and Jupile, gives the formula for theoretical plates as N=16(t_r/W_h)² or N=5.54(t_r/W_b)² -- where t_r is retention time of the peak you're using, and W_b is the width at baseline and W_h is the width at half height.  I wouldn't use sigma as width, or to compute width.  If you Google for theoretical plates, you'll see these formulas again, but not yours.  In theory, both formulas give the same answer.  In practice, we use the width at half height, to avoid baseline issues.

*EDIT* correct typo, thanks jennatbee:

Are you sure it is not:

N=16(t_r/W_b)² or N=5.54(t_r/W_h)²

For resolution you could use R=1.18(t₂-t₁)/(W_{0.5, 1}+W_{0.5, 2})

[Arkcon]

Gah. I fixed it, and made it wrong.  Hard to keep track when using subscripts. Yes, you use the 16 constant for baseline width, you use the 5.54 constant for width at half height.  And you always use the width at half height, because that is a more accurate measurement to make.