Chemical reactions (stoichiometry)
Spectrophotometry Example Spectrophotometry Example - Determining concentration based on absorbance
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- Let's see if we can tackle this
- spectrophotometry example.
- I took this from the Kotz, Treichel and Townsend
- Chemistry & Chemical Reactivity book and did it
- with their permission.
- So let's see what the problem is.
- It says a solution of potassium permanganate-- let
- me underline that in a darker color-- potassium permanganate
- has an absorbance of 0.539 when measured at 540 nanometer
- in a 1 centimeter cell.
- So this 540 nanometers is the wavelength of light that we're
- measuring the absorbance of.
- And so this is probably a special wavelength of light
- for potassium permanganate, one that it tends to be good
- at absorbing.
- So it'll be pretty sensitive to how much solute we have in
- the solution.
- OK, and the beaker is 1 centimeter.
- So that's just the length right there.
- What is the concentration of potassium permanganate?
- Prior to determining the absorbance for the unknown
- solution, the following calibration data were
- collected for the spectrophotometer.
- The absorbances of these known concentrations
- were already measured.
- So what we're going to do is we're going to plot these.
- And then, essentially, this absorbance is going
- to sit on the line.
- We learned from the Beer-Lambert law, that is a
- linear relationship between absorbance and concentration.
- So this absorbance is going to sit some place on this line.
- And we're just going to have to read off where that
- concentration is.
- And that will be our unknown concentration.
- So let's plot this first. Let's plot our concentrations
- first. So this axis, the horizontal axis, will be our
- concentration axis.
- I'll draw the axis in blue right there.
- Let me scroll down a little bit more.
- I just need to make sure I have all this data here.
- So this is concentration in molarity.
- And let's see, it goes from 0.03 all the way to 0.15.
- So let's make this 0.03, then go three more.
- This over here is 0.06.
- One, two, three, then this over here is 0.09.
- This over here is 0.12.
- And then this over here is 0.15.
- And then the absorbances go-- well it's close to 0, or close
- to 0.1-- all the way up to close to 1.
- So let's make this right here 0.1.
- Let's make this 0.2, 0.3, 0.4, 0.5-- almost done-- 0.6, 0.7,
- 0.8, and then 0.9.
- And that, essentially, covers all of the values of
- absorbency that we have here.
- So let's plot the first one.
- When we had a concentration of potassium permanganate at 0.03
- molar, our absorbance was 0.162.
- So 0.03, and then it goes to 0.16.
- This is 0.15, so 0.162 is going to be right over there.
- And then when we had 0.06 molarity of potassium
- permanganate our absorbance was 0.33.
- So 0.06, 0.33 which is right about-- this is 0.35, so 0.33
- would be right about there.
- And we already see an interesting line form, but
- I'll plot all of these points.
- So at 0.09 molarity, we have 0.499.
- So almost 0.5 right over there.
- That's that value.
- And then at 0.12, we have 0.67 absorbance.
- So at 0.12, we have 0.67.
- So this is 0.12.
- This would be 0.65, so we have 0.67
- absorbance right over there.
- And actually, what we're doing here, we're actually showing
- you that the Beer-Lambert law is true.
- At specific concentrations, we've measured the absorbance
- and you see that it's a linear relationship.
- Anyway, let's do this last one.
- At 0.15 molarity, we have absorbance of 0.84.
- So this right here is 0.15.
- I want to make sure I don't lose track of that line.
- And 0.84 is right over there.
- So you see the linear relationship?
- Let me draw the line.
- I don't have a line tool here, so I'm just going to try to
- freehand it.
- I'll draw a dotted line.
- Dotted lines are a little bit easier to adjust. I'm doing it
- in a slight green color, but I think you see this linear
- This is the Beer-Lambert law in effect.
- Now let's go back to our problem.
- We know that a solution, some mystery solution, has an
- absorbance of 0.539-- let me do our mystery solution in--
- well, I've pretty much run out of colors.
- I'll do it in pink-- of 0.539.
- So our absorbance is 0.5-- this is 0.55, so 0.539 is
- going to be right over there.
- And we want to know the concentration of potassium
- Well, if we just follow the Beer-Lambert law, it's got to
- sit on that line.
- So the concentration is going to be pretty darn close to
- this line right over here.
- And this over here looks like 0.10 molar.
- So this right here is 0, or at least just estimating it,
- looking at this, that looks like 0.10 molar, or 0.10
- molarity for that solution.
- So that's the answer to our question just eyeballing it
- off of this chart.
- Let's try to get a little bit more exact.
- We know the Beer-Lambert law, and we can even
- figure out the constant.
- The Beer-Lambert law tells us that the absorbance is equal
- to some constant, times the length, times the
- concentration, where the length is measured in
- So that is measured in centimeters.
- And the concentration is measured in moles per liter,
- or molarity.
- So we can figure out-- just based on one of these data
- points because we know that it's 0-- at 0 concentration
- the absorbance is going to be 0.
- So that's our other one.
- We can figure out what exactly this constant is right here.
- So we know all of these were measured at the same length,
- or at least that's what I'm assuming.
- They're all in a 1 centimeter cell.
- That's how far the light had to go through the solution.
- So in this example, our absorbance, our length, is
- equal to 1 centimeter.
- So let's see if we can figure out this constant right here
- for potassium permanganate at-- I guess this is probably
- standard temperature and pressure right here-- for this
- frequency of light.
- Which they told us up here it was 540 nanometers.
- So if we just take this first data point-- might as well
- take the first one, we get-- the absorbance was 0.162.
- That's going to be equal to this constant of
- proportionality times 1 centimeter.
- That's how wide the vial was.
- Times-- now what is the concentration?
- Well when the absorbance was 0.162, our concentration was
- 0.03 times 0.-- actually, I'll write all the significant
- digits there-- 0.0300.
- So if we want to solve for this epsilon, we can just
- divide both sides of this equation by 0.0300.
- So you divide both sides by 0.0300 and what do we get?
- These cancel out, this is just a 1.
- And so you get epsilon is equal to-- let's figure out
- what this number in blue is here.
- And I'll take out my calculator.
- And I have 0.162 divided by 0.03 is equal to 5.4.
- And actually more significant is, we could really say it's
- 5.40 since we have at least three significant digits in
- both situations.
- So 5.40 is our proportionality constant.
- And you would actually divide by 1 in both cases.
- We just want the number here.
- But if you wanted the units, you'd want to divide by that 1
- centimeters as well.
- Now we can use this to figure out the exact answer to our
- problem without having to eyeball it like we just did.
- We know that for potassium permanganate at 540
- nanometers, the absorbance is going to be equal to 5.4
- times-- and I'll put the units here.
- The units of this proportionality constant right
- here is liters per centimeter mole.
- And you'll see it'll just cancel out with the distance
- which is in centimeters, or the length, and the molarity
- which is in moles per liter.
- And it just gives us a dimension list, absorbance.
- So times-- in our example the length is 1 centimeter-- times
- 1 centimeter, times the concentration.
- Now in our example they told us the absorbance was 0.539.
- That's going to be equal to 5.4 liters per centimeter
- mole, times 1 centimeter, times our concentration.
- Well this centimeter cancels out with that centimeter right
- over there.
- And then we can just divide both sides by
- 5.4 liters per mole.
- So let's do that.
- Let's divide both sides by 5.4 liters per mole,
- and what do we have?
- So on the right-hand side, all of this business is going to
- cancel out.
- We're just going to have this concentration left over.
- So our concentration is equal to-- let's figure out what
- this number is.
- So we have 0.539 divided by 5.4 gives us-- so we only
- have-- well this is actually 5.40.
- So we actually have three significant digits.
- So we could say 0.0998.
- So this is 0.0998.
- And then if you're dividing by liters per mole, that's the
- same thing as moles per liter.
- So we're able to get a much more exact answer by actually
- just going through the math.
- But this is pretty darn close.
- This exact answer's pretty darn close to what we
- estimated just by eyeballing it off the chart.
- 0.1 is only a little bit more than 0.0998.
- Anyway, hopefully you enjoyed that.
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