Dear Reader,
Sometimes we want to estimate a metal concentration, now before we get started it is often important to calibrate our measuring device. We normally do this by feeding the device with a series of samples and looking at the graph of the response of the device against concentration.
There is nothing magic about this process, it is simply the one where the device is measured against a set of external yardsticks which we will have made. Now in the best traditions of blue peter here is one which I did earlier. This is for chromium.
A  B  C  D  E  F  G  H  I  J  K  
1  Concentration (ppm)  0  0,05248  0,101157  0,5128  0,93  1,746  4,8612  9,674  18,428  
2  Line  267.7 nm  0,05248  0,0926  0,189  0,9628  1,722  3,223  9,447  20,72  49,35 
3  Line  283.5 nm  0,0926  0,1938  0,412  2,179  4,01  7,815  23,56  52,62  127,3 
4  Line  284.3 nm  0,1938  0,1022  0,1892  0,8899  1,603  3,045  8,947  19,78  47,37 
Now before we go any further there is always more than one way to deal with the problem. One method is to use excel and the slope function. If we type in a cell
=Slope(C2:K2;C1:K1)
We will then get the slope of the line in the graph which would be made by plotting the intensity data for 267.7 nm against the concentration.
This will get us a slope of 2.63, now this is quite close to the slope of the graph which I obtained from the trend line fitting function in excel. This is the old fashioned method in modern form. The next step is to use the intercept function in the following way
Type in a cell
=intercept(C2:K2;C1:K1)
This should give you a value of 0.95669
When I did the graph drawing in the old fashioned way then the best linear line which I could get for the data was intensity = (2.5993 . conc) – 0.9567. Here is my graph.
Now armed with this equation we can work out an expression for giving us conc from the intensity.
(Intensity + 0.9567) = 2.5993 . conc
Then (Intensity + 0.9567) / 2.5993 = conc
Now we can use our linear calibration graph to estimate concentrations.
But before we get carried away with ourselves it is important to note what can go wrong.
If we were to try the same thing with the following zinc data then we would get a nasty shock.
A  B  C  D  E  F  G  H  I  J  K  
1 
Concentration (ppm) 
0 
0,05248 
0,101157 
0,5128 
0,93 
1,746 
4,8612 
9,674 
18,428 

2 
Line  202.5 nm 
0,0019 
0,2543 
0,5266 
2,7 
4,897 
9,647 
26,95 
18,94 
45,35 
3 
Line  206.2 nm 
0,0011 
0,1386 
0,2857 
1,464 
2,645 
5,214 
14,73 
10,5 
7,135 
4 
Line  213.8 nm 
0,0012 
0,0757 
0,1598 
0,8028 
1,453 
2,797 
7,354 
4,874 
2,357 
If you have drawn a graph at home I am hoping that you got something which looked like this.
Frankly it is not nice, if we use the loglog graph which will stretch out the lower end of the graph then we can see what has happened.
What has happened is that the highest two of the calibration samples have failed, my advice is not to panic. A solution to the problem does exist. If none of your samples are in the upper end of the graph and you are sure that the upper two failed for some reason then just ignore the two most right hand sets of points and make a calibration graph for the lower concentrations of the zinc.
In this case the sample vials were not quite full enough, so the machine only managed to measure one of the three replicates for the last two standards. Here is the data from the machine.
Conc  Rep 1  Rep 2  Rep 3  Mean  ESD 
0 
0,002 
0,002 
0,0017 
0,0019 
0,0002 
0,05248 
0,2563 
0,2555 
0,2512 
0,2543 
0,0028 
0,101157 
0,5248 
0,5285 
0,5265 
0,5266 
0,0019 
0,5128 
2,691 
2,696 
2,713 
2,7 
0,0116 
0,93 
4,955 
4,849 
4,885 
4,897 
0,0538 
1,746 
10,09 
9,288 
9,564 
9,647 
0,4073 
4,8612 
26,83 
26,85 
27,19 
26,95 
0,203 
9,674 
56,17 
0,6349 
0,0096 
18,94 
32,24 
18,428 
135,9 
0,1582 
0,0072 
45,35 
78,4 
Now if you plot a graph of this you should end up with the following.
Now you should see that the data based on the first rep is OK for the last two points, it is still in a nice straight line. But as only a single measurement worked the data for the last two points are less reliable. I would not like to dictate rules to you as to when you should or should not use a single measurement.
But I would like to say that if you are going to use the SLOPE and INTERCEPT functions in EXCEL then it is important to look at a log log graph of the intensity against concentration, to check that nothing bad has happened.
One thing to watch for is contamination of the acid with the metal which you are using in the standards, if you have a high background of a metal. If you see the following in a log log graph then be careful and take expert advice. Here is a log log graph with a high background of metal in the acid.
Now here is the data without the background metal which I had to add, this is what you should see when you draw a log log graph.
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