Posted by: Mark Foreman | March 2, 2012

How to estimate metal concentrations

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.

Chromium data, this is good data

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.

Not so good zinc data, best not to use the last two points

Frankly it is not nice, if we use the log-log graph which will stretch out the lower end of the graph then we can see what has happened.

log log view of the zinc data

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.

The individual data points which were averaged to form the zinc data for one of the lines (the first one)

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.

High background, I have had to tamper with the data to make the background this high. I have never seen a background this high before.

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.

This is good data

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