Calculating dilutions

With every addition of sock solution you increased amount of Trp in the sample. However, you also increased the volume and thus diluted the sample somewhat. When you withdrew sample from the cuvette, you decreased both volume and amount, but did not change concentration. These changes in volume-amount-concentration need to be taken into account when analyzing intensity of absorption.

Handling dilutions can be done in Igor, but his particular task can be handled easier in spreadsheet program like Excel.

Open a new spreadsheet. You will use one line for each step – addition or withdrawal. Calculation will use several columns as shown in the example:


Remember to label columns with data type and units.

Fill the first and second data columns with concentration of stock solution in mM and volume added in mL. Notice that zero volume is added in the first row. When you reach withdrawal step leave concentration blank and fill in volume reduction as a negative number. Continue with the next concentration of stock until you fill parameters of all steps.

In the third column calculate the amount of substance (Trp) added in each step, which equals volume multiplied by concentration. For the above example cell D4 will contain =C4*B4. Copy this value to the rest of columns. Notice that withdrawal step will produce negative number which means that amount has been reduced.

In the fourth column calculate total amount of substance that accumulated in the sample at each step. Because nothing was added in the first step, type in zero. In the subsequent rows add total amount from the preceding line with amount of stock added at this step. For cell E5 this will be =E4+D5.

Likewise, calculate total current volume of sample in the fifth column. In the first row, which corresponds to blank measurement, type in initial volume that you started with. In the subsequent rows add total volume from the preceding line with volume of stock added at this step. For cell F5 this will be =F4+C5. 

Finally, calculate current concentration of sample at each step by dividing current amount by current volume. Because amount is in nmol (x10^-9) and volume is in mL (10^-6) calculated concentration is in mM (10^-3).

These calculations are identical for all rows, with small difference in withdrawal steps. Therefore, you can copy most fields from second row throughout the rest of the table. The only difference in the withdrawal steps is that you do not know sample concentration at that step ahead of time. However, you can copy concentration calculated in the step immediately above withdrawal. Notice that withdrawal does not cause change in the concentration (column G), although both volume (column F) and amount (column E) decrease. 

After calculations are complete, save the file, select values of calculated concentration, and copy them to the clipboard. You are now ready to paste calculations into calibration wave back in Igor.

After transferring concentration values back to Igor, proceed to plot overlay spectra and concentration-absorption dependence.