# Preparing gold nanoparticle dilutions for molar extinction coefficient estimation

Q30: Consider the 2:1 pH 5.4 gold nanoparticle preparation. Given that the concentration of the stock solution is of the order of 3 x 10-9 M, how many milliliters of this solution will you have to pipette to prepare 5.00 mL of the following dilutions?

Students will use the dilution formula: M1 x V1 = M2 x V2 where M1 and V1 are the molarity and volume of the stock and M2 and V2 are the molarity and volume of the dilute solution.

For example, if we wish to prepare 5.00 mL of a 1.5 x 10-9 M solution from a 3 x 10-9 M stock:

$\mathrm{3 \times 10^{-9}\: M \times V_x = 1.5 \times 10^{-9}\: M \times 5.00\: mL}\nonumber$

Solving for Vx:

$\mathrm{V_x = \dfrac{1.5 \times 10^{-9}\: M \times 5.00\: mL}{3 \times 10^{-9}\: M} = 2.5\: mL}\nonumber$

To prepare the dilution, 2.5 mL of the stock solution (3 x 10-9 M) would have to be pipetted using a volumetric pipette into a 5.00 mL volumetric flask and brought to volume with water.

The best approach will be to make a number of serial dilutions as preparation of the more diluted solutions from the stock solution is not feasible in light of very small volumes that would have to be measured. Such small volumes would increase the inaccuracy of the analysis.

Q31. What is the purpose of preparing a 0.00 M dilution? How is it used in the analysis?

A solution containing zero concentration of analyte is considered a blank and it is used to zero the instrument to eliminate interferences from any reagents used in the analysis.

Q32. What relationship do you observe between the absorbance and concentration of nanoparticles?

There is a very linear relationship between the absorbance and the concentration for any of the nanoparticles preparations.

Q33. Do any of the data points deviate from the general behavior observed in the plot?

In general, there is very small deviation in any of the plots. The absorbance of nanoparticles solutions displays a high linearity with changes in concentration.

Q34. What parameter allows us to determine whether there is a good fit between absorbance and gold nanoparticle concentration?

The correlation coefficient is a measure of good fit. For most solutions examined in this study the correlation coefficient is 0.999 or better.

Q35. What is the molar extinction coefficient for this specific gold nanoparticle preparation? How does this value compare to the extinction coefficient reported in Table 1 for a gold nanoparticle of similar size?

Students can analyze the data provided in the experimental results. Based on the absorbance vs. concentration plot, the slope of the curve is 831284607.8 or 8.3 x 108 M-1cm-1. By comparison, the extinction coefficient for a 20 nm particle is approximately 9 x 108 M-1cm-1 as reported in Table 1.

Q36. How can you estimate the uncertainty on the molar extinction coefficient from the regression analysis?

The Summary Output from the regression analysis is displayed for each set of absorbance vs. concentration data. The Standard Error associated with X Variable 1 is the uncertainty on the slope. In this particular case it is 4289294.315. Thus the extinction coefficient can be reported as (8.3 ± 0.4) x 108 M-1cm-1.