Dear friend Adele Mastroyannis

Absolutely, my inquisitive friend Adele Mastroyannis! Calculating the concentration of gold nanoparticles post-reaction involves a bit of chemical finesse. Let me guide you Adele Mastroyannis through this.

**Using Beer's Law for Concentration Calculation:**

1. **Understand Beer's Law:**

Beer's Law relates the absorbance of a substance in a solution to its concentration. The equation is A = ε * c * l, where:

- A is the absorbance,

- ε is the molar absorptivity (extinction coefficient),

- c is the concentration of the absorbing species,

- l is the path length of the sample.

2. **Calibrate Your System:**

You Adele Mastroyannis need to have a calibration curve to determine the molar absorptivity (ε) for your gold nanoparticles. This involves measuring the absorbance at different known concentrations of gold nanoparticles.

3. **Measure Absorbance:**

After the reaction, measure the absorbance of your solution containing gold nanoparticles.

4. **Apply Beer's Law:**

Rearrange the Beer's Law equation to solve for concentration (c):

c=A​/ε×l

Plug in the measured absorbance, the known molar absorptivity, and the path length of your sample.

5. **Consider Dilution:**

If you've diluted your sample during the experiment, make sure to account for this in your concentration calculation.

Remember, this is a simplified explanation, and real-world applications might have additional factors to consider. Always follow good scientific practices, and if possible, refer to specific protocols or literature in your field for precise methods used by other researchers.

And there you Adele Mastroyannis have it! The mysterious world of gold nanoparticles unraveled through the almighty Beer's Law.

Hi,

You can get your nanoparticle concentration based on this method:

1- Calculation of average number of gold atoms per nanoparticle (for spherical shapes):

N=π ρD3/6M

the average number of gold atoms ( N )

ρ is the density for fcc gold (19.3 g/cm3 )

M stands for atomic weight of gold (197 g/mol)

D is the average core diameters of the particles

2- Determination of molar concentrations of nanoparticle solution

C=NTotal/NVNA

Ntotal is the total number of gold atoms

N is the average number of gold atoms per nanosphere

V is the volume of the reaction solution in liter

NA is the Avogadro’s constant.

Ref:

Article Extinction coefficient of gold nanoparticles with different ...

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