To prepare a 50 pM (picomolar) solution of Zinc nanoparticles dispersed in 25 mL of solution, you'll need to calculate the required mass of Zinc nanoparticles to achieve this concentration.

First, determine the molar mass of Zinc (Zn), which is approximately 65.38 g/mol.

Then, use the formula:

Concentration (in mol/L)=Amount of solute (in mol)​ / Volume of solution (in L)

To convert picomoles to moles, use the conversion factor 1pM=10−12mol..

Given that you want a concentration of 50 pM in a 25 mL solution:

Concentration=50×10−12mol/ 25×10−3L​

= 2 x10-9 mol/L

Now, use the formula:

Concentration=Mass (in g)/[Molar mass (in g/mol)×Volume (in L)]​

Rearranging for mass:

{Mass} = {Concentration} x{Molar mass} x{Volume}

{Mass} = (2x10-9{mol/L}) x 65.38{g/mol}) x (25 x 10-3{L})

{Mass} = 3.25 x 10-6{g}

So, you'll need approximately 3.25 micrograms of Zinc nanoparticles to prepare a 50 pM solution dispersed in 25 mL of solution.

Sanjeev Kumar

The theory is deceptively and seductively simple: pico is 10-12. Thus 50 pM is 50 X 10-12 moles/liter. 1 mole of Zn is 65.38 g. This is 65.38 X 50 X 10-12 g of zinc in 1 liter; you actually want a final volume of 25 mL which is 1/40th of a liter; thus, the required mass of zinc is [65.38/40] X 50 X 10-12 g

[Note: The calculation in the above answer is incorrect (it has 2 divisions by 25 x 10-3)].

Now to the practicalities of the situation. Such a system will be impossible to prepare in the manner envisaged:

- In a powder there are no free, independent discrete particles < 100 nm present. Any powder is a fused mass of post- and sub-micron primary particles. This would be easily demonstrated by attempting to suspend such a powder in water where it would not form a clear or colored liquid (all material < 100 nm) but rather settling would occur indication post-micron material (simple Stokes’ Law)

- Standard balances do not exist for weighing micrograms of material. Ultra-microbalances go down to about 30 µg. Balances that allow you to do microgram weighings are in the $30K range but still need great care in usage. For example:

https://www.scalesplus.com/ultra-microbalances/

- Even wetting and getting the material into suspension will be impossible – the separation stage would contaminate the system with the sonication probe material

- The zinc is almost certainly mostly in the oxidized state – ESCA/XPS would show this - and not in the free-metal, Zn0, state - and, anyway, slow hydrolysis will take place in water (Zn + 2H2O → Zn(OH)2 + H2)

Thus, the proposed route to make such a system is completely impractical. Even a bottom-up process will be difficult as zinc metal cannot be the end result of a process such as sol gel. It could possible or feasible to make a much larger quantity of liquid (say 1 L) and take 25 mL from it, but even so the quantities of ‘metal’ would still be extremely small to weigh out. The obvious question is ‘Why do you require 50 pM of zinc metal in 25 mL of colloidal suspension’?