# Sample: How to calculate mass of nanopaticles with given density and Vol % [closed]

I'm trying to calculate the wt% and the mass of the nanoparticles in a ferrofluid solution.

Attached is data from the supplier:

**EMG 605 Specifications and Physical Properties**
- Appearance:   Black-brown fluid
- Carrier Liquid:   Water
- Nominal Particle Diameter:    10 nm

- Saturation Magnetization (Ms): 220 Gauss or 22 mT (SI)
- Viscosity @27°C:  <5 cP or <5 mPa·s
- Density @25°C:    1.18 g/cc or 1.18x10^3 kg/m3 (SI)
- Initial Magnetic Susceptibility:  0.24    or 3.02 (SI)
- :Magnetic Particle Concentration  3.9 % vol.
- pH:   9-10
- Nature of Surfactant: Cationic

• Note the site requests posters show their attempt to solve homework type problems. I answered anyway (hopefully correctly). – Buck Thorn May 14 at 21:27
• Is this ferrofluid solution $\ce{Fe}$ nanoparticle in water? – Mathew Mahindaratne May 14 at 21:32

Defining the following

• Density of solution: $$\rho = \pu{1.18 g/cc}$$
• Density of water: $$\rho_w$$
• Density of nanoparticles: $$\rho_{np}$$
• % (v/v) n.p.s: $$p_v=3.9$$%
• % (w/w) n.p.s: $$p_{wt}$$

Then solve for $$\rho_{np}$$ in the following equation (you'll need to look up missing value of water density):

$$\rho = \frac{p_v}{100}\rho_{np} + \frac{100-p_v}{100}\rho_{h2o}$$

With $$\rho_{np}$$ you can compute $$p_{wt}$$

$$p_{wt} = 100\frac{p_{v}\rho_{np}}{p_{v}\rho_{np}+(100-p_{v})\rho_{w}}$$

As noted in the comments, the resulting density of the particles ignores the effect of the added cationic surfactant. Also, the solvent density is assumed that of water, free (not particle bound) detergent or other additives assumed to be negligible.

• Up voted but it is assumed that the surfactants don't change the liquid density much. And I think is a reasonable assumption. If OP has the sample s/he can validate the result, at least roughly, by weighing a V of it. – Alchimista May 15 at 8:05
• @Alchimista Thanks, and yes, that's a good point, I thought of the surfactant and ignored it. I could estimate concentration from monolayer coverage (but this would of course be particle bound) or estimated cmc, just for the fun of it, and if I find some time I'll add that. I'm guessing added surfactant won't affect the density too much, but it should be straightforward enough to estimate the uncertainty from that. – Buck Thorn May 15 at 8:45
• I am not sure if I get whats going on, is there a way I can share my data sheet? I want to determine the number of nano-particles in 1 grams similar to what I determined for my milled fibers – user642407 May 21 at 20:27
• @user642407 Depending on the document in question you can insert an image (photo or screenshot) to your question, or include a link. If you can provide more information about how you are stuck on this question that might help get it reopened (no guarantees though). – Buck Thorn May 21 at 20:39