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

Question

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

Answer 1

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.