How to convert to the number of sand and Nylon particles from mass

[Skw]

Homework Statement

In a sample of 1 kg of sand, we add 108 g of Nylon particles (spherical) of diameter 15.5 µm. The concentration is therefore at 108 g/kg (w/w). How would you convert this concentration to express in number of particles/kg of sand ?

Relevant Equations

number of particles = (mass of all particles) / (mass of 1 particle)
mass of 1 particle = volume x density
density of Nylon = 1.14 g/cm3
Vsphere = (4/3)x π x r3

I calculate 4.8x10(^10) particles /kg of sand in the sample. Do you find the same ? Is my solution correct ? How many particles do you find ?
Thanks in advance !

 

[BvU]

Hello @Skw,

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are you rounding off in a specific manner ?

I do find the exercise wording a bit strange. Concentration is not mass fraction (and mass fraction is not 0.108 but 0.108/1.108). And I wouldn't call 'number of particles/kg of sand' a concentration either.

The SI unit of concentration (of amount of substance) is the mole per cubic meter (mol/m3).

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[Mark44]

Concentration is not mass fraction (and mass fraction is not 0.108 but 0.108/1.108).

IMO we could be talking about the relative concentration/composition, in which the masses could be compared. However, the 0.108 figure doesn't take into account that adding the nylon particles to the sand increases the total quantity of stuff.

 

[Skw]

Hello @BvU, Hello @Mark44,

Thank you for your replies!

Ah ok thank you for the tip for the concentration in moles per cubic meter, I'll have a thought about it but it looks complicated.

Yes I was rounding to the third decimal (for simplicity) at intermediate stages, otherwise, a closer approximation would be 4.859 x10(^10) particles, so actually a more accurate final rounding to the first decimal would be 4.9 x10(^10) particles rather than 4.8x10(^10).

Do you find the same ?