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

  • #1
Skw
8
0
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 !
 
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  • #2
Hello @Skw,

:welcome:

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.

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

##\ ##
 
  • #3
BvU said:
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.
 
  • #4
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 ?
 

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

How do I calculate the number of sand particles from a given mass?

To calculate the number of sand particles from a given mass, you need to know the average mass of a single sand particle. First, determine the density of sand (typically around 2.65 g/cm³) and the average volume of a sand particle, often approximated as a sphere with a diameter in micrometers. Once you have the average mass of a single particle, you can divide the total mass by this value to get the number of particles.

What is the average mass of a single sand particle?

The average mass of a single sand particle can vary, but a common approximation is based on a diameter of 0.5 mm. Given the density of sand (2.65 g/cm³), the mass of a single particle can be calculated using the formula for the volume of a sphere and then converting this volume to mass. For a 0.5 mm diameter particle, the mass is approximately 1.74 x 10-4 grams.

How do I convert the mass of Nylon particles to the number of particles?

To convert the mass of Nylon particles to the number of particles, you need to know the average mass of a single Nylon particle. This involves knowing the density of Nylon (approximately 1.15 g/cm³) and the average size or volume of a Nylon particle. Once you have the average mass of a single Nylon particle, you can divide the total mass by this value to determine the number of particles.

What is the average mass of a single Nylon particle?

The average mass of a single Nylon particle depends on its size and shape. For example, if you assume a spherical Nylon particle with a diameter of 1 mm, you can calculate its volume and then use the density of Nylon (1.15 g/cm³) to find the mass. For a 1 mm diameter particle, the mass is approximately 6.02 x 10-4 grams.

How accurate are these calculations for converting mass to the number of particles?

The accuracy of these calculations depends on the assumptions made about the size, shape, and uniformity of the particles. Real-world samples may have a distribution of particle sizes and shapes, which can affect the average mass. Therefore, while these calculations provide a good estimate, they may not be perfectly accurate for all samples. More precise measurements and characterizations of the particle size distribution can improve accuracy.

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