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Why doesn't a metre cube of box containing common salt weigh $2170\ kg$ if the density of NaCl lattice is $2170\ kg/m^3$?

As Mass = Volume x Density then for a unit volume shouldn't Mass= 1 x 2170= 2170 $kg$? What is the reason behind this?

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    $\begingroup$ Does your common salt contain air? $\endgroup$ Oct 7, 2018 at 14:35
  • $\begingroup$ @AndersSandberg yeah, just what you would do when someone tells you to pack a metre cube of salt $\endgroup$ Oct 7, 2018 at 16:56

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The sort of salt you use in the kitchen is made up from (approximately) cubic grains, and when you put these into a container then pack randomly with air gaps between the grains.

The packing fraction for randomly packed spheres is around 60%. I don't know what the figure for randomly packed cubes is, but I'd guess it will be similar. So the density of a box of salt grain will be around 60% of the density of a single salt crystal.

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  • $\begingroup$ So u mean that remaining 40% space would be occupied by air and this leading to a considerable reduction of weight? $\endgroup$ Oct 7, 2018 at 16:55
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    $\begingroup$ @Vivekkarunakaran yes $\endgroup$ Oct 7, 2018 at 18:23

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