# Can you offer some advice on how to get the density of calcium carbonate (kg/L) in this problem?(I'm not asking for answer, just a guide)?

Limestone (calcium carbonate) particles are stored in 50-L bags. The void fraction of the particulate matter is 0.30 (liter of void space per liter of total volume) and the specific gravity of solid calcium carbonate is 2.93.

a) Estimate the bulk density of the nag contents (kg CaCO3/liter of total volume) b) Estimate the weight (W) of the filled bags. State what you are neglecting in yourestimate.c) The contents of three bags are fed to a ball mill, a device something like rotating clothes  dryer containing steel balls. The tumbling action of the balls crushes the limestone  particles and turns them into a powder. The limestone coming out of the mill is put back into 50-L bags. Would the limestone (i) just fill three bags, (ii) fall short of filling three bags, or(iii) fill more than three bags? Briefly explain your answer.

Relevance
• 1 month ago

Given data

Volume of bags V = 50 L

Fraction of empty space fvoid = 0.30

Fraction of filled space = 1 - fvoid = 1-0.30 = 0.70

Specific gravity of CaCO3 = 2.93

Density of CaCO3 = 2.93 x 1 kg/L = 2.93 kg/L

Part a

Bulk density of bag content = mass of CaCO3 / total volume

= density of CaCO3 x volume of CaCO3 / total volume

= density of CaCO3 x Fraction of filled space

= 2.93 kg/L x 0.70

= 2.05 kg/L

Part b

Weight of bag = mass of CaCO3 x gravity constant

= bulk density of bag content x volume of bag x g

= 2.05 kg/L x 50 L x 9.81 m/s2

= 1006.01 N x (1kN/1000N)

= 1.01 kN

Part c

If CaCO3 is crushed, void space will decrease, filled space of bag will increase due to which bulk density of bag content increases from part a. Therefore volume will decrease. It means the content of 3 bags will be put in less than 3 bags. No need of more than 3 bags. The crushed limestone powder will fall short of filling three bags.

Please Rate my work!! Thank You!!

• Dr W
Lv 7
1 month ago

via dimensional analysis

.. . .. ...... ... ... .... .. 2.93 * 1kg solid.... 0.70 L solid(a).. bulk density = ---- ----- ---- ----- x ---- ---- ---- ---- = 2.05 kg CaCO3 / L.. ... ... ... ... ... ... .. .... . . 1 L solid.. .. 1.00 L product

(b).. 50L * 2.05kg / L = 102.5 kg

.. . . (neglecting weight of bag material and volume headspace)

... . .if you really want weight instead of mass. F = ma to YOU.

(c).. fill more than 3 bags.  note the bulk density is lower for the

. . . .crushed powder (2.05kg / L) with the voids than for crystals with

.. . . no voids (2.93kg/L).