imagine that you have a cube of CaCo3 whose edge length is 1 cm. What is the sur

Question

imagine that you have a cube of CaCo3 whose edge length is 1 cm. What is the surface area of the cube ( in square cm)? Now imagine that you pulverize it to form small cubes of edge length .05 cm. How many of the little cubes form? what is the surface area of each little cube? What is the new surface area of the pulverized CaC)3? if the rate of reaction of HCL with CaCO3(s) is proportional to the surface area of the CaCO3, how much faster would the HCL react with the pulverized CaCO3 than it did with the original large cube?

Explanation / Answer

1 cm edge means that there is 1 cm2 area on one side; there are 6 sides to a cube, so the total surface area = 6cm2
(one side surface area = 1 cm x 1 cm = 1 cm2 ; total surface area = 1 cm2 per side x 6 sides = 6 cm2 )
number of little cubes will be: 1/0.05 = 20 so there are 20 x 20 x 20 = 8000 cubes
surface area of little cube will be: one side surface area = 0.05 cm x 0.05 cm = 0.0025 cm2 ; total surface area = 0.0025 cm2 per side x 6 sides = 0.015 cm2

Now we have 8000 cubes with a surface area of 0.015cm2, that is 8000 x 0.015cm2= 120cm2  

Rate of reaction = 120cm2/6cm2 = 20                 

If the rate of reaction of HCl with CaCO3(s) is proportional to the surface area of the CaCO3, then HCl will react with the pulverized CaCO3 20 times as fast as with the original large cube.

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