Question 179275: A porous catalyst for chemical reactions has an internal surface area (800m^2)/(cm^3) of bulk material . Fifty percent of the bulk volume consist of the pores-[holes] , while the other 50% is made up of the solid substance . Assume that the pores are all cylindrical tubules of uniform diameter d and length L , and that the measured internal surface area is the total area of the curved surfaces of the tubules . What is the diameter of each pore . Hint-[find the number of tubules per bulk cm^3, n , in terms of L and d , by using the formula for the volume of a cylinder V=.25(pi)d^2L . Then apply the surface area formula S=(pi)dL , to the cylindrical surfaces to the n tubules ] Please explain in detail , step by step , I have been working on this for three days , and I am not sure how to aproach question . The answer to this is 25 Angstroms , signed Michael
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the hint is a good one
look at one cm^3 of bulk material
50% is pores, or .5cm^3
__ so .5cm^3 = n * .25 * π * d^2 * L
__ rearranging (commutative principle) __ .5cm^3 = .25 * d * n * π * d * L
the internal surface area is 800m^2
__ so 800m^2 = n * π * d * L
__ or 8x10^6cm^2 = n * π * d * L
substituting the 2nd equation into the 1st
__ .5cm^3 = .25 * d * 8x10^6cm^2
dividing by .25 * 8x10^6 gives 2.5x10^(-7)cm = d
__ or 25 angstroms
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