Question

Lead metal can be extracted from a mineral called galena, which contains 86.6 % lead by mass. A particular ore contains 68.5 % galena by mass.If the lead can be extracted with 92.5 % efficiency, what mass of ore is required to make a lead sphere with a 4.00 cm radius?

Answer 1

Solution :-

Radius of sphere = 4.00 cm

Now lets calculate the volume of the sphere

Volume of spehere = 4/3 pi r^3

                                 = (4/3)*3.14*(4.00cm)^3

                                = 268 cm3

Now lets calculate the mass of lead using the density and volume

Density of the lead is = 11.34 g /cm3

Mass of lead sphere = volume * density

                                     = 268 cm3 * 11.34 g per cm3

                                     = 3039.12 g

Now lets calculate the mass of galena needed to give this amount of lead

3039.12 g lead *(100 % / 86.6 % )*(100 % / 92.5%) = 3794 g galena

Now lets calculate the mass of ore needed

3794 g galena * (100 % / 68.5 % ) =5539 g ore

So the mass of ore needed is 5539 g