Answer : The correct option is, (5) 5.5 kg
Explanation :
As we are given that yellow cake is a uranium ore that contains about 75 % [tex]U_3O_8[/tex]. That means,
Mass of [tex]U_3O_8[/tex] = 75 g
Mass of yellow cake = 100 g
Molar mass of uranium = 238 g/mol
Molar mass of [tex]U_3O_8[/tex] = 842 g/mol
First we have to calculate the mass of pure uranium.
As, 842 g of [tex]U_3O_8[/tex] contains [tex]3\times 238g[/tex] of pure uranium
So, 75 g of [tex]U_3O_8[/tex] contains [tex]\frac{75}{842}\times 3\times 238g=63.59g[/tex] of pure uranium
Now we have to calculate the mass of yellow cake.
As, 63.59 g of pure uranium present in 100 g of yellow cake
So, 3.5 kg of pure uranium present in [tex]\frac{100g}{63.59g}\times 3.5kg=5.5kg[/tex] of yellow cake
Thus, the mass of yellow cake processed to produce 3.5 kg of pure uranium must be, 5.5 kg
