Question

Yellow cake is a uranium ore that contains about 75% U3O8 (842 g/mol), and can be further refined to extract pure uranium. How many grams of yellow cake must be processed to produce 3.5 kg of pure uranium?
1) 2.6 kg.
2) 3.0 kg.
3) 4.1 kg.
4) 4.7 kg.
5) 5.5 kg.

Answer 1

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 % $U_3O_8$. That means,

Mass of $U_3O_8$ = 75 g

Mass of yellow cake = 100 g

Molar mass of uranium = 238 g/mol

Molar mass of $U_3O_8$ = 842 g/mol

First we have to calculate the mass of pure uranium.

As, 842 g of $U_3O_8$ contains $3\times 238g$ of pure uranium

So, 75 g of $U_3O_8$ contains $\frac{75}{842}\times 3\times 238g=63.59g$ 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 $\frac{100g}{63.59g}\times 3.5kg=5.5kg$ of yellow cake

Thus, the mass of yellow cake processed to produce 3.5 kg of pure uranium must be, 5.5 kg