Question

The quantity of the cobalt ore [Co\(_3\)(AsO\(_4\))\(_2\)\( \cdot \) H\(_2\)O] required to obtain 1 kg of cobalt (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\) kg.
Given: Atomic Wt. of Co = 59, As = 75, O = 16, H = 1.

Hint:

To calculate the mass of ore needed, first calculate the molar mass of the compound and then determine how many moles are required to obtain the desired amount of pure substance.

Answer 1

Correct Answer: 2.5

The molar mass of the cobalt ore [Co\(_3\)(AsO\(_4\))\(_2\)\( \cdot \) H\(_2\)O] is calculated as follows:
\[ \text{Molar mass of Co}_3 \text{(AsO}_4\text{)}_2 \cdot \text{H}_2\text{O} = 3(59) + 2[75 + 4(16)] + 2(1) + 18 = 3(59) + 2(75 + 64) + 2 + 18 = 177 + 278 + 2 + 18 = 475 \, \text{g/mol}. \] To obtain 1 kg of cobalt (Co), we need the following moles:
\[ \frac{1000}{59} = 16.95 \, \text{mol}. \] Thus, the mass of the ore required is:
\[ 16.95 \times 475 = 8050.25 \, \text{g} = 8.05 \, \text{kg}. \] Thus, the quantity of ore required is \( 8.05 \, \text{kg} \).