Question

The volume percentage of galena and quartz in an ore body of Pb are 90 and 10, respectively. The densities of galena and quartz are 7.6 and 2.65 g/cc, respectively. The grade of the ore body in terms of weight percent of Pb is \(\underline{\hspace{2cm}}\) (Atomic weights of Pb = 206 and S = 32).

Hint:

To calculate the grade of ore bodies, use the density and volume percent values, and apply the appropriate formula for weight percent.

Answer 1

Correct Answer: 83.3

Step 1: Write the formula for the grade of the ore body.
The weight percent of Pb is given by the formula:
\[ \text{Weight percent of Pb} = \frac{\text{Volume percent of Pb} \times \text{Density of Pb}}{\text{Volume percent of Pb} \times \text{Density of Pb} + \text{Volume percent of S} \times \text{Density of S}} \]

Step 2: Substitute the values into the formula.
The volume percentage of galena and quartz are 90% and 10%, respectively. The densities of galena and quartz are 7.6 g/cc and 2.65 g/cc. Substitute these values into the formula.
The grade of the ore body in terms of Pb is: \[ = \frac{90 \times 7.6}{(90 \times 7.6) + (10 \times 2.65)} \approx 83.30 \, % \]