Question

A sandstone sample with 100 % quartz has a porosity of 30 %. The sample is dry and the density of quartz is 2.65 g/cc. The bulk density of the sandstone sample is ............ g/cc. (Round off to one decimal place)

Hint:

When calculating bulk density for a porous sample, multiply the density of the material by the fraction of solid material (1 - porosity).

Answer 1

Correct Answer: 1.9

Step 1: What bulk density means.
For a dry rock, only the solid grains carry mass, since the pores are filled with air. So the bulk density is the grain density times the solid fraction.

Step 2: Write the relation.
With porosity $\phi$, \[ \rho_b = (1-\phi)\,\rho_{grain}. \]

Step 3: Plug in.
Here $\phi = 0.30$ and quartz density is 2.65 g per cc, so \[ \rho_b = 0.70 \times 2.65. \]

Step 4: Multiply and round.
This gives $1.855$, which rounds to 1.9 g per cc.

Step 5: State the answer.
The bulk density is about 1.9 g per cc.
\[ \boxed{1.9\ \text{g/cc}} \]