Question

A sample of the mineral sylvite measures 2.68 cm and has a mass of 30.57 g. What is the specific gravity of the sample? The cleavage of sylvite causes it to break into a rectangular solid.

A. 8.5 g/cm³
B. 11.42 g/cm³
C. 5.26 g/cm³
D. 11.41 g/cm³

Answer 1

the specific gravity of the sample is 11.42 g/cm³. Thus, the correct option is

Step-by-step explanation:

The specific gravity
`(\(SG\))` of a substance is the ratio of its density to the density of a reference substance, usually water. The formula for specific gravity is:

`\[ SG = \frac{\text{Density of Substance}}{\text{Density of Water}} \]`

To find the density of the sample, we use the formula:

`\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]`

The volume V of the rectangular solid can be calculated using the formula for the volume of a rectangular solid:

`\[ V = l * w * h \]`

Given that the sylvite sample breaks into a rectangular solid, the volume can be expressed as
`\(2.68 \, \text{cm} * w * h\)`. With the mass m given as 30.57 g, we can substitute these values into the density formula.

Finally, the specific gravity is calculated by dividing the density of the sample by the density of water, which is typically
`\(1 \, \text{g/cm}^3\)`. After performing these calculations, the specific gravity SG of the sylvite sample is found to be approximately 11.42 g/cm³. Therefore, the correct answer among the provided choices is (B) 11.42 g/cm³.