A technique once used by geologists to measure the density of a mineral is to mix two dense liquids in such proportions that the mineral grains just float. When a sample of the mixture in which the mineral calcite just floats is put in a special density bottle, the weight is 15.4448 g. When empty, the bottle weighs 12.4631 g, and when filled with water, it weighs 13.5441 g. What is the density of the calcite sample? (All measurements were carried out at 25 °C, and the density of water at 25 °C is 0.9970 gmL)

Question

A technique once used by geologists to measure the density of a mineral is to mix two dense liquids in such proportions that the mineral grains just float. When a sample of the mixture in which the mineral calcite just floats is put in a special density bottle, the weight is 15.4448 g. When empty, the bottle weighs 12.4631 g, and when filled with water, it weighs 13.5441 g. What is the density of the calcite sample? (All measurements were carried out at 25 °C, and the density of water at 25 °C is 0.9970 g>mL)

Vocaloid · Answer

let's first consider the water only

when filled w/ water, the bottle weighs 13.5441g
and when empty, it weighs 12.4631g

therefore 13.5441g - 12.4631g = 1.081 g water
using the density of water: 0.9970g/mL = 1.081/x
to solve for x, the volume of the bottle

now, let's consider the calciate sample

it weighs 15.4448 g. subtracting 15.4448 g - 12.4631 g gives the mass of the calcite sample

divide by x to get the density of the calcite