Question

Archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. suppose a chunk of iron with a mass of 390.0 g in air is found to have an apparent mass of 350.5 g when completely submerged in an unknown liquid. (a) what mass of fluid does the iron displace? (b) what is the volume of iron, using its density as given in table 11.1 (c) calculate the fluid's density and identify it.

Answer 1

(a) 39.5 g (b) 49.53 cm^3 (c) 0.7975 g/cm^3, liquid is an alcohol (a) This will be the difference between the weight of the iron in air and the weight submerged in fluid. So: 390.0 g - 350.5 g = 39.5 g (b) The density of iron is 7.874 g/cm^3, so the volume of the iron chunk is 390.0 g / 7.874 g/cm^3 = 49.53 cm^3 (c) The density of the fluid will be the mass of the fluid divided by the volume, so: 39.5 g / 49.53 cm^3 = 0.7975 g/cm^3 Since the density is very dependent upon the temperature and since the temperature wasn't specified, the actual substance can't be completely identified. Although some candidates are: 1. Mixture of Alcohol and water. Density ranges from 0.785 g/cm^3 to 1.000 g/cm^3. 2. Crude oil. Density 0.790 g/cm^3 3. Hydrazine. Density 0.795 g/cm^3 4. Methanol. Density 0.791 g/cm^3 5. Ocimene. Density 0.798 g/cm^3 The most likely candidate is a high concentration of an alcohol of some sort.