Question

A pycnometer is a device used to measure densities. You are in the lab and need to measure the density of an unknown solid. The pycnometer is weighed empty and once again when it is filled with methanol at 18°C (the density of methanol at 18°C is 0.7914 g/mL). The following data is obtained:

        Mass of the pycnometer: 127.111 g

        Mass of the pycnometer and the methanol: 378.024 g

The pycnometer is emptied and 17.66 g of solid are placed into it. It is then refilled with water at 18°C (density of water at 18°C = 0.99862 g/mL) and is found to have a mass of 459.704 g.  You are told the solid is one of the following:

Copper: (d = 8.96 g/mL)

Gold: (d = 19.30 g/mL)

Silver (d = 10.50 g/mL)

What is the identity of the solid?

Answer 1

The Pycnometer is that measuring instrument whose volume is known and allows to know the density or specific weight of any liquid by gravimetry at a certain temperature. The methodology that studies the results obtained through this instrument is called Picnometry.

Density is a scalar quantity referred to the amount of mass in a given volume of a substance or solid object.

Data

T = 18 ºC

d_methanol = 0.7914 g/mL,

Mass of the pycnometer = 127.111 g

Mass of the pycnometer and the methanol: 378.024 g

Mass of the pycnometer and the methanol - Mass of the pycnometer = Mass of methanol

Mass of methanol = 378.025g - 127.11g = 250.914g

V_methanol = 317.05 mL = V_{volume within the pycnometer}

Mass of solid = 17.66 g

Mass of pycnometer, solid and water = 459.704 g

d_water = 0.99862 g/mL

Mass of water = Mass of pycnometer, solid and water - Mass of solid - Mass of the pycnometer

Mass of water = 459.704 g - 17.66 g - 127.11 g = 314.934 g

V_water = 314.934 g / 0.99862 g/mL = 315.369 mL

V_solid = V_{volume within the pycnometer} - V_water = 317.05 mL - 315.369 mL = 1.681 mL

Being the density corresponding to silver (d = 10.50 g/mL)