Answer to Question #129897 in Chemistry for Justine

Question

The true volume of a 50-mL volumetric flask is 50.037 mL at20OC. What mass of water measured (a) in vacuum and (b) in air at
20OC would be contained in the flask?

Answer 1

The mass in vacuum and in air is different due to the buoyancy. The buoyant force is the upward force exerted by a liquid or a gaseous fluid and is related to Archimedes' principle. The buoyancy error in weighing occurs whenever the density of the object weighed is not equal to the density of the standard mass used for calibration. In order to calculate the mass of water measured in vacuum and in air, it is handy to use the table of the densities of water (true and corrected for buoyancy), presented in table 2.7 of Quantitative Chemical Analysis, 8th edition. In this table, for 20 °C, the true density of water is 0.998207 g/mL, while the volume of 1 g of water corrected for buoyancy is 1.029 mL. Therefore, the mass of water measured in vacuum (true mass) will be:

$m = V·d =50.037·0.998207 = 49.947$ g

and the mass of water in air will be:

$m = \frac{V}{1/d} =\frac{50.037}{1.0029} = 48.892$ g.

As you can see, the mass of the same volume of water measured in air is slightly less.