Module 1.3 Density Quiz

[figure out how to turn this into a meaningful assessment]

The densities of liquids in example 3 are listed in Table 1.2.  Imagine you have five bottles containing colorless liquids (labeled A–E). You must identify them by measuring the density of each.  Using a pipette, a laboratory instrument for accurately measuring and transferring liquids, you carefully measure 25.00 mL of each liquid into five beakers of known mass (1 mL = 1 mL). You then weigh each sample on a laboratory balance.  Use the tabulated data to calculate the density of each sample.  Based solely on your results, can you unambiguously identify all five liquids?

Masses of samples: (1) 17.72 g; (2) 19.75 g; (3) 24.91 g; (4) 19.65 g; (5) 27.80 g

Table 1.2 Densities of liquids in example 3

Solution:

Given: volume and mass

Asked for: density

Strategy:

1.  Calculate the density of each liquid from the volumes and masses given.
2.  Check to make sure that your answer makes sense.
3.  Compare each calculated density with those given in Table 1. 2.  If the calculated density of a liquid is not significantly different from that of one of the liquids given in the table, then the unknown liquid is most likely the corresponding liquid.
4.  If none of the reported densities corresponds to the calculated density, then the liquid cannot be unambiguously identified.

Solution:

1. Density is mass per unit volume and is usually reported in grams per cubic centimeter (or grams per milliliter because 1 mL = 1 mL). The masses of the samples are given in grams, and the volume of all the samples is 25.00 mL. The density of each sample is calculated by dividing the mass by its volume. The density of sample 1, for example, is

density = 17.72 g/25.00 mL=0.7088 g/mL

Both the volume and the mass are given to four significant figures, so four significant figures are permitted in the result.  The densities of the other samples (in grams per cubic centimeter) are as follows: (2) 0.7900; (3) 0.9964; (4) 0.7860; and (5) 1.112.

(2) Except for sample E, the calculated densities are slightly less than 1 g/cm3. This makes sense because the masses (in grams) of samples A–D are all slightly less than the volume of the samples, 25.00 mL. In contrast, the mass of sample E is slightly greater than 25 g, so its density must be somewhat greater than 1 g/cm3.

(3) Comparing these results with the data given in shows that sample 1 is probably diethyl ether (0.708 g/mL and 0.7088 g/mL are not substantially different), sample C is probably water (0.998 g/mL in the table versus 0.9964 g/mL measured), and sample E is probably ethylene glycol (1.113 g/mL in the table versus 1.112 g/mL measured).

(4) Samples 2 and 4 are more difficult to identify for two reasons: (1) Both have similar densities (0.7900 and 0.7860 g/mL), so they may or may not be chemically identical. (2) Within experimental error, the measured densities of 2 and 4 are indistinguishable from the densities of ethanol (0.789 g/mL), methanol (0.792 g/mL), and isopropanol (0.785 g/mL). Thus, some property other than density must be used to identify each sample.