Question

Some bottles of colourless liquids were being labelled when the technicians accidentally mixed them up and lost track of their contents. A \(15.0 \mathrm{ml}\) sample withdrawn from one bottle weighed \(22.3 \mathrm{~g}\). The technicians knew that the liquid was either acetone, benzene, chloroform or carbon tetrachloride (which have densities of \(0.792 \mathrm{~g} / \mathrm{cm}^{3}, 0.899 \mathrm{~g} / \mathrm{cm}^{3}, 1.489 \mathrm{~g} / \mathrm{cm}^{3}\) and \(1.595 \mathrm{~g} / \mathrm{cm}^{3}\), respectively). What was the identity of the liquid? (a) Carbon tetrachloride (b) Acetone (c) Chloroform (d) Benzene

Short answer

(a) Acetone (0.792 g/cm³), (b) Benzene (0.899 g/cm³), (c) Chloroform (1.489 g/cm³), and (d) Carbon tetrachloride (1.595 g/cm³). Answer: (c) Chloroform

Step-by-step solution

Convert volume to the same unit as densities

The volume of the unknown liquid is given in milliliters (ml), but the densities are given in grams per cubic centimeter (g/cm³). We need to convert the volume to cubic centimeters (1 ml = 1 cm³). 15.0 ml = 15.0 cm³

Calculate the density of the unknown liquid

Now, we can use the mass and volume to calculate the density of the unknown liquid. Density = Mass / Volume Density = 22.3 g / 15.0 cm³ Density ≈ 1.487 g/cm³

Compare the density to the given liquid densities

Now that we know the density of the unknown liquid (1.487 g/cm³), we can compare it to the given densities of the four known liquids: acetone (0.792 g/cm³), benzene (0.899 g/cm³), chloroform (1.489 g/cm³), and carbon tetrachloride (1.595 g/cm³). The unknown liquid's density is closest to chloroform, which has a density of 1.489 g/cm³.

Identify the unknown liquid

Based on the comparison of the calculated density of the unknown liquid and the given densities of the known liquids, the unknown liquid is most likely chloroform. Therefore, the answer is (c) Chloroform.

Key concepts

Density Determination

Determining the density of a substance is a fundamental practice in chemistry, often essential for identifying materials, as well as for understanding how they will behave in different environments. Density, fundamentally described as mass per unit volume, is expressed by the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).
For the problem given, where a liquid's identity was to be determined, a density determination exercise was crucial. By accurately measuring the mass and volume of the liquid and then applying the density formula, the technicians could calculate its density. In this case, the sample's mass was 22.3 grams and the volume was 15.0 milliliters. After converting milliliters to cubic centimeters—since densities given for comparison were in \( \frac{g}{cm^3} \)—the density was conveniently determined to be approximately 1.487 g/cm³.
Understanding the theory behind density allows us to deduce properties of substances and even identify them, when their properties are known and documented. This logic is fundamental to the identification of the mystery liquid in the given exercise.

Chemical Identity

Chemical identity refers to the unique characteristics that define a particular chemical substance. These characteristics include but are not limited to molecular structure, boiling and melting points, solubility, and density. Establishing the chemical identity of a substance is paramount, especially in scenarios where precise outcomes are required, such as in pharmaceuticals or safety-related industries.
In the context of our exercise, knowledge of the chemical identity of various liquids and their associated densities allows for the comparison and eventual determination of the unknown liquid. It was a mere relative comparison of the calculated density value—1.487 g/cm³—with those of known substances: acetone, benzene, chloroform, and carbon tetrachloride. Out of these options, the liquid density closest to the calculated value was that of chloroform, at 1.489 g/cm³, allowing for the assertion of the unknown liquid’s chemical identity.
Determining chemical identity through properties like density is an essential skill. Among other things, it ensures proper labeling and safe handling of chemical substances in environments like laboratories or industrial settings.

Conversion of Units

Understanding Measurements and Equivalencies

Conversions between units of measurement are commonly performed in scientific calculations and are crucial for accurate data analysis and reporting. In chemistry, failing to convert units appropriately can lead to errors in experimental results and conclusions.
The initial step in the solution required conversion of volume from milliliters to cubic centimeters. This step is necessary, since density was to be calculated in g/cm³. In general, 1 milliliter is equivalent to 1 cubic centimeter, thus making the conversion direct and straightforward for this exercise. However, it's worth noting that not all unit conversions are so simple, and sometimes it may require multiplying or dividing by conversion factors according to the relationship between the units.
Being proficient in unit conversion ensures consistency in the values used throughout calculations, which is vital for the integrity of scientific communication. Proper conversion supports the accuracy of the chemical identity determination as seen in this exercise, allowing the technicians to pinpoint which substance was in the bottle.