Problem 127 - General Chemistry

Question

Some bottles of colorless liquids were being labeled 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 A \(15.0-\mathrm{mL}\) sample withdrawn from one bottle weighed \(22.3 \mathrm{~g}\).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?

Step-by-Step Solution

Answer

The liquid is likely chloroform.

Step 1: Calculate Volume in Cubic Centimeters

Given the volume of the liquid in milliliters, let's first convert this to cubic centimeters since 1 mL = 1 cm³. Thus, the volume of the sample is 15.0 cm³.

Step 2: Calculate the Density of the Liquid

Density is defined as mass per unit volume. Using the given mass of 22.3 g and the volume of 15.0 cm³, the density can be calculated as:\[\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{22.3 \text{ g}}{15.0 \text{ cm}^3} = 1.487 \text{ g/cm}^3\]

Step 3: Compare Calculated Density with Known Densities

Compare the calculated density (1.487 g/cm³) with the densities provided: - Acetone: 0.792 g/cm³ - Benzene: 0.899 g/cm³ - Chloroform: 1.489 g/cm³ - Carbon tetrachloride: 1.595 g/cm³ The calculated density (1.487 g/cm³) is closest to the density of chloroform (1.489 g/cm³).

Step 4: Identify the Liquid

Based on the comparison in Step 3, the identity of the liquid is most likely chloroform since its density is nearly identical to the calculated density of 1.487 g/cm³.

Key Concepts

Density Calculation

Understanding density is vital in many scientific fields. It is defined as the amount of mass per unit volume of a substance. The formula for density is given by the equation: \[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]In the context of our exercise, with a mass of 22.3 grams and a volume of 15.0 milliliters, the density is calculated to be 1.487 g/cm³. This calculation is crucial in determining the identity of a mysterious liquid by comparing it against known densities of possible candidates. Practicing how to perform these calculations accurately is essential for identifying substances based on their physical properties.

Identifying Substances

Identifying liquid substances is often done by comparing calculated or measured parameters like density with known values from reference materials. In our problem, the unknown liquid's density was determined and compared against the densities of acetone, benzene, chloroform, and carbon tetrachloride.

• Acetone: 0.792 g/cm³
• Benzene: 0.899 g/cm³
• Chloroform: 1.489 g/cm³
• Carbon tetrachloride: 1.595 g/cm³

The calculated density of 1.487 g/cm³ was closest to chloroform, suggesting that the unknown liquid shared similar properties. Recognizing patterns like these in density values can aid in correctly labeling or identifying substances in the lab.

Conversion of Units

Before diving into density calculations, it's important to have unity in the units used for measurement. Here, the volume of the liquid is given in milliliters (mL), which is numerically equivalent to cubic centimeters (cm³).

• 1 mL = 1 cm³

This simple conversion ensures that the formula for density can be correctly applied without additional unit conversion steps. Understanding how to convert and align different units can greatly simplify mathematical computations in experimental settings.

Liquid Density Comparison

Comparing liquid densities provides a method of identifying substances and testing purity. In this exercise, after calculating the density of the unknown liquid sample, it was important to compare it against known values. This process involved:

• Identifying the number closest to the calculated density, which was 1.487 g/cm³.
• Noting the small difference from 1.489 g/cm³, the density of chloroform.

Such comparisons require careful attention to detail and understanding that even small variations in density measurements can point to different substances. This skill is particularly useful in chemistry and materials science when distinguishing between materials with similar physical properties.