Problem 77 - Chemistry The Molecular Nature of Matter

Question

Chloroform, a chemical once used as an anesthetic, has a density of \(1.492 \mathrm{~g} / \mathrm{mL}\). What is the mass in grams of \(185 \mathrm{~mL}\) of chloroform?

Step-by-Step Solution

Answer

Mass of chloroform = 276.02 g

Step 1: Understand the Problem

We are asked to find the mass of 185 mL of chloroform using its density, which is 1.492 g/mL. To find the mass, we will use the formula: mass (m) = density (d) × volume (V).

Step 2: Plug in the Given Values

Insert the given values for density (1.492 g/mL) and volume (185 mL) into the formula to calculate the mass.

Step 3: Calculate the Mass

Multiply the density of chloroform by the volume to get the mass: m = 1.492 g/mL × 185 mL.

Step 4: Perform the Multiplication

m = 276.02 g. This is the mass of 185 mL of chloroform.

Key Concepts

Chemical Density

Chemical density is a fundamental property of any substance that shows the relationship between its mass and volume. It is commonly expressed in units of grams per milliliter (g/mL) or kilograms per cubic meter (kg/m^3) for liquids and solids, and grams per liter (g/L) for gases. The density of a chemical is unique and can be used to identify it, as well as to predict how it will behave in different situations. For example, an object made of a material with a higher density than water will sink when placed in water.

In the case of chloroform with a density of \(1.492 \mathrm{\ g/mL}\), this information tells us that for every milliliter of chloroform, the mass is 1.492 grams. This is critical for calculating the mass of specific volumes, which often applies in chemical labs and pharmaceutical applications where precise measurements are necessary.

Mass-Volume Relationship

The mass-volume relationship is a direct application of the concept of density. It tells us that the mass of a substance can be determined by multiplying its volume by its density. This concept is rooted in the definition of density itself, \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), and it allows scientists and engineers to calculate the quantity of a substance required or produced in a reaction.

When we are given the volume of a chemical, such as chloroform, and we know its chemical density, we can calculate the mass without the need to physically measure it on a scale. This is extremely helpful in situations where a precise amount of a chemical is needed to carry out a reaction or when packaging and transporting chemicals with known densities.

Density Formula Application

The density formula, \( m = d \times V \), where \( m \) is mass, \( d \) is density, and \( V \) is volume, is a straightforward expression that allows for the calculation of mass when density and volume are known. Applying this formula is a routine task in many scientific and industrial fields.

In our chloroform example, the mass of the chloroform can be calculated by applying its density to the formula: \( m = 1.492 \mathrm{\ g/mL} \times 185 \mathrm{\ mL} \). By multiplying these values, we find that the mass of the chloroform is 276.02 grams. This practical application of the density formula is essential in dosage calculation for medications, mixing ratios for solutions, and material requirements in manufacturing, among other uses. It provides an efficient way to quantify substances without excess waste or the need for trial and error.