Problem 66 - Chemistry Matter and Change

Question

A 5 -mL sample of water has a mass of 5 g. What is the density of water?

Step-by-Step Solution

Answer

The density of water is 1 g/mL.

Step 1: Identify the mass and volume given

The mass of water is 5 g, and the volume is 5 mL.

Step 2: Set up the density formula

Density = Mass / Volume

Step 3: Plug in the values

Density = (5 g) / (5 mL)

Step 4: Calculate the density

Density = 1 g/mL

Key Concepts

Mass and Volume Relationship

Understanding the relationship between mass and volume is crucial for comprehending various physical properties of materials, including density. Mass refers to the amount of matter in an object and is usually measured in grams (g) or kilograms (kg). Volume, on the other hand, is the space that an object occupies, and its units are often cubic centimeters (cm³), milliliters (mL), or liters (L). While mass is a measure of an object's inertia, volume indicates its size.

When considering the mass and volume relationship, it is important to realize that two objects with the same volume can have different masses depending on their material. For instance, 1 mL of lead is much heavier than 1 mL of water. This implies that the material's density varies, which leads us to the concept of density itself. This connection is used extensively in sciences and everyday situations such as cooking, where ingredients might be measured by volume but their properties, like heaviness, are related to mass.

For a given substance, increasing the mass while keeping the volume constant will result in an increase in density, while increasing the volume with constant mass will lead to a decrease in density. This principle helps in identifying substances and plays a critical role in applications like buoyancy in fluids.

Density Formula

The density of a substance can be calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
This formula allows us to compare different materials and understand their properties more thoroughly. In the given exercise, the mass of water is 5 grams and the volume is 5 milliliters. By applying the formula, we find that water's density is 1 gram per milliliter. This calculation gives us an insight into one of water's most defining physical properties – its consistent density at 1 g/mL at room temperature, which is used as a reference point in many scientific measurements.

When interpreting the density formula, it is essential to ensure that the mass and volume values are in proper units that can cancel out to give density's units. Consequently, if one were to use kilograms and cubic meters, the density result would be in kilograms per cubic meter (kg/m³), a standard SI unit of density. It is the consistency and uniformity of this property that makes it particularly useful in various scientific and industrial applications.

Units of Density

In scientific contexts, density is typically expressed in units like grams per cubic centimeter (g/cm³) for solids, grams per milliliter (g/mL) for liquids, and kilograms per cubic meter (kg/m³) for gases. These units are derived from the mass and volume units used in the density calculation formula. It is important to use the appropriate units when performing calculations to ensure accuracy and consistency.

The choice of units will depend on the context and the substance being measured. For example, buoyancy calculations in engineering applications might require the use of kilograms per cubic meter (kg/m³) for compatibility with other measurements in the SI system. On the other hand, in a chemistry lab, the use of grams per milliliter (g/mL) might be more common due to the small quantities of chemicals typically used.

Understanding and converting between these units is an important skill in scientific endeavors. Notably, 1 g/cm³ is equivalent to 1 g/mL, since 1 cm³ is equal to 1 mL. This conversion is useful when comparing densities of different substances or scaling up measurements, a skill which enhances a student's ability to analyze and interpret scientific data.