Density is a fundamental physical property that describes the concentration of mass within an object or substance. To determine density, you must calculate the ratio of an object’s mass to its volume. This relationship is expressed by the formula: Density equals Mass divided by Volume, or \(D = M/V\).
Understanding the Components: Mass and Volume
Measuring density requires accurate measurements of mass and volume. Mass is the measure of the amount of matter present in an object. Unlike weight, which is influenced by gravity, mass is an intrinsic property that remains constant regardless of location. Volume quantifies the three-dimensional space the object occupies.
Density is an intensive property, meaning it does not change based on the sample size. A small sliver of gold will have the same density as a large bar of gold because the ratio of mass to volume remains constant.
Accurate Measurement of Mass
The mass of an object is measured using a balance, an instrument designed to measure mass rather than weight. Accurate measurement begins with calibrating and zeroing the instrument. Before placing any sample, the balance should be “tared” or zeroed so that the display reads \(0.00\text{ g}\).
Never place a sample directly onto the balance pan, as this can contaminate the sensor. Instead, the sample should be placed in a clean weighing boat or container. You can then use the tare function to automatically subtract the container’s mass, leaving only the mass of the material displayed. For precise work, a technique called “weighing by difference” is used, where the container’s mass is recorded before and after adding the sample, and the difference is calculated manually.
Techniques for Determining Volume
Determining volume is often the most variable step in the density calculation process, as the method depends on the object’s physical state and shape.
Volume of Liquids
The volume of a liquid is measured using a graduated cylinder, a narrow, cylindrical piece of glassware marked with volume increments. Liquids poured into a cylinder form a curved surface called a meniscus due to the forces between the liquid and the glass. For water and most aqueous solutions, this curve dips downward, forming a concave shape.
To ensure an accurate reading, your eye must be level with the surface of the liquid. The measurement is taken from the lowest point of the concave meniscus. This technique minimizes parallax error, which is the apparent shift in reading caused by viewing the scale from an angle.
Volume of Regular Solids
A regular solid is an object with defined, measurable dimensions, such as a cube, a cylinder, or a rectangular prism. For these shapes, the volume is determined using geometric formulas. For example, the volume of a rectangular prism is calculated by multiplying its length, width, and height (\(V = L \times W \times H\)).
For a cylinder, the formula is \(V = \pi r^2 h\), where \(r\) is the radius of the circular base and \(h\) is the height. The measurements for these dimensions are taken using a precise instrument like a ruler or calipers.
Volume of Irregular Solids
For objects with irregular shapes, like a small rock, the water displacement method, also known as Archimedes’ principle, is used. This principle states that the volume of an object submerged in a fluid is equal to the volume of the fluid it displaces.
The process begins by adding a known volume of water to a graduated cylinder, noting this as the initial volume (\(V_{initial}\)). The solid object is then carefully lowered into the cylinder, ensuring it is completely submerged. The new reading is recorded as the final volume (\(V_{final}\)). The volume of the irregular object is the difference between the final and initial readings: \(V_{object} = V_{final} – V_{initial}\). This method is effective because \(1\text{ milliliter}\) (\(\text{mL}\)) of displaced water is equivalent to \(1\text{ cubic centimeter}\) (\(\text{cm}^3\)) of volume.
Calculation and Standard Units
Once the mass and volume have been measured, the final step is to calculate the density using the formula \(D = M/V\). For example, if a sample of metal has a mass of \(14.0\text{ grams}\) and occupies a volume of \(2.5\text{ cubic centimeters}\), the density calculation is \(14.0\text{ g} / 2.5\text{ cm}^3\). This calculation yields a density of \(5.6\text{ g/cm}^3\).
Density is expressed by combining the units of mass and volume. Common laboratory units include grams per milliliter (\(\text{g/mL}\)) or grams per cubic centimeter (\(\text{g/cm}^3\)). Since one milliliter is equal to one cubic centimeter, these units are interchangeable. For larger quantities, the standard international unit is kilograms per cubic meter (\(\text{kg/m}^3\)). Mass and volume units must be consistent before performing the division to ensure the resulting density unit is meaningful.