Density is a fundamental physical property of matter that quantifies how much mass is contained within a specific volume. It is an intensive property, meaning density remains constant regardless of the sample size. The relationship is expressed by the formula: Density equals Mass divided by Volume. Determining density requires two laboratory measurements: finding the mass of the sample and establishing its volume. Mass is consistently measured using a precise balance, but the technique for measuring volume differentiates the process for liquids and solids.
Determining Density for Liquids
The methodology for finding the density of a liquid involves a precise sequence of measurements because liquids conform to the shape of their container. To determine the mass of the liquid alone, the container is first weighed empty on an analytical balance; this initial measurement is often referred to as the tare weight. The liquid sample is then added, and the combined mass is measured a second time. Subtracting the initial mass of the empty container from the final combined mass yields the true mass of the liquid sample.
Measuring the volume of a liquid is accomplished using calibrated volumetric glassware, most commonly a graduated cylinder or a volumetric flask for high precision. The liquid is poured into the cylinder, and the volume is read from the scale etched on the glass. Because the liquid’s surface tension causes a slight curvature where it meets the glass wall, a phenomenon known as the meniscus forms. For most liquids, the measurement must be taken by reading the lowest point of this concave curve, with the observer’s eye positioned exactly level with the meniscus to prevent parallax error. Once both the mass and the volume are obtained, the density is calculated by dividing the mass value by the volume value, typically resulting in units of grams per milliliter (g/mL).
Measuring Density for Regularly Shaped Solids
For a solid object with a regular, easily definable geometric shape, such as a rectangular block, a cylinder, or a sphere, the mass is measured directly using a balance. Unlike liquids, the volume of these solids is calculated from their physical dimensions rather than being read directly from a container. Highly precise tools, like rulers or calipers, are used to measure the object’s length, width, and height or its diameter and length.
These linear measurements are applied to the standard geometric formula corresponding to the object’s shape to calculate the volume. For instance, the volume of a rectangular prism is found by multiplying its length, width, and height. The resulting volume, typically expressed in cubic centimeters (cm³), is then used with the measured mass in the density formula.
Measuring Density for Irregularly Shaped Solids
When a solid object has an irregular shape, such as a rock, determining its volume using geometric formulas becomes impossible. The water displacement method must be employed, based on the principle that an object displaces a volume of fluid equal to its own volume. The object’s mass is still measured first on a standard balance.
To find the volume, a graduated cylinder is partially filled with a liquid, usually water, and the initial volume is carefully recorded. The irregularly shaped solid is then gently submerged into the water, ensuring it is fully covered and no air bubbles are trapped on its surface. The submerged object causes the water level to rise, and the final volume reading is recorded from the graduated scale. The difference between the final volume and the initial volume represents the volume of the displaced water, which is precisely the volume of the solid object. With the mass and this derived volume, the density calculation is completed as with any other substance, often yielding a result in grams per cubic centimeter (g/cm³).