Density is a fundamental physical property of matter, representing the amount of mass contained within a specific volume. It is mathematically expressed by the formula \(D = M/V\), where \(D\) is density, \(M\) is mass, and \(V\) is volume. The result is typically measured in units like grams per cubic centimeter (\(g/cm^3\)). Determining the density of any substance requires two distinct experimental measurements: the mass of the sample and the precise volume it occupies.
Testing Density of Regular Solids
Measuring the density of a solid with a recognizable geometric shape, such as a cube or cylinder, begins with determining its mass. A balance or scale is used to accurately weigh the object, providing the mass measurement in grams. This measurement should be recorded with the precision allowed by the instrument.
The next step involves determining the object’s volume through direct linear measurement. Tools like rulers or calipers are used to measure the object’s dimensions, such as its length, width, and height. Precision is important here, and calipers offer greater accuracy for smaller objects than a standard ruler.
Once the dimensions are recorded, the appropriate geometric formula is applied to calculate the volume. For instance, the volume of a rectangular solid is found by multiplying the length, width, and height. A cylindrical object requires measuring the height and the radius of the circular base.
With both the mass and the calculated volume established, the final density is found by dividing the mass by the volume. The resulting figure is the object’s density, typically expressed as grams per cubic centimeter. This straightforward method is only suitable for objects whose dimensions can be easily and precisely measured.
Testing Density of Irregular Solids
For objects that do not possess a simple, measurable shape, such as a rock, the volume must be determined using the water displacement method, which is based on Archimedes’ Principle. The initial step remains the same: the mass of the irregular solid is measured accurately using a scale or balance and recorded carefully.
The principle of displacement states that when an object is fully submerged in a fluid, it pushes aside a volume of that fluid exactly equal to its own volume. To apply this, a graduated cylinder is partially filled with water, and the initial volume reading is noted at the bottom of the meniscus. The solid must be one that sinks in water and does not react with it, ensuring the volume measurement is accurate.
The irregular solid is then gently lowered into the graduated cylinder until it is completely submerged without splashing or trapping air bubbles. The water level will rise, and the new, final volume reading is recorded from the cylinder’s markings. The difference between the final and initial volume readings gives the volume of the solid.
This volume difference, expressed in milliliters (\(mL\)), is numerically equivalent to the volume in cubic centimeters (\(cm^3\)). After establishing the solid’s mass and its volume through displacement, the density is calculated by dividing the mass by the determined volume. This method is effective because it bypasses the need for complex geometric calculations entirely.
Testing Density of Liquids
Determining the density of a liquid requires a specific approach to isolate the liquid’s mass from its container. The procedure begins by accurately measuring a specific volume of the liquid using a graduated cylinder. The volume should be read by observing the bottom of the meniscus, which is the curve formed by the liquid’s surface.
Isolating the mass of the liquid itself is the next step. First, the empty, clean, and dry graduated cylinder is placed on a balance, and its mass (the tare mass) is recorded. Alternatively, the balance can be “tared” or zeroed with the empty container on it, effectively setting the container’s mass to zero.
The measured volume of the liquid is then added to the container, and the total mass of the container plus the liquid is measured. If the balance was tared, this reading is the mass of the liquid directly. If the balance was not tared, the mass of the liquid is calculated by subtracting the initial tare mass of the empty container from the total mass measurement.
Finally, the measured mass of the liquid is divided by the volume that was carefully measured in the graduated cylinder. This calculation yields the density of the liquid, often expressed in grams per milliliter (\(g/mL\)). This technique ensures that the container’s weight does not interfere with the final density value.