Density is defined as the mass per unit volume of a substance, and it is a physical property of matter. A physical property can be measured without changing the chemical identity of the substance. Since pure substances have unique density values, measuring the density of a substance can help identify that substance. Density is determined by dividing the mass of a substance by its volume: \[Density = \frac{Mass}{Volume}\] The units of density are commonly expressed as g/cm3 for solids, g/mL for liquids, and g/L for gases. Density is also an intensive property of matter. This means that the value of density is independent of the quantity of matter present. For example, the density of a gold coin and a gold statue are the same, even though the gold statue consists of the greater quantity of gold. This is in contrast to extensive properties, like volume (the amount of space occupied by matter), which depend of the quantity of mater present. The more matter present, the larger the volume. In Part A of this lab, the mass and volume of distilled water will be measured in order to determine the density of water. Measurements will be performed on three samples of water to improve precision and accuracy. Mass will be measured with an electronic balance, in grams (g), and volume will be measured directly with a graduated cylinder, in milliliters (mL). Recall that when measuring liquid volumes, the graduated scale must be read from the lowest point of the curved surface of the liquid (the meniscus). The accuracy of the experimentally determined density of water will then be evaluated by comparison to the true, accepted density of water. Measuring the Volume of a Liquid The graduated cylinder markings are every 1-milliliter. When read from the lowest point of the meniscus, the correct reading is 30.0 mL. The first 2 digits 30.0 are known exactly. The last digit 30.0 is uncertain. Even though it is a zero, it is significant and must be recorded. In Part B of this lab, the density of aluminum will be determined using aluminum pellets. Again, mass will be measured using an electronic balance, in grams (g). However, since the pellets have irregular shapes, their volume must be measured indirectly using the technique of water displacement (also known as Archimedes Principle). This is because the volume of water that the solid displaces when it is immersed in the water is the same as the volume of the solid itself. The accuracy of this experimentally determined density will also be evaluated by comparison to the true, accepted density of aluminum. Measuring the Volume of an Irregularly Shaped Solid \[\text{Volume water displaced} = \text{Final volume } – \text{Initial volume}\] \[\text{Volume water displaced} = \text{Volume of solid}\] Note that 1 mL = 1 cm3. The density of aluminum will then be used in an applied problem to determine the thickness of a piece of aluminum foil. The piece of foil used can be considered to be a very flat rectangular box, where \[\text{Volume of foil} = length \times width \times thickness\] The foil volume can be obtained from the measured mass of the foil and the density of aluminum. Thus, if the length and width of the foil rectangle are measured, then the foil’s thickness may be calculated.
Laboratory investigations involve collecting data, which is often numeric. One common method of interpreting data is graphical analysis. In Part C of this lab, the mass and volume of several cylindrical pieces of an unknown solid material will be measured. Once again mass will be obtained using an electronic balance, in grams (g). But since the cylinders are regularly-shaped solids, their volumes (in cubic centimeters, cm3) will be calculated from their measured dimensions by using the appropriate volume formula: \[\text{Volume of a cylinder} =\pi r^{2} h\] \[h = \text{cylinder height or length}\] \[r = \text{cylinder radius } = \frac{1}{2} \text{ the diameter}\] Each pair of mass and volume values will then be plotted on graph paper as a scatter plot, with mass plotted on the y-axis and volume plotted on the x-axis. Since the plotted data generate (or at least approximate) a straight line, a “best-fit line” can be added to the graph. A best-fit line is a single line that comes as close as possible to all the plotted points. The equation of this best-fit line will have the familiar form \(y = mx + b\), where \(m\) represents the slope of the line, and \(b\) represents the y-intercept. This is illustrated in the figure below. Best-fit line equation: \[y = mx + b\] where
The y-intercept (\(b\)) is the point on the y-axis where the line crosses the axis. In this experiment, the value of \(b\) should be equal to zero. This is because if there is no mass, the volume must also be zero. However, note that your best-fit line might not pass exactly through the origin (0,0) due to experimental error – but it should be quite close. The slope of the line (\(m\)) is the change in the y-axis values divided by the change in x-axis values (or, rise over run): \[\begin{align*} m &= \frac{ \Delta y}{ \Delta x} \\[5pt] &= \frac{y_2 − y_1}{x_2−x_1} \end{align*} \] Since \( \Delta y\) is really the change in mass (\(\Delta \text{mass}\)), and \(\Delta x\) is really the change in volume (\( \Delta \text{volume}\)), this means that the slope of the best-fit line yields the density of the unknown material: \[m = \frac{\Delta y}{\Delta x} = \frac{\Delta \text{mass}}{ \Delta \text{volume}} = \text{density}\] Once the density is determined in this manner, it will be used to identify the unknown material analyzed.
Materials and Equipment 100-mL graduated cylinder, metric ruler*, aluminum pellets, small beaker, aluminum foil, thermometer, electronic balance, distilled water, tube of unknown solid cylinders* and graph paper. Be especially careful when adding the aluminum to your graduated cylinder, as the glass could break. Tilt the graduated cylinder and allow the pellets to gently slide to the bottom. Part A: The Density of Water
The Density of Aluminum
The Thickness of Aluminum Foil
Density is a physical / chemical property of matter and an intensive /extensive property of matter.
Experimental Data
Temperature of Water: ______________ Data Analysis
Experimental Data Table 1 – The Density of Aluminum
Table 2 – The Thickness of Aluminum Foil
Data Analysis
Experimental Data ID Code of Unknown Solid:
Show a sample calculation for volume using your measured dimensions for the small cylinder below. Data Analysis
Instructions for Graphing Data
Now calculate the slope (\(m\)) of your best-fit line using the equation: \(m = \dfrac{y_2-y_1}{x_2-x_1}\). Show your work, and report your result to the correct number of significant figures.
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