Determination of The Density of Solid Objects

The objective of this lab is to determine the densities of solid objects, specifically aluminum and zinc cylinders. The lab aims to familiarize students with the tools and equipment used in scientific analysis, develop skills in interpreting numerical and graphical data, and demonstrate safe practices in the chemical laboratory.

Density is defined as the mass of a substance per unit volume. In this lab, the density of the cylinders will be determined using the formula d = m/V, where d is the density, m is the mass, and V is the volume. The units commonly used for density are grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL).

The lab introduces two methods for determining the volume of regularly shaped solids. The first method involves using the geometrical formula for volume after measuring the dimensions of the object. The second method is the water displacement method, where the solid is submerged in a known volume of water, and the increase in volume is equal to the volume of the object.

For the aluminum cylinders, the mass will be measured using an analytical balance, and the volume will be calculated using the measurements of length and diameter with a Vernier caliper. The lab provides step-by-step instructions for weighing the cylinders and measuring their dimensions.

For the zinc cylinders, the mass will be measured using a top loading balance, and the volume will be determined by the water displacement method. The lab provides instructions for weighing the cylinders and measuring the volume by carefully placing them in a graduated cylinder containing water.

Calculations involve computing the volume of each cylinder using the formula V = (πd²h)/4, where d is the diameter and h is the height (length) of the cylinder. The density of each cylinder is then calculated by dividing the mass by the volume.

To analyze the data, graphs will be constructed for both the aluminum and zinc cylinders. The mass of the cylinders will be plotted on the y-axis, and the volume will be plotted on the x-axis. A straight line will be drawn through the points, and the slope of the line will be calculated. The slope represents the density of the cylinders.

By conducting the lab activities, students will gain hands-on experience in measuring mass, volume, and dimensions of objects. They will also learn how to calculate density and interpret data through graphical analysis. Additionally, the lab promotes an understanding of the concept of density and its application in distinguishing different substances.

Objective

·         Use the tools and equipment necessary for basic scientific analysis and research

·         Interpret the numerical and graphical presentation of scientific data

·         Demonstrate how to measure the Density of Solids

·         Demonstrate safe practices in the Chemical Laboratory

·         Demonstrate the proper use of Exponential Notation and Significant Figures

·         Demonstrate an understanding of the composition of matter and energy

·         Record the results of investigation through writing

·         Use scientific reasoning to evaluate physical and natural phenomena

·         Identify the unifying themes of the scientific field of study

Materials

·         5 zinc cylinders

·         5 aluminum cylinders

·         Vernier caliper

·         100 ml graduated cylinder

Discussion

Density is a fundamental property of any substance, defined as the mass of the substance divided by its volume. In other words, density represents the ratio of mass to volume and can be expressed as:

(1)                                                                       

where d is the density, m is the mass, and V is the volume. The units used to measure density depend on the units used for mass and volume. In the laboratory, mass is typically measured in grams (g) and volume in cubic centimeters (cm³) or milliliters (mL). Therefore, the most common units for density are grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL). It's important to note that while both mass and volume depend on the size of the sample, density remains constant because it is a ratio between mass and volume.

For example, let's consider two samples of gold. One sample has a volume of 4.00 cm³ and a mass of 77.2 g, while the other sample has a volume of 1.00 cm³ and a mass of 19.3 g. The density of each sample can be calculated as follows:

(2)                                                   d = m/V = 77.2 g/4.00 cm3 = 19.3 g/cm3

d m/V = 19.3 g/1.00 cm3 = 19.3 g/cm3

Even though the two gold samples have different masses and volumes, their densities are the same. This demonstrates that density can be used to distinguish between different pure substances.

In this experiment, we will determine the densities of aluminum and zinc cylinders. The masses will be measured using the top loading balance for zinc and the analytical balance for aluminum. The volume of regularly shaped solids can be determined through either of two methods: (1) using the geometric formula for volume after measuring the object's dimensions, or (2) using the water displacement method, where the solid is submerged in a known volume of water and the resulting increase in volume is measured. Both of these methods will be utilized in this experiment.

When a set of data points can be connected by a straight line, the relationship between the data can be described using the mathematical equation y = mx + b. In this expression, y represents the values plotted on the vertical axis (ordinate), x represents the values plotted on the horizontal axis (abscissa), m represents the slope of the straight line, and b represents the y-intercept (the value of y when x is zero).

By applying this graphical approach, we can determine the relationship between mass and volume for various samples of the same substance. If we determine the mass and volume of each sample, we can plot the mass on the y-axis and the corresponding volume on the x-axis. The density of the substance can then be determined from the graph as the slope of the line. It's worth noting that the slope of a straight line is calculated as the ratio of the difference in y values to the difference in the corresponding x values:

(3)                                                  Slope = ∆y / ∆x = (y1 - y2) / (x1 - x2) = m = density

Procedure

Obtain a set of zinc and aluminum cylinders (5 of each) and work in pairs for this experiment.

A. Density of Aluminum.

To obtain accurate measurements, follow the steps below:

1.   Utilize the analytical balance to measure the mass of the aluminum sample. Record the mass to the nearest 0.0001 g.

2.   Measure the diameter of each cylinder using a Vernier caliper, ensuring precision to the nearest 0.01 cm. All cylinders should have the same diameter. Note down this value on the report sheet.

3.   Weigh each aluminum cylinder individually on the analytical balance, ensuring measurements are rounded to the nearest 0.0001 g. Record the weights on the report sheet.

4.   Use the Vernier caliper to measure the length (height) of each cylinder, with accuracy to the nearest 0.01 cm. Record these values on the report sheet.

B. Density of Zinc.

Using a top loading balance, ascertain the mass of the zinc sample, and employ the displacement method to calculate its volume.

Individually weigh the zinc cylinders on the top loading balance, rounding to the nearest 0.01 g, and document the weights in the report sheet.

Fill a 100 ml graduated cylinder with sufficient water to submerge the object. Accurately measure the volume of water in the cylinder to the nearest 0.1 ml by observing the bottom of the meniscus (refer to Figure 4).

Gently place the zinc cylinder in the graduated cylinder. You will have to tip the graduated cylinder on an angle and slowly slide the zinc down into the water in order to avoid breaking the graduated cylinder. Read the new volume and determine the volume of each piece of zinc.

Calculations

A. Density of Aluminum.

To determine the volume of each cylinder in cubic centimeters, apply the formula:

(1)                                                                 V = (π d2h) / 4

Here, d represents the diameter of the cylinder, h denotes the height (length) of the cylinder, and π is approximately equal to 3.14. Please record the results of these calculations in the report sheet. Next, calculate the density of each cylinder by dividing the measured mass by the calculated volume. Make sure to note down the density values on the report sheet.

To visualize the relationship between the mass and volume of the aluminum cylinder, create a graph. Plot the mass of the aluminum cylinder on the y-axis (ordinate) and the volume of the aluminum cylinder on the x-axis (abscissa). Ensure that you choose suitable scales to construct a graph of reasonable size. Draw the best possible straight line through the plotted points. To determine the slope of this line, refer to Equation (3) mentioned above. Record this slope value as the density of the aluminum from the graph on the report sheet.

B. Density of zinc.

After measuring the mass and volume of each cylinder, you can calculate their densities by dividing the mass by the volume. Record these density values in the report sheet.

Plot the mass of the zinc on the y-axis and the volume of the zinc on the x-axis. Draw a straight line that best fits the data points and determine the slope of the graph. Enter this slope as the density of zinc in the report sheet.

To compare the densities (slopes) of aluminum and zinc, it would be beneficial to graph both metals on the same graph.

Report Sheet for Density of Metal Objects

Name_______________________________________                          Date___________________________

Lab / Section_________________________________

Zinc

Mass 1 (Grams) ____________________

Mass 2 (Grams) ____________________

Mass 3 (Grams) ____________________

Mass 4 (Grams) ____________________

Mass 5 (Grams) ____________________

Volume 1 (mL) ____________________

Volume 2 (mL) ____________________

Volume 3 (mL) ____________________

Volume 4 (mL) ____________________

Volume 5 (mL) ____________________

Aluminum

Mass 1 (Grams) ____________________

Mass 2 (Grams) ____________________

Mass 3 (Grams) ____________________

Mass 4 (Grams) ____________________

Mass 5 (Grams) ____________________

Length 1 (cm) ____________________

Length 2 (cm) ____________________

Length 3 (cm) ____________________

Length 4 (cm) ____________________

Length 5 (cm) ____________________

Review Questions

1.       Define density and explain how it is calculated.

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2.       What are the units commonly used to express density?

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3.       Describe the two methods for determining the volume of regularly shaped solids.

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4.       What tools are used to measure the mass of the aluminum cylinders in the lab?

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5.       How is the volume of the aluminum cylinders calculated using a Vernier caliper?

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6.       Explain the water displacement method for determining the volume of the zinc cylinders.

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7.       Why is it important to read the bottom of the meniscus when measuring the volume of water?

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8.       How is the density of a cylinder calculated using its mass and volume?

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9.       What factors determine whether an object will float or sink in a liquid?

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10.    How does the density of aluminum compare to the density of zinc based on the experimental data?

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11.    Interpret the slope of a graph representing the relationship between mass and volume.

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12.    What does it mean if the slope of the graph is positive, negative, or zero?

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13.    Describe the relationship between mass, volume, and density based on the experimental results.

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14.    Why is it important to conduct multiple trials and calculate the mean density for each type of cylinder?

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15.    Discuss the sources of error that could affect the accuracy of the density measurements.

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16.    Explain the significance of the concept of density in distinguishing between different substances.

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17.    How does the density of a substance remain constant regardless of the size of the sample?

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18.    Compare and contrast the analytical balance, triple beam balance, and top loading balance in terms of their uses and characteristics.

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19.    Describe the precautions and proper handling techniques for using the analytical balance in the lab.

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20.    Discuss the implications and applications of density measurements in various scientific fields and industries.

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