This lab report documents the experimental determination of density for multiple substances using two primary methods: geometric measurement for regular-shaped objects and water displacement for irregular-shaped objects. Students measured mass and volume for an unknown metal block (identified as aluminum with average density 2.76 g/cm³), an irregular metal sample (also aluminum, 2.43 g/ml), and distilled water (1.02 g/ml at 22°C). The report includes detailed calculations, results comparing experimental values to literature standards, and analysis of sources of measurement error. Post-lab questions address how experimental variables affect density calculations and the mathematical relationship between mass, volume, and density.
The purpose of this lab was to determine the density of different unknown substances using multiple methods and to identify unknown metals based on their calculated density values. Density, defined as mass per unit volume, was calculated for a regular-shaped object, an irregular-shaped object, and distilled water. The experimental results were then compared to known reference values to verify accuracy.
For the regular-shaped object (unknown code 3), dimensions were measured using a metric ruler. The object was a cube with length, width, and height each measuring 2.5 cm. Two independent determinations were performed, with each yielding a volume of 15.6 cm³ calculated using the formula V = L × W × H.
Calculations for Determination 1:
Volume = 2.5 cm × 2.5 cm × 2.5 cm = 15.6 cm³
Density = 42.9 g ÷ 15.6 cm³ = 2.74 g/cm³
Calculations for Determination 2:
Volume = 2.5 cm × 2.5 cm × 2.5 cm = 15.6 cm³
Density = 43.3 g ÷ 15.6 cm³ = 2.77 g/cm³
The average density of the block was calculated as (2.74 + 2.77) ÷ 2 = 2.76 g/cm³. This value matched the known density of aluminum, leading to the identification of the unknown object as aluminum.
The irregular-shaped metal sample (unknown code 2) required the water displacement method to determine volume. The metal sample was placed in a graduated cylinder filled with water, and the volume of the sample was calculated from the difference between final and initial water levels.
Calculations for Determination 1:
Volume = Final volume − Initial volume = 7.01 mL − 5.03 mL = 1.98 mL
Density = 4.83 g ÷ 1.98 mL = 2.43 g/mL
Calculations for Determination 2:
Volume = Final volume − Initial volume = 7.03 mL − 5.02 mL = 2.01 mL
Density = 4.86 g ÷ 2.01 mL = 2.42 g/mL
The average density was calculated as (2.43 + 2.42) ÷ 2 = 2.43 g/mL. This value also matched aluminum's known density, confirming the identification of the irregular sample as aluminum.
"Water density determination via mass-difference method"
Calculations for Determination 1:
Mass of water = 59.50 g − 49.36 g = 10.14 g
Density = 10.14 g ÷ 100.00 mL = 1.01 g/mL (at 21°C)
Calculations for Determination 2:
Mass of water = 59.62 g − 49.36 g = 10.26 g
Density = 10.26 g ÷ 100.00 mL = 1.03 g/mL (at 22°C)
The average density of water was (1.01 + 1.03) ÷ 2 = 1.02 g/mL. The literature value for water density is 1.00 g/mL at standard conditions, making the experimental result only 0.02 g/mL higher than expected.
The experiment successfully determined the density of unknown substances and identified the metals through comparison to known values. For the regular-shaped object, the mass was measured on a balance and the volume was calculated from geometric dimensions. The calculated density of 2.76 g/cm³ matched aluminum's known density. The same procedure was repeated to obtain a second independent measurement, ensuring greater confidence in the result.
"Critical evaluation of measurement errors and density relationships"
Sample Problem Calculation: For a regularly-shaped object with mass 56.88 g and dimensions 3.65 cm × 8.97 cm × 6.35 cm:
Volume = 3.65 cm × 8.97 cm × 6.35 cm = 208 cm³
Density = 56.88 g ÷ 208 cm³ = 0.27 g/cm³
Different materials exhibit different densities, which serve as identifying characteristics. When the masses and volumes of metal samples were measured using appropriate techniques for their geometry, the calculated densities closely matched reference values provided in the lab manual. Neither the regular-shaped nor the irregular-shaped samples yielded exactly identical density values to literature standards, primarily because measurement of both mass and volume introduces some uncertainty.
Both unknown metal samples were identified as aluminum, with average densities of 2.76 g/cm³ and 2.43 g/mL respectively. The consistency between these values confirmed that density is an intensive property that remains constant regardless of sample size or shape. The experimental density of water (1.02 g/mL at 22°C) differed from the literature value of 1.00 g/mL by only 2%, demonstrating that the laboratory procedures yielded results of acceptable accuracy. This small error margin is typical of undergraduate-level density determination experiments and illustrates the inherent limitations of manual measurement techniques.
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