Density Determination: Comparative Study of Volumetric Glassware and Unknown Materials

Lab Notes: Density Determination Using Volumetric Glassware
Experiment 1: Measuring the Density of Water with Volume

Objective

The primary objective of this experiment was to determine the accuracy of different types of volumetric glassware, specifically a buret, a graduated cylinder, and a volumetric flask, in accurately determining the density of water.

General Approach Overview

The general procedure for each type of glassware involved several steps. First, a sample of deionized water was prepared, and its temperature was recorded. Next, the specific volumetric glassware was primed with deionized water. A clean, dry 125 mL125 \text{ mL} Erlenmeyer flask was used as the destination vessel, and its empty mass was measured using an analytical balance to 0.0001 g0.0001 \text{ g}. Approximately 25 mL25 \text{ mL} of water was then dispensed from the volumetric glassware into the Erlenmeyer flask, and the actual dispensed volume was recorded. Following this, the mass of the flask with the dispensed water was measured using the same analytical balance. The mass of the water was subsequently calculated by subtracting the empty flask mass from the flask-plus-water mass. Finally, the water was disposed of, and the flask was cleaned, dried, and re-massed before repeating the experiment for a second trial.

Specific Approach for Each Glassware

A. Buret

For the buret experiment, a large beaker was filled with deionized water, and its temperature was measured at 20.5∘C20.5^{\circ}\text{C} using a digital thermometer. The buret was then primed by rinsing it with the deionized water; this involved closing the stopcock, pouring a small amount of liquid into the top, opening the stopcock, and allowing some liquid to flow through to coat the inner surface. Afterward, the buret was refilled to begin the experiment. A clean, dry 125 mL125 \text{ mL} Erlenmeyer flask was massed to 0.0001 g0.0001 \text{ g} before the buret was filled to the 0.00 mL0.00 \text{ mL} mark. As close to 25.00 mL25.00 \text{ mL} of water as possible was dispensed into the Erlenmeyer flask, and the exact volume was recorded. The mass of the flask with water was then measured, and the entire process was repeated for a second trial.

B. Graduated Cylinder (50.0 mL50.0 \text{ mL})

In the graduated cylinder experiment, a large beaker was filled with deionized water, and its temperature was also measured at 20.5∘C20.5^{\circ}\text{C} with a digital thermometer. A 50.0 mL50.0 \text{ mL} graduated cylinder was primed with water. A clean, dry 125 mL125 \text{ mL} Erlenmeyer flask was massed to 0.0001 g0.0001 \text{ g}. Approximately 25 mL25 \text{ mL} of water was then filled into the flask using the graduated cylinder, with the meniscus carefully checked at eye level for accuracy, and the volume was recorded in mL. The mass of the flask with water was measured, and the process was repeated for a second trial.

C. Volumetric Flask (25 mL25 \text{ mL})

For the volumetric flask, a large beaker was filled with deionized water, and its temperature was measured at 20.5∘C20.5^{\circ}\text{C} with a digital thermometer. A 25 mL25 \text{ mL} volumetric flask was primed by rinsing it with a small amount of deionized water, and its outside was dried. The empty mass of the volumetric flask was measured to 0.0001 g0.0001 \text{ g}. The volumetric flask was then carefully filled with water until the bottom of the meniscus exactly touched the calibration line etched on the neck of the flask, using a dropper for precise adjustment. The volume was recorded as exactly 25.00 mL25.00 \text{ mL}. The mass of the flask containing water was measured, and the process was repeated for a second trial.

Experimental Data

Temperature for all trials: 20.5∘C20.5^{\circ}\text{C}

A. Buret Data

B. Graduated Cylinder (50 mL50 \text{ mL}) Data

C. Volumetric Flask (25 mL25 \text{ mL}) Data

Calculations and Results

Reference Density of Water at 20.5∘C20.5^{\circ}\text{C}: 0.9980 g/mL0.9980 \text{ g/mL}

A. Buret Calculations

  • Mass of water 1: 113.1302 g−88.1565 g=24.9737 g113.1302 \text{ g} - 88.1565 \text{ g} = 24.9737 \text{ g}

  • Volume 1: 25.00 mL25.00 \text{ mL}

  • Density 1: 24.9737 g25.00 mL=0.9989 g/mL\frac{24.9737 \text{ g}}{25.00 \text{ mL}} = 0.9989 \text{ g/mL}

  • Mass of water 2: 112.9436 g−88.1832 g=24.7604 g112.9436 \text{ g} - 88.1832 \text{ g} = 24.7604 \text{ g}

  • Volume 2: 24.96 mL24.96 \text{ mL}

  • Density 2: 24.7604 g24.96 mL=0.9920 g/mL\frac{24.7604 \text{ g}}{24.96 \text{ mL}} = 0.9920 \text{ g/mL}

  • Average Density: (0.9989 g/mL+0.9920 g/mL)2=0.99545 g/mL\frac{(0.9989 \text{ g/mL} + 0.9920 \text{ g/mL})}{2} = 0.99545 \text{ g/mL}

  • Percent Error: ∣(0.99545 g/mL−0.9980 g/mL)∣0.9980 g/mL×100=0.26%\frac{|(0.99545 \text{ g/mL} - 0.9980 \text{ g/mL})|}{0.9980 \text{ g/mL}} \times 100 = 0.26\%

B. Graduated Cylinder Calculations

  • Mass of water 1: 112.7475 g−88.3635 g=24.3840 g112.7475 \text{ g} - 88.3635 \text{ g} = 24.3840 \text{ g}

  • Volume 1: 24.9 mL24.9 \text{ mL}

  • Density 1: 24.3840 g24.9 mL=0.979 g/mL\frac{24.3840 \text{ g}}{24.9 \text{ mL}} = 0.979 \text{ g/mL}

  • Mass of water 2: 112.3822 g−88.2587 g=24.1235 g112.3822 \text{ g} - 88.2587 \text{ g} = 24.1235 \text{ g}

  • Volume 2: 24.7 mL24.7 \text{ mL}

  • Density 2: 24.1235 g24.7 mL=0.977 g/mL\frac{24.1235 \text{ g}}{24.7 \text{ mL}} = 0.977 \text{ g/mL}

  • Average Density: (0.979 g/mL+0.977 g/mL)2=0.9780 g/mL\frac{(0.979 \text{ g/mL} + 0.977 \text{ g/mL})}{2} = 0.9780 \text{ g/mL}

  • Percent Error: ∣(0.9780 g/mL−0.9980 g/mL)∣0.9980 g/mL×100=2.00%\frac{|(0.9780 \text{ g/mL} - 0.9980 \text{ g/mL})|}{0.9980 \text{ g/mL}} \times 100 = 2.00\%

C. Volumetric Flask Calculations

  • Mass of water 1: 45.0209 g−20.3391 g=24.6818 g45.0209 \text{ g} - 20.3391 \text{ g} = 24.6818 \text{ g}

  • Volume 1: 25.00 mL25.00 \text{ mL}

  • Density 1: 24.6818 g25.00 mL=0.9873 g/mL\frac{24.6818 \text{ g}}{25.00 \text{ mL}} = 0.9873 \text{ g/mL}

  • Mass of water 2: 44.9906 g−20.2674 g=24.7232 g44.9906 \text{ g} - 20.2674 \text{ g} = 24.7232 \text{ g}

  • Volume 2: 25.00 mL25.00 \text{ mL}

  • Density 2: 24.7232 g25.00 mL=0.9889 g/mL\frac{24.7232 \text{ g}}{25.00 \text{ mL}} = 0.9889 \text{ g/mL}

  • Average Density: (0.9873 g/mL+0.9889 g/mL)2=0.98810 g/mL\frac{(0.9873 \text{ g/mL} + 0.9889 \text{ g/mL})}{2} = 0.98810 \text{ g/mL}

  • Percent Error: ∣(0.98810 g/mL−0.9980 g/mL)∣0.9980 g/mL×100=0.99%\frac{|(0.98810 \text{ g/mL} - 0.9980 \text{ g/mL})|}{0.9980 \text{ g/mL}} \times 100 = 0.99\%

Lab Observations (Summary of Procedures)

During the experiment, the buret was primed with deionized water, and approximately 25 mL25 \text{ mL} was dispensed into an Erlenmeyer flask. The flask was then weighed both before and after the dispensing process. For the graduated cylinder, it was also primed with deionized water, filled to a volume of 25 mL25 \text{ mL}, dispensed into an Erlenmeyer flask, and the flask's mass was recorded before and after. Finally, the volumetric flask was primed with deionized water and filled precisely to the calibration line on its neck, with the flask weighed before and after filling.

Experiment 2: Determining the Density of Unknown Material

Objective

The objective of Experiment 2 was to determine the densities of both an unknown solid and an unknown liquid by utilizing volumetric glassware and an analytical balance.

Approach

A. Unknown Solid

The unknown solid, described as a clear, spherical marble, was initially characterized and sketched. Its mass was measured once using an analytical balance to the nearest 0.0001 g0.0001 \text{ g}. For volume measurement, two methods were employed. First, dimensional measurement involved using a plastic ruler to measure the marble's diameter to the nearest 0.01 cm0.01 \text{ cm}, and the volume was subsequently calculated using the geometric formula for a sphere. Second, the submersion (water displacement) method was used. This involved placing an appropriate volume of water in either a 10 mL10 \text{ mL} or 50 mL50 \text{ mL} graduated cylinder, ensuring the solid could be fully submerged. The initial water volume was recorded. The solid was carefully slid into the graduated cylinder to prevent air bubbles, and the final volume was recorded. The object's volume was then calculated by subtracting the initial from the final volume. Volume estimations were made to the nearest 0.1 mL0.1 \text{ mL} for the 50 mL50 \text{ mL} graduated cylinder and 0.01 mL0.01 \text{ mL} for the 10 mL10 \text{ mL} graduated cylinder. This submersion method was repeated twice with new water samples for each trial.

B. Unknown Liquid

For the unknown liquid, it was identified as 'Liquid A' and this identifier was recorded. The mass of the liquid was measured using an analytical balance to the nearest 0.0001 g0.0001 \text{ g}. The liquid's volume was measured using the most accurate glassware available, which, based on the data, was a buret. The entire process of measuring mass and volume was repeated twice for accuracy.

Experimental Data

A. Unknown Solid: Marble (Spherical), Clear

  • Mass Data:

    • Mass of weigh boat: 2.6907 g2.6907 \text{ g}

    • Mass of weigh boat + solid: 8.8642 g8.8642 \text{ g}

  • Solid Mass: 8.8642 g−2.6907 g=6.1735 g8.8642 \text{ g} - 2.6907 \text{ g} = 6.1735 \text{ g}

  • Volume by Dimensional Measurement:

    • Diameter of marble: 1.67 cm1.67 \text{ cm} (measured with a ruler)

  • Volume by Submersion (50 mL50 \text{ mL} Graduated Cylinder):

    • Trial 1:

    • Initial volume: 35.8 mL35.8 \text{ mL}

    • Final volume: 38.5 mL38.5 \text{ mL}

    • Volume of solid: 2.7 mL2.7 \text{ mL}

    • Trial 2:

    • Initial volume: 31.5 mL31.5 \text{ mL}

    • Final volume: 34.0 mL34.0 \text{ mL}

    • Volume of solid: 2.5 mL2.5 \text{ mL}

B. Unknown Liquid: A

  • Glassware Used: Buret

  • Trial 1:

    • Dry Erlenmeyer Flask Mass: 87.7785 g87.7785 \text{ g}

    • Flask with Liquid Mass: 114.6590 g114.6590 \text{ g}

    • Liquid Mass: 26.8805 g26.8805 \text{ g}

    • Liquid Volume: 25.19 mL25.19 \text{ mL}

  • Trial 2:

    • Dry Erlenmeyer Flask Mass: 88.1574 g88.1574 \text{ g}

    • Flask with Liquid Mass: 114.7011 g114.7011 \text{ g}

    • Liquid Mass: 26.5437 g26.5437 \text{ g}

    • Liquid Volume: 24.93 mL24.93 \text{ mL}

Calculations and Results

A. Solid Calculations

For the unknown solid, the measured mass was 6.1735 g6.1735 \text{ g}. The density derived from dimensional measurement began with a diameter of 1.67 cm1.67 \text{ cm}, giving a radius of 0.835 cm0.835 \text{ cm}. Using the volume formula for a sphere (V=43πr3V = \frac{4}{3} \pi r^3), the volume was calculated as 43×π×(0.835 cm)3=2.44 cm3\frac{4}{3} \times \pi \times (0.835 \text{ cm})^3 = 2.44 \text{ cm}^3. This resulted in a density of 6.1735 g2.44 cm3=2.53 g/cm3\frac{6.1735 \text{ g}}{2.44 \text{ cm}^3} = 2.53 \text{ g/cm}^3. For the density determined by submersion (water displacement), the average of the two volume measurements was (2.7 mL+2.5 mL)2=2.6 mL\frac{(2.7 \text{ mL} + 2.5 \text{ mL})}{2} = 2.6 \text{ mL}. This yielded a density of 6.1735 g2.6 mL=2.37 g/mL\frac{6.1735 \text{ g}}{2.6 \text{ mL}} = 2.37 \text{ g/mL}.

B. Liquid Calculations (Using Buret)

For the unknown liquid measured using a buret, the first trial yielded a liquid mass of 26.8805 g26.8805 \text{ g} and a volume of 25.19 mL25.19 \text{ mL}, resulting in a density of 26.8805 g25.19 mL=1.067 g/mL\frac{26.8805 \text{ g}}{25.19 \text{ mL}} = 1.067 \text{ g/mL}. In the second trial, the liquid mass was 26.5437 g26.5437 \text{ g} and the volume was 24.93 mL24.93 \text{ mL}, leading to a density of 26.5437 g24.93 mL=1.065 g/mL\frac{26.5437 \text{ g}}{24.93 \text{ mL}} = 1.065 \text{ g/mL}. The average density for the unknown liquid was calculated as (1.067 g/mL+1.065 g/mL)2=1.066 g/mL\frac{(1.067 \text{ g/mL} + 1.065 \text{ g/mL})}{2} = 1.066 \text{ g/mL}.