Density Determinations True Density of Aluminum: 2.70 g/cm³ Weight of Your Aluminum: 26.975 g PART 4: Aluminum Displacement Method Trial 1: 40.0 mL Trial 2: 42.5 mL Trial 3: 51.3 mL Initial water volume in cylinder: 51.5 mL Final water volume in cylinder: 54.2 mL Volume of rod: 62.5 mL Density of aluminum rod: 0.826 g/mL Percent error in value (NOTE: mL cm³)
The Correct Answer and Explanation is:
Let’s calculate the missing values step by step using the given data:
Volume of rod (by displacement method)
The volume of the rod is calculated by subtracting the initial water volume from the final water volume: Volume of rod=Final volume−Initial volume\text{Volume of rod} = \text{Final volume} – \text{Initial volume}Volume of rod=Final volume−Initial volume
- Trial 1: 51.5 mL−40.0 mL=11.5 mL51.5\ \text{mL} – 40.0\ \text{mL} = 11.5\ \text{mL}51.5 mL−40.0 mL=11.5 mL
- Trial 2: 54.2 mL−42.5 mL=11.7 mL54.2\ \text{mL} – 42.5\ \text{mL} = 11.7\ \text{mL}54.2 mL−42.5 mL=11.7 mL
- Trial 3: 62.5 mL−51.3 mL=11.2 mL62.5\ \text{mL} – 51.3\ \text{mL} = 11.2\ \text{mL}62.5 mL−51.3 mL=11.2 mL
Density of aluminum rod
Density is calculated using the formula: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Given mass = 26.975 g
- Trial 1: 26.97511.5=2.3457 g/mL\frac{26.975}{11.5} = 2.3457\ \text{g/mL}11.526.975=2.3457 g/mL
- Trial 2: 26.97511.7=2.3056 g/mL\frac{26.975}{11.7} = 2.3056\ \text{g/mL}11.726.975=2.3056 g/mL
- Trial 3: 26.97511.2=2.4085 g/mL\frac{26.975}{11.2} = 2.4085\ \text{g/mL}11.226.975=2.4085 g/mL
Percent error calculation
Percent error is determined by: Percent Error=∣Measured−True∣True×100\text{Percent Error} = \frac{|\text{Measured} – \text{True}|}{\text{True}} \times 100Percent Error=True∣Measured−True∣×100
True density = 2.70 g/mL
- Trial 1: ∣2.3457−2.70∣2.70×100=13.11%\frac{|2.3457 – 2.70|}{2.70} \times 100 = 13.11\%2.70∣2.3457−2.70∣×100=13.11%
- Trial 2: ∣2.3056−2.70∣2.70×100=14.60%\frac{|2.3056 – 2.70|}{2.70} \times 100 = 14.60\%2.70∣2.3056−2.70∣×100=14.60%
- Trial 3: ∣2.4085−2.70∣2.70×100=10.81%\frac{|2.4085 – 2.70|}{2.70} \times 100 = 10.81\%2.70∣2.4085−2.70∣×100=10.81%
Summary Table
| Trial 1 | Trial 2 | Trial 3 | |
|---|---|---|---|
| Volume of rod (mL) | 11.5 | 11.7 | 11.2 |
| Density (g/mL) | 2.3457 | 2.3056 | 2.4085 |
| Percent error (%) | 13.11 | 14.60 | 10.81 |
Explanation
The density determination of aluminum through the displacement method depends on accurate measurements of water displacement and mass. The volume of the rod is calculated from the difference between the final and initial water levels. This value directly affects the density calculation, as density is the ratio of mass to volume. Small deviations in volume readings result in noticeable changes in calculated density. Percent error helps evaluate the accuracy of these results compared to the true density of aluminum. The percent error values show deviations, likely caused by experimental errors such as parallax in reading the meniscus, air bubbles clinging to the submerged sample, or incomplete immersion of the rod.
