Density Determination Using Various Methods to Measure Volume Experiment 1

Experiment 1 Goal: Method: To accurately determine densities of objects Method: Determine volume of objects (3 methods) Calculate densities from mass and volume

Increasing “heaviness” Densities Substance Density (g/mL) wood 0.35 water 1.00 quartz 2.65 diamond 3.51 Al 2.7 brass 8.4 Au 19.3 Os 22.4 Increasing density = Increasing “heaviness”

Density from lab data  Analytical balance  Three methods Volume measurements: by geometry by water displacement by pycnometry

Uncertainties/Error Mass: balance ±0.0001 g Geometry: calipers ±1 of last digit cm Displacement: grad. cylinder ±0.1 mL probably Pycnometry: pynometer from average Propagate: all but mass fractions

Procedure 1. Four cylinders brass aluminum plugged hollow 2. Number # Record: 2. Number # 3. Type type 4. Mass (analytical balance) m#

1) Volume by geometry 1. Lengths and diameters l, d 2. Calculate volume and error V, sV diameter, d length, l

1) Al example – density using volume by geometry Mass 17.4640 g Length 5.08 cm Diameter 1.29 cm

Using vernier calipers Line on auxiliary scale matches at 8 Length: 3.38 ± 0.01 cm Section 3B in manual Object falls between 3.3 and 3.4 cm

2) Volume by water displacement 1. Record initial volume of water Vi 2. Add metal cylinder 3. Record final volume Vf 4. Calculate volume and error V, sV

2) Al example using volume by water displacement mass 17.4640 g Vwater+cylinder 66.55 mL 0.05mL  Vwater 60.00 mL 0.05mL Vcylinder 6.55 mL 0.1mL

Water displacement Meniscus: liquid’s curved surface 66.0 mL 46.5 mL (object’s volume)

3) Volume by pycnometry Pycnometry: pertaining to specific gravity V = mH2O/H2O 1. Make pycnometer 2. Calibrate

Calibration example Calibration – multiple trials (how well you fill to the mark) trial masswater+pycnometer 1 92.7829 g 2 92.7825 g 3 92.7826 g 4 92.7831 g Average: 92.7828 g σmass: 0.0003g (using big equation)

Pycnometry continued 3. Add H2O to mark record initial mass mi 4. Add metal cylinder 5. Remove H2O until at mark 6. Record final mass mf 7. Calculate volume and error V, sV

Pycnometry continued A B

3) Al example using volume by pycnometry massA 92.7828 g (calibration average) 0.0003g massB 103.7227 g 0.0003g masscylinder 17.4640 g 0.0001g

Record temperature, T

4) Volume of void in hollow cylinder metal V = pycnometry

Example void calculation – brass cylinder If Vcylinder = 4.970 mL (by pycnometry) & mcylinder =34.5964 g (analytical balance) & ρbrass = 8.387g/mL (pycnometry of solid cylinder) No error propagation required for this

5) Mass Fractions in Mixed Cylinder Let: mAl = X.mcyl mbrass = (1-X)mcyl

 to isolate X Mixed cylinder m  V = mAl = X.mcyl mbrass = (1-X)mcyl  by mcyl Collect terms with X Solve for X  to isolate X

No error propagation required for this Mixed cylinder Pycnometry: volume Vmixed Balance: mass mmixed X = Al fraction 1-X = brass fraction No error propagation required for this

Mixed cylinder – example Use pycnometry data to find: density of pure brass 8.387 g/mL density of pure Al (solid cylinders) 2.671 g/mL density of mixed cylinder (example) 6.457 g/mL X = Al fraction (here: 13.97%) 1-X = brass fraction (here: 86.03%) No error propagation required for this

Report Abstract Results/ Samples calculations including: Mass and volume by each method Volume of void Mass fraction Error analysis (parts 1 – 4) Volume of objects (3 methods) yes Volume of inner void no Mass fractions for mixed cylinder no Discussion/review questions

Equipment cylinders: brass, aluminum, mixed, hollow Vernier calipers 50 mL Erlenmeyer flask lab marker Pasteur pipet 100 mL graduated cylinder 400 mL beaker thermometer (analytical balance)

Caution NO YES