1. Density Determination Using Various Methods to Measure Volume
Experiment 1

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

3. 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”

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

5. 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

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

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

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

9. 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

10. 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

11. 2) Al example using volume by water displacement
mass g
Vwater+cylinder mL 0.05mL
 Vwater mL 0.05mL
Vcylinder mL 0.1mL

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

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

14. Calibration example
Calibration – multiple trials (how well you fill to the mark)
trial masswater+pycnometer g g g g
Average: g
σmass: 0.0003g (using big equation)

15. 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

16. Pycnometry continued A B

17. 3) Al example using volume by pycnometry
massA g (calibration average) 0.0003g
massB g 0.0003g
masscylinder g 0.0001g

18. Record temperature, T

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

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

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

22.  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

23. 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

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

25. 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

26. 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)

27. Caution NO
YES