Density Determination Using Various Methods to Measure Volume

1
Density Determination Using Various Methods to
Measure Volume

• Experiment 1

2
Experiment 1

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

3
Densities
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
• 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 17.4640 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 17.4640 g
• Vwatercylinder 66.55 mL ?0.05mL
• ? Vwater 60.00 mL ?0.05mL
• Vcylinder 6.55 mL ?0.1mL

12
Water displacement
Meniscus liquids curved surface
66.0 mL
46.5 mL
66.0 mL 45.5 mL 20.5 mL (objects
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 masswaterpycnometer
• 1 92.7829 g
• 2 92.7825 g
• 3 92.7826 g
• 4 92.7831 g
• Average 92.7828 g
• smass ?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 92.7828 g (calibration average) ?0.0003g
• massB 103.7227 g ?0.0003g
• masscylinder 17.4640 g ?0.0001g

18
Record temperature, T
19
4) Volume of void in hollow cylinder
pycnometry
20
Example void calculation brass cylinder

• If Vcylinder 4.970 mL (by pycnometry)
• mcylinder 34.5964 g (analytical balance)
• ?brass 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
Mixed cylinder
m ?
V
mAl X.mcyl mbrass (1-X)mcyl
? by mcyl
Collect terms with X
Solve for X
? to isolate X
23
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 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
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