Density Determination Using Various Methods to Measure Volume

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Density Determination Using Various Methods to
Measure Volume

• Experiment 2

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Experiment 2

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

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Densities
Increasing density Increasing heaviness
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Density from lab data
? Analytical balance
? Three methods

• Volume measurements
• by geometry
• by water displacement
• by pycnometry

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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

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Procedure

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

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1) Volume by geometry

• 1. Lengths and diameters l, d
• 2. Calculate volume and error V, sV

diameter, d
length, l
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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
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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

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Water displacement
Meniscus liquids curved surface
66.0 mL
46.5 mL
66.0 mL 45.5 mL 20.5 mL (objects
volume)
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3) Volume by pycnometry

• Pycnometry pertaining to specific gravity
• V mH2O/?H2O
• 1. Make pycnometer
• 2. Calibrate

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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

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Pycnometry continued
A
B
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Record temperature, T
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4) Volume of void in hollow cylinder
pycnometry
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5) Mass Fractions in Mixed Cylinder
Let mAl X.mcyl mbrass (1-X)mcyl
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Mixed cylinder
m ?
V
mAl X.mcyl mbrass (1-X)mcyl
? by mcyl
Collect terms with X
Solve for X
? to isolate X
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Mixed cylinder
Pycnometry volume Vmixed Balance mass
mmixed
X Al fraction 1-X brass fraction
No error propagation required for this
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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

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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)

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Caution
NO
YES