Density Determination Using Various Methods to Measure Volume. Experiment 1
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1 Density Deterination Using Various Methods to Measure Volue Experient
2 Experient Goal: To accurately deterine densities of objects Method: Deterine volue of objects (3 ethods) Calculate densities fro ass and volue
3 Densities Substance Density (g/l) wood 0.35 water.00 quartz 2.65 diaond 3.5 Al Au 9.3 Os 22.4 Increasing density Increasing heaviness
4 Density fro lab data ass volue V Analytical balance Three ethods Volue easureents: by geoetry by water displaceent by pycnoetry
5 Uncertainties/Error Mass: balance ±0.000 g Geoetry: calipers ± of last digit c Displaceent: grad. cylinder ±0. L probably Pycnoetry: pynoeter fro average Propagate: all but ass fractions
6 . Four cylinders Procedure aluinu plugged hollow Record: 2. Nuber # 3. Type type 4. Mass (analytical balance) #
7 ) Volue by geoetry. Lengths and diaeters l, d 2. Calculate volue and error V, σ V diaeter, d length, l V π d 2 2 l π 4 d 2 l
8 ) Al exaple density using volue by geoetry Mass g Length 5.08 c Diaeter.29 c g d V. 29c π c g c 3 σ ± ± ( σ σ σ σ ) + l + d + d ( g 2 ) g 0. 0c 0. 0c g 5. 08c. 29 ± c g c 3 l d d c
9 Using vernier calipers Length: 3.38 ± 0.0 c Line on auxiliary scale atches at 8 Section 3B in anual Object falls between 3.3 and 3.4 c
10 2) Volue by water displaceent. Record initial volue of water V i 2. Add etal cylinder 3. Record final volue V f 4. Calculate volue and error V, σ V V cylinder V final V initial
11 2) Al exaple using volue by water displaceent ass g V water+cylinder L ±0.05L V water L ±0.05L V cylinder 6.55 L ±0.L V g 6. 55L 2.67 g L σ ± ( σ ) ( ) σv g g 0. L g + ± ± 0 04 L V 2 L g 6. 6L.
12 Water displaceent Meniscus: liquid s curved surface 66.0 L 46.5 L 66.0 L 45.5 L 20.5 L (object s volue)
13 3) Volue by pycnoetry Pycnoetry: pertaining to specific gravity. Make pycnoeter 2. Calibrate V H2O / H2O
14 Calibration exaple Calibration ultiple trials (how well you fill to the ark) Average: σ ass : trial ass water+pycnoeter g g g g g ±0.0003g (using big equation)
15 Pycnoetry continued 3. Add H 2 O to ark record initial ass 4. Add etal cylinder 5. Reove H 2 O until at ark i 6. Record final ass f 7. Calculate volue and error V, σ V V cyl V displaced water displaced water water
16 Pycnoetry continued A d π 2 Area π l d l B d π 2 Area π l d l V ass + ass ass + A object B ass displaced water
17 3) Al exaple using volue by pycnoetry ass A g (calibration average) ±0.0003g ass B g ±0.0003g ass cylinder g ±0.000g ass σ displaced water ass displaced water ass A + ass object ass g g ± ( g g g ) ± g B g g V cyl V displaced water g L g L ( ) σ σ σ g + ± V ( ) ± L( ) ± 0. L σv ± V cyl cyl cyl g 0007 V σ ± g L ( σ ) ( ) σv g g L g + ± L + ± L V g L g L
18 Record teperature, T Density of Water vs. Teperature.0000 Density (g/l) Teperature ( o C)
19 4) Volue of void in hollow cylinder V V + cyl etal V void pycnoetry V etal
20 Exaple void calculation cylinder If V cylinder L (by pycnoetry) & cylinder g (analytical balance) & 8.387g/L (pycnoetry of solid cylinder) V void V cyl V etal L ( ) g L L g No error propagation required for this
21 5) Mass Fractions in Mixed Cylinder + cyl Al Let: Al X. cyl (-X) cyl cyl X + cyl ( X ) cyl
22 V V + V cylinder Al Al Mixed cylinder V Al V cyl + Al X. cyl Al (-X) cyl X cyl ( X ) cyl Vcyl + by cyl cyl X Al + ( X ) Collect ters with X cyl X Al X Solve for X cyl X Al to isolate X
23 Mixed cylinder Pycnoetry: volue V ixed Balance: ass ixed X cyl Al X Al fraction -X fraction No error propagation required for this
24 Use pycnoetry data to find: density of pure Mixed cylinder exaple density of pure Al (solid cylinders) density of ixed cylinder (exaple) X X cyl Al g L g L g L g L X Al fraction (here: 3.97%) -X fraction (here: 86.03%) g/l 2.67 g/l g/l No error propagation required for this
25 Report Abstract Results/ Saples calculations including: Mass and volue by each ethod Volue of void Mass fraction Error analysis (parts 4) Volue of objects (3 ethods) Volue of inner void Mass fractions for ixed cylinder yes no no Discussion/review questions
26 Equipent cylinders:, aluinu, ixed, hollow Vernier calipers 50 L Erleneyer flask lab arker Pasteur pipet 00 L graduated cylinder 400 L beaker theroeter (analytical balance)
27 Caution NO YES
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