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| Page 1: Introduction/Basics |
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| Page 2: Introduction/Basics (cont.) |
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| Page 3: Method for Calculations/Logic |
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| Page 4: Procedure |
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| Page 5: Data Chart and Conclusion |
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| Page 6: Calculating the actual molecule length |
Title: Dimensions of a Molecule
Purpose: To determine experimentally the length and cross sectional area of a molecule of stearic acid and compare the experimental length to one calculated from the known structure using proper significant figures and metric conversions.
Hypothesis: (varied from individual to individual) A molecule of stearic acid will have a length of about 180 nanometers (nm).
Raw Data and Calculations:
Outer diameter of petri dish: 89.5 nm
Calibrated 1.0 mL Hexane: 141 drops
Drops to form monolayer: 6 drops
Concentration of stearic acid in Hexane: 0.14 g/L
Average drop volume: 7.09 x 10^-3 mL/drop
1.0 mL Hexane/141 drops = 7.09 x 10^-3 mL/drop
*This is simply the volume of liquid per drop so that there is a general idea of how much the pipet drops each time
Mass of stearic acid: 5.96 x 10^-6 g
V = drop volume x drops
= (7.09 x 10^-3 mL/drop)(6 drops)
= 4.25 x 10^-2 mL = 4.25 x 10^-5 L
m = cV
= (0.14 g/L)(4.25 x 10^-5 L)
= 5.96 x 10^-6 g
*finds the approximate mass of the stearic acid in the amount dropped
Volume of stearic acid in monolayer: 7.01 x 10^-6 mL
V = m/d
= 5.96 x 10^-6 g/0.85 g/mL
= 7.01 x 10^-6 mL
* uses the definition of density to calculate the volume of stearic acid in the solution
Area of monolayer: 62.9 cm^2
A = (.5d)^2π
= (.5 x 89.5mm)^2π
= 6291 mm^2 = 62.9 cm^2
*area of a circle using the measured diameter of the petri dish
Thickness of monolayer: 1.11 x 10^-7 cm
V = tA
7.01 x 10^10^-6 mL = t(62.9 cm^2)
t = 1.11 x 10^-7 cm
* definition of volume used to find the thickness of the monolayer
Length of a stearic acid molecule: 1.11 x 10^-7 cm = 1110 pm
m/[A(Dsa)] = 5.96 x 10^-6 g/[62.9 cm^2(0.85 g/mL)] = 1110 pm
* essentially, the thickness of the monolayer is the length of the stearic acid molecule because of the way stearic acid molecules align themselves on the surface of a polar substance (vertically; see diagram on page 2 for visuals)
Molar mass of stearic acid: 284.54 g/mol
MMsa = 18( molar mass of carbon) + 36 (molar mass of hydrogen) + 2(molar mass of oxygen)
= 18(12.01) + 36(1.01) +2(16.00)
= 284.54 g/mol
* use the chemical formula of stearic acid given on page 1 to calculate the constituent masses that compose stearic acid as a whole
Number of molecules: 1.26 x 10^16 molecules
N = mNa/MMsa
= 5.96 x 10^-6 g(6.02 x 10^23 molecules/mol)/284.54 g/mol
= 1.26 x 10^16 molecules
* simply the number of stearic acid molecules covering the surface of the petri dish
Cross sectional area of a stearic acid molecule: 4.99 x 10^-15 cm^2 = 4.99 x 10^5 pm^2
Cross sectional area = A/N
= 62.9 cm^2/1.26 x 10^16 molecules
= 4.99 x 10^-15 cm^2
4.99 x 10^-15 cm^2 x 1 pm^2/1.0 x 10^-20 cm^2 = 4.99 x 10^5 pm^2
* metric conversion from cm to pm to match the rest of the data
Calculated molecule length: 2142 pm
Percent Error: 48.2%
[(Experimental - Accepted)/Accepted] x 100
= [(1110 - 2142)/2142] x 100
= 48.2%
*This value would be mathematically negative, but a percent error is always positive; the negative sign just indicates which direction the error was. In this case, the experimental value obtained is too LOW compared to the accepted value.
Data:
Procedure:
Obtain a glass Petri dish, a sterile pipet, distilled water, Hexane, and a stearic acid in Hexane solution between 0.12 and 0.15 g/L. Take proper safety precautions and wear a lab apron and goggles. Rinse the Petri dish with distilled water and then fill to the brim so that the water level is just visible above the dish's edge. Measure the diameter of the water's surface. Do not contaminate the sample by touching the inside of the Petri dish. Use the pipet to next measure out 1.0 mL of Hexane and count the number of drops to calibrate. Carefully draw up a small amount using the calibrated pipet (around 5 mL) of the Hexane-stearic acid solution and drop individual droplets into the water. When a drop lingers for about 20 seconds, record the previous number of drops and record. Dispose of the waste properly and clean the equipment and lab table.
Conclusion:
Stearic acid, C18H36O2, is a molecule that possesses a long nonpolar hydrocarbon tail bound to a polar carboxyl group; the polarity of each component and the respective properties allowed both the length and cross sectional area of a single stearic acid molecule to be experimentally determined. Specifically, the carboxyl group dissolves readily in polar substances, like water, while the rest of the molcule, the hydrophobic tail, is attracted to other nonpolar tails and does not easily dissolve in polar solvents. Experimentally, stearic acid was found to be around 1110 pm long which proved to be 48.2% shorter than the calculated value of 2142 pm that was found based on the molecular structure of the carbon backbone. The molecule's cross sectional area was determined to be 4.99 x 10^5 pm^2. Despite being able to experimentally determine stearic acid's molecular dimensions, there existed both random and systematic errors in the system that contributed to the errors observed; random errors included system contamination and accuracy limitations in both volumetric and scalar measuments while systematic errors include the effects of atmospheric pressure and temperature on the length of the molecule. However, such error is expected, as small data values, rounded values, and an open system are not ideal conditions. Though there existed error, the length and cross sectional area of a molecule of stearic acid were able to be experimentally determined by utilizing the properties of polarity and appropriate metric conversions and accuracy through significant figures.
Disclaimer: I do not own any of the above materials associated with the published lab and I do not encourage copying verbatim my answers for honesty sake and for the sake of risking your grade should others choose to copy also. While I do not own the lab materials, the work is my original work that I have typed from my laboratory notebook.
1.0 mL Hexane/141 drops = 7.09 x 10^-3 mL/drop
*This is simply the volume of liquid per drop so that there is a general idea of how much the pipet drops each time
Mass of stearic acid: 5.96 x 10^-6 g
V = drop volume x drops
= (7.09 x 10^-3 mL/drop)(6 drops)
= 4.25 x 10^-2 mL = 4.25 x 10^-5 L
m = cV
= (0.14 g/L)(4.25 x 10^-5 L)
= 5.96 x 10^-6 g
*finds the approximate mass of the stearic acid in the amount dropped
Volume of stearic acid in monolayer: 7.01 x 10^-6 mL
V = m/d
= 5.96 x 10^-6 g/0.85 g/mL
= 7.01 x 10^-6 mL
* uses the definition of density to calculate the volume of stearic acid in the solution
Area of monolayer: 62.9 cm^2
A = (.5d)^2π
= (.5 x 89.5mm)^2π
= 6291 mm^2 = 62.9 cm^2
*area of a circle using the measured diameter of the petri dish
Thickness of monolayer: 1.11 x 10^-7 cm
V = tA
7.01 x 10^10^-6 mL = t(62.9 cm^2)
t = 1.11 x 10^-7 cm
* definition of volume used to find the thickness of the monolayer
Length of a stearic acid molecule: 1.11 x 10^-7 cm = 1110 pm
m/[A(Dsa)] = 5.96 x 10^-6 g/[62.9 cm^2(0.85 g/mL)] = 1110 pm
* essentially, the thickness of the monolayer is the length of the stearic acid molecule because of the way stearic acid molecules align themselves on the surface of a polar substance (vertically; see diagram on page 2 for visuals)
Molar mass of stearic acid: 284.54 g/mol
MMsa = 18( molar mass of carbon) + 36 (molar mass of hydrogen) + 2(molar mass of oxygen)
= 18(12.01) + 36(1.01) +2(16.00)
= 284.54 g/mol
* use the chemical formula of stearic acid given on page 1 to calculate the constituent masses that compose stearic acid as a whole
Number of molecules: 1.26 x 10^16 molecules
N = mNa/MMsa
= 5.96 x 10^-6 g(6.02 x 10^23 molecules/mol)/284.54 g/mol
= 1.26 x 10^16 molecules
* simply the number of stearic acid molecules covering the surface of the petri dish
Cross sectional area of a stearic acid molecule: 4.99 x 10^-15 cm^2 = 4.99 x 10^5 pm^2
Cross sectional area = A/N
= 62.9 cm^2/1.26 x 10^16 molecules
= 4.99 x 10^-15 cm^2
4.99 x 10^-15 cm^2 x 1 pm^2/1.0 x 10^-20 cm^2 = 4.99 x 10^5 pm^2
* metric conversion from cm to pm to match the rest of the data
Calculated molecule length: 2142 pm
Percent Error: 48.2%
[(Experimental - Accepted)/Accepted] x 100
= [(1110 - 2142)/2142] x 100
= 48.2%
*This value would be mathematically negative, but a percent error is always positive; the negative sign just indicates which direction the error was. In this case, the experimental value obtained is too LOW compared to the accepted value.
Data:
Calibration
of pipet
|
|
a)
drops (±?)
|
141
|
b)
volume of hexane (±?) (mL)
|
1.0
|
c)
average drop volume (±?) (mL/drop)
|
7.09 x 10-3
|
Molecular
Dimensions
|
|
a)
Diameter of water surface (±?) (cm)
|
895
|
b)
number of drops needed to cover surface (±?)
|
6
|
c)
The mass of stearic acid (±?) (g)
|
5.96 x 10-6
|
d)
The volume of stearic acid in the monolayer (±?)
(cm3)
|
7.01 x 10-6
|
e)
The area of the monolayer (±?) (cm2)
|
62.9
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f)
Thickness of the monolayer (±?) (cm)
|
1.11 x 10-7
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g)
Length of the molecules (±?) (pm)
|
1110
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h)
Number of molecules in film (±?)
|
1.26 x 1016
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i)
Cross sectional area of a stearic acid
molecule (±?) (pm2)
|
4.99 x 105
|
j)
Calculated molecule length (±?) (pm)
|
2142
|
k)
Percent error (±?) (%)
|
48.2
|
Procedure:
Obtain a glass Petri dish, a sterile pipet, distilled water, Hexane, and a stearic acid in Hexane solution between 0.12 and 0.15 g/L. Take proper safety precautions and wear a lab apron and goggles. Rinse the Petri dish with distilled water and then fill to the brim so that the water level is just visible above the dish's edge. Measure the diameter of the water's surface. Do not contaminate the sample by touching the inside of the Petri dish. Use the pipet to next measure out 1.0 mL of Hexane and count the number of drops to calibrate. Carefully draw up a small amount using the calibrated pipet (around 5 mL) of the Hexane-stearic acid solution and drop individual droplets into the water. When a drop lingers for about 20 seconds, record the previous number of drops and record. Dispose of the waste properly and clean the equipment and lab table.
Conclusion:
Stearic acid, C18H36O2, is a molecule that possesses a long nonpolar hydrocarbon tail bound to a polar carboxyl group; the polarity of each component and the respective properties allowed both the length and cross sectional area of a single stearic acid molecule to be experimentally determined. Specifically, the carboxyl group dissolves readily in polar substances, like water, while the rest of the molcule, the hydrophobic tail, is attracted to other nonpolar tails and does not easily dissolve in polar solvents. Experimentally, stearic acid was found to be around 1110 pm long which proved to be 48.2% shorter than the calculated value of 2142 pm that was found based on the molecular structure of the carbon backbone. The molecule's cross sectional area was determined to be 4.99 x 10^5 pm^2. Despite being able to experimentally determine stearic acid's molecular dimensions, there existed both random and systematic errors in the system that contributed to the errors observed; random errors included system contamination and accuracy limitations in both volumetric and scalar measuments while systematic errors include the effects of atmospheric pressure and temperature on the length of the molecule. However, such error is expected, as small data values, rounded values, and an open system are not ideal conditions. Though there existed error, the length and cross sectional area of a molecule of stearic acid were able to be experimentally determined by utilizing the properties of polarity and appropriate metric conversions and accuracy through significant figures.
_________________________________________________________________________
Disclaimer: I do not own any of the above materials associated with the published lab and I do not encourage copying verbatim my answers for honesty sake and for the sake of risking your grade should others choose to copy also. While I do not own the lab materials, the work is my original work that I have typed from my laboratory notebook.
