Experiment 3
Counting
and Measuring Atoms
This experiment involves
taking measurements and ultimately determining the radius of a single Al atom
or a glucose molecule. There is an 
Answer
Sheet for you to record your data, but you must print this sheet from
online.
During this experiment,
you will determine the dimensions of an Al bar (not a sheet of Al foil) and
its mass. From these measurements you will determine the volume and density
of this piece of metal. Using these measurements you will determine the volume
of a single Al atom (total volume divided by total number of atoms) and then
the radius of a single Al atom. To reinforce these calculations, you will also
determine the volume, using the known density of Al, and its measured mass.
In fact, this is the procedure you would follow if you had an irregularly shaped
object, such as a gold nugget. After working with an Al bar, you will perform
similar calculations to determine the volume and radius of glucose, which makes
up cellulose in paper.
List all answers in the
places indicated on the answer sheet. Use the correct number of significant
figures in all your answers.
Calculations to determine
the radius of an Al atom.
- Measure the diameter
(d) and length (L) of the Al bar.
- Determine its mass
to three decimal places.
- Calculate its volume
using its radius (d/2) and length (vol= πr2L), using your
measured values.
- Determine the density
of this Al bar using your mass (ii) and calculated volume (iii). Determine
the %Error for your calculated density compared to the actual density of Al
(2.702 g/cm3). To calcuate percent error (%Error) use
the formula at the end of this sheet.
- Calculate the number
of Al atoms in this bar. Use the molar mass of Al to determine number of moles
(divide your measured mass (ii) by the molar mass). Multiple the number of
moles by Avogadro's number (6.02 x 1023 atoms/mol) to determine
the total number of atoms in the Al bar.
- To calculate the volume
of a single Al atom, you will divide the total volume of the Al bar (iii)
by the total number of Al atoms (v). This is the volume of a single Al atom.
- Calculate the radius
of an Al atom. (Derive the formula for the radius of a sphere from the formula
of a sphere: vol=4/3 π r3.)
- What is the % error
of the Al atom radius that you determined compared to its actual radius (143
pm)?
- We are now going to
calculate the volume of the Al bar, not using its dimensions, but using its
mass. For this part of the experiment, you will divide the mass of the
Al bar (ii) by its density (2.702 g/cm3) to determine its volume.
(Remember: the density you use for this part of the experiment is the
theoretical Al density. The volume you calculate is based only on mass
and density, not its dimensions. This approach is what can be used for
an irregularly shaped object.)
- Based on the volume(ix)
above, calculate the volume of a single Al atom using this volume (ix) and
the number of Al atoms in the bar (v).
- Calculate the radius
of an Al atom based on (x) above.
- Calculate the % error
of this Al radius (xi) compared to the actual radius (143 pm).
Determining the radius
of a glucose molecule
In a manner similar to
the procedure outlined above, you will determine the average radius of a glucose
molecule. Cellulose, the main component of paper is a polymer of glucose. Therefore,
you can consider paper to be composed only of glucose for this experiment.
You will need to determine
the volume of a sheet of paper. The length and width of a piece of paper are
easy to measure, and, in fact, these dimensions are known. The thickness of
a sheet of paper needs to be determined using a micrometer. The use of the micrometer
is straight forward, but is sometimes difficult to use. Your instructor will
explain how to use a micrometer.
- Measure the thickness
of a single sheet of paper. Alternatively, you can measure the thickness of
several sheets of paper, and then divide your measured value by the number
of sheets. Express your thickness in cm.
- Express the dimensions
of the sheet of paper in cm (Length & Width).
- Calculate the volume
of a sheet of paper using the L x W x thickness (i)
- Weigh one sheet of
paper. It is easiest to crumble a sheet of paper into a ball before weighing.
- Calculate the number
of glucose molecules using its molar mass (180 g/mol), its mass (iv), and
Avogadro's number (6.02 x 1023 molecules/mol)
- Calculate the volume
of a single glucose molecule by dividing the total volume (iii) by the total
number of molecules (v).
- Determine the average
radius based on the volume (vi) and rearranging the formula for a sphere to
solve for radius.
Useful Formulas:
- volume of a sphere
is 4/3 π r3 or
(π d3)/6
- volume of a cylinder
is π r2 L (r = radius; radius
= diameter/2; L = length)
- Avogadro's Number:
6.02 x 1023 atoms/mol or 6.02 x 1023
molecules/mol
- atomic radius equals
the cube root of [(3 vol)/4π] where
the vol is the Al atomic volume shown in (vi) and (x) above, or the glucose
volume (vi).
To
obtain %Error for a measurement, you need to know the Theoretical
and Experimental values for your measurement, or set of calculations.
Use this formula to obtain the %Error, which is always a
positve (absolute) value (your answer will never have a negative sign). |
 |
Go To Experiment:
1 2 3
4 5 6
7 8 9
10 11 12
Return to Chem110 Experiments Index
Copyright © Donald L.
Robertson (Modified:
09/20/2006)