1. Data Tables For Determining Avogadro's Number
2. Avogadro's Number Example
3. How Was Avogadro's Number Determined

To derive Avogadro’s number (the number of molecules in a mole of a substance), using an oil layer on water. A) Purpose B) Theory Avogadro’s number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.022140857 × 10 23.The units may be electrons, atoms, ions, or molecules, de-pending on the nature of the substance and the character of the. Start by calculating the volume of one mole of solid Al =(26.98 g/mol)/(2.70 g/mL)= 9.99 mL/mol. According to the packing density, only 0.74 og this is atoms (the rest is empty space), so the volume of the atoms alone is (9.99 mL/mol)x0.74 = 7.39. The number of atoms or molecules (n) in a mass (m) of a pure material having atomic or molecular weight (M) is easily computed from the following equation using Avogadro's number (NA = 6.022×10 23 atoms or molecules per gram-mole): M mN n A (1) In some situations, the atomic number density (N), which is the concentration of atoms or molecules per. Determining Avogadro’s Number The basic counting unit in chemistry, the mole, has a special name, Avogadro’s number, in honor of the Italian scientist Amadeo Avogadro (1776-1856). The commonly accepted definition of Avogadro’s number is the number of atoms in exactly 12 g of the isotope 12C, and the quantity itself is 6.02214199 × 1023.1. From this we can calculate the number of carbon-12 atoms in 12 grams of carbon-12: 12 g X 1 carbon-12 atom = 6.021 X 1023 carbon-12 atoms 1 1.993 X 10–23 g (from Clugston and Flemming, Advanced Chemistry) This is the basis of Avogadro's number. Better experimental methods have yielded the more accurate value of Avogadro's number we have today.

Introduction

Atoms and molecules are incredible tiny and weigh hardly anything, so scientists usually count them in terms of moles, which is 6.022140857 x 10²³ particles. Why? For the same reason that we measure distance in terms of miles and donuts in terms of dozens: when you are counting to big numbers, it is easier to use big units. When eating donuts, it makes more sense to count in dozens than attempt to count individual donuts, and it is simpler to tell someone that you live 5 miles down the road than 26,400 feet.

Avogadro’s number is named to honor Amedeo Avogadro who pioneered some of the molecular theory that led to the discovery of Avogadro’s number. In this lab, you will estimate the number of molecules in a monolayer of stearic acid in order to calculate Avogadro’s number.

Background

To estimate Avogadro’s number, you must count the number of molecules. Most of the time, chemists simply use the mass to count molecules because molar mass relates mass and number of molecules:

mass of carbon (g) / molar mass of carbon (g/mole) = number of moles of carbon

number of moles of carbon (moles) x 6.022 x 10²³ atoms per mole (atoms/mole) = number of atoms of carbon

However, this approach assumes you know Avogadro’s number, so we have to get a little more creative.

When measuring lots of little things, it helps to have a lot of them piled up.

Remember that molecules are physical things that take up space. One molecule is a very little thing that takes up just a little space (microscopic), but if you have a lot of them all lined up, they take up enough space for you to measure (macroscopic). When the dimensions of the stearic acid molecule are known, we can effectively count stearic acid molecules by measuring a volume of stearic acid.

Stearic acid is a non-polar hydrocarbon chain that has a polar carboxylic acid end. When you add it to water, each molecule aligns with the polar end pointing towards the water and the non-polar portion pointing up, and the molecules form a monolayer on top of the water. You can picture each molecule like a tall, skinny rectangle with dimensions 1:5.44, and the monolayer can be approximated as a cylinder. By measuring the volume and surface area of the stearic acid layer, you will be able to calculate the dimensions of the individual molecules via geometry, which is all you need to calculate the volume of the individual molecule. Comparing the volume of the monolayer to the volume of an individual molecule gives you the number of molecules in the monolayer. Since the monolayer has a known mass, and stearic acid has a known molar mass, you can calculate Avogadro’s number. Step-by-step instructions for completing the calculations are on the worksheet.

Procedure

Note: this should all take place in a hood to protect you from fumes.

Calibration of a pipet

I. Wash a 10 mL beaker (or the smallest beaker you have).

1. Wash with soap and water.
2. Rinse with ~1 mL of ammonia solution three times. Put the rinsate in the ammonia waste container.
3. Rinse with DIH2O three times.
4. Rinse with ~1 mL of acetone. Put the rinsate in the acetone waste container. Wait for the beaker to dry (a minute or two).
5. Rinse the beaker with ~1/2 mL of hexane[CAUTION!] three times. Put the rinsate in the hexane waste container.

II. Wash a 10 mL graduated cylinder.

1. Wash with soap and water.
2. Rinse with ~1 mL of acetone. Wait for it to dry.

III. Calibrate the pipet

1. Put approximately 3 mL of hexane into the clean beaker.
2. Use the pipet and the hexane in the beaker to fill the graduated cylinder up to exactly 1.0 mL. Count the number of drops it takes to fill it to 1 mL. Record the number of drops. Tips to ensure consistent drop size:
   • Have one designated dropper. Preferably whoever has steadier hands.
   • Be sure to hold the pipet straight up and down.
   • Make sure no drops stick to the side of the graduated cylinder.
   • Don’t let the dropper touch the sides of the cylinder.
   • Work slowly and be patient.
3. Pour the hexane out of the graduated cylinder and into the hexane waste container. Wait for the graduated cylinder to dry. Blowing nitrogen on the glassware will help it dry faster.
4. Repeat the calibration procedure again. Record the number of drops in 1 mL.
5. Repeat again if the first two calibration measurements are not within 10% of one another (example: 20 and 22 drops would be acceptable, but 20 and 25 drops would warrant another calibration).

Make a stearic acid monolayer

I. Prepare a large watch glass

1. Measure and record the diameter of the watch glass with your ruler.
2. Wash the watch glass with soap and water.
3. Rinse with ammonia solution. Put rinsate in the ammonia waste container.
4. Rinse thoroughly with DIH2O. Wait for it to dry.
5. Once clean, be sure to avoid getting fingerprints on it. Handle wearing gloves, and hold it on the edges.
6. Place the watch glass on a 400 mL beaker, which will simply hold it steady for you. Make sure the watch glass is parallel to the bench top.

II. Form the monolayer

1. Using your wash bottle, fill the watch glass to the brim with DIH2O.
2. Pour about 3 mL of the stearic acid solution into the clean 10 mL beaker.
3. Fill the pipet with the stearic acid solution. Holding it straight up and down, add one drop of stearic acid solution to the water-filled watch glass. If the watch glass is sufficiently clean, the drop should disappear quickly.
4. Add the stearic acid solution drop wise until the last drop, which will remain a lens and not disappear. Record the number of drops you used. You will know you are close when you see a circular pattern forming. If you see a second lens forming, you added too much stearic acid and no longer have a monolayer.

Procedure adapted from http://chemskills.com/?q=avogadro

Data analysis

Report

The number of moles in a system can be determined using the atomic mass of an element, which can be found on the periodic table. This mass is usually an average of the abundant forms of that element found on earth. An element's mass is listed as the average of all its isotopes on earth.

Avogadro's Constant

One mole of oxygen atoms contains (6.02214179 times 10^{23}) oxygen atoms. Also, one mole of nitrogen atoms contains (6.02214179 times 10^{23}) nitrogen atoms. The number (6.02214179 times 10^{23}) is called Avogadro's number ((N_A)) orAvogadro's constant, after the 19^th century scientist Amedeo Avogadro.

Each carbon-12 atom weighs about (1.99265 times 10^{-23}; g); therefore,

[(1.99265 times 10^{-23}; g) times (6.02214179 times 10^{23}; atoms) = 12; g; text{ of carbon-12} nonumber ]

Applications of the Mole

The mass of a mole of substance is called the molar mass of that substance. The molar mass is used to convert grams of a substance to moles and is used often in chemistry. The molar mass of an element is found on the periodic table, and it is the element's atomic weight in grams/mole (g/mol). If the mass of a substance is known, the number of moles in the substance can be calculated. Converting the mass, in grams, of a substance to moles requires a conversion factor of (one mole of substance/molar mass of substance).

The mole concept is also applicable to the composition of chemical compounds. For instance, consider methane, CH₄. This molecule and its molecular formula indicate that per mole of methane there is 1 mole of carbon and 4 moles of hydrogen. In this case, the mole is used as a common unit that can be applied to a ratio as shown below:

[2 text{ mol H } + 1 text{ mol O }= 1 text{ mol } ce{H2O} nonumber]

In this this chemical reactions, the moles of H and O describe the number of atoms of each element that react to form 1 mol of (ce{H_2O}).

To think about what a mole means, one should relate it to quantities such as dozen or pair. Just as a pair can mean two shoes, two books, two pencils, two people, or two of anything else, a mole means 6.02214179×10²³ of anything. Using the following relation:

[text{1 mole} = 6.02214179 times 10^{23}]

is analogous to saying:

[text{1 Dozen} = text{12 eggs}] Tony terry with you mp3 juice.

It is quite difficult to visualize a mole of something because Avogadro's constant is extremely large. For instance, consider the size of one single grain of wheat. If all the people who have existed in Earth's history did nothing but count individual wheat grains for their entire lives, the total number of wheat grains counted would still be much less than Avogadro's constant; the number of wheat grains produced throughout history does not even approach Avogadro's Number.

Example (PageIndex{1}): Converting Mass to Moles

How many moles of potassium ((ce{K})) atoms are in 3.04 grams of pure potassium metal?

Solution

In this example, multiply the mass of (ce{K}) by the conversion factor (inverse molar mass of potassium):

[dfrac{1; mol; K}{39.10; grams ;K} nonumber ]

39.10 grams is the molar mass of one mole of (ce{K}); cancel out grams, leaving the moles of (ce{K}):

[3.04; cancel{g; K} left(dfrac{1; mol; K}{39.10; cancel{g; K}}right) = 0.0778; mol; K nonumber ]

Similarly, if the moles of a substance are known, the number grams in the substance can be determined. Converting moles of a substance to grams requires a conversion factor of molar mass of substance/one mole of substance. One simply needs to follow the same method but in the opposite direction.

Example (PageIndex{2}): Converting Moles to mass

Acdsee pro 10.4 build 686. How many grams are 10.78 moles of Calcium ((ce{Ca}))?

Solution

Multiply moles of Ca by the conversion factor (molar mass of calcium) 40.08 g Ca/ 1 mol Ca, which then allows the cancelation of moles, leaving grams of Ca.

[10.78 cancel{;mol; Ca} left(dfrac{40.08; g; Ca}{1; cancel{mol; Ca}}right) = 432.1; g; Ca nonumber ]

The total number of atoms in a substance can also be determined by using the relationship between grams, moles, and atoms. If given the mass of a substance and asked to find the number of atoms in the substance, one must first convert the mass of the substance, in grams, to moles, as in Example (PageIndex{1}). Then the number of moles of the substance must be converted to atoms. Converting moles of a substance to atoms requires a conversion factor of Avogadro's constant (6.02214179×10²³) / one mole of substance. Verifying that the units cancel properly is a good way to make sure the correct method is used.

Example (PageIndex{3}): Atoms to Mass

How many atoms are in a 3.5 g sample of sodium (Na)?

Solution

[3.5; cancel{g; Na} left(dfrac{1; mol; Na}{22.98; cancel{g; Na}}right) = 0.152; mol; Na nonumber ]

[0.152; cancel{mol; Na} left(dfrac{6.02214179times 10^{23}; atoms; Na}{1;cancel{ mol; Na}}right) = 9.15 times 10^{22}; atoms; of; Na nonumber ]

In this example, multiply the grams of Na by the conversion factor 1 mol Na/ 22.98 g Na, with 22.98g being the molar mass of one mole of Na, which then allows cancelation of grams, leaving moles of Na. Then, multiply the number of moles of Na by the conversion factor 6.02214179×10²³ atoms Na/ 1 mol Na, with 6.02214179×10²³ atoms being the number of atoms in one mole of Na (Avogadro's constant), which then allows the cancelation of moles, leaving the number of atoms of Na.

Using Avogadro's constant, it is also easy to calculate the number of atoms or molecules present in a substance (Table (PageIndex{1})). By multiplying the number of moles by Avogadro's constant, the mol units cancel out, leaving the number of atoms. The following table provides a reference for the ways in which these various quantities can be manipulated:

Example (PageIndex{4}): Mass to Moles

How many moles are in 3.00 grams of potassium (K)?

Solution

[3.00 ; cancel{g; K} left(dfrac{1; mol; K}{39.10; cancel{g; K}}right) = 0.0767; mol; K nonumber ]

Data Tables For Determining Avogadro's Number

In this example, multiply the mass of K by the conversion factor:

[dfrac{1; mol; K}{39.10; grams; K} nonumber ]

39.10 grams is the molar mass of one mole of K. Grams can be canceled, leaving the moles of K.

Example (PageIndex{5}): Moles to Mass

How many grams is in 10.00 moles of calcium (Ca)?

Solution

This is the calculation in Example (PageIndex{2}) performed in reverse. Multiply moles of Ca by the conversion factor 40.08 g Ca/ 1 mol Ca, with 40.08 g being the molar mass of one mole of Ca. The moles cancel, leaving grams of Ca:

[10.00; cancel{mol; Ca} left(dfrac{40.08; g; Ca}{1;cancel{ mol; Ca}}right) = 400.8; grams ;of ;Ca nonumber ]

The number of atoms can also be calculated using Avogadro's Constant (6.02214179×10²³) / one mole of substance.

Example (PageIndex{6}): Mass to Atoms

How many atoms are in a 3.0 g sample of sodium (Na)?

Solution

Convert grams to moles

[3.0; cancel{g; Na} left(dfrac{1; mol; Na}{22.98; cancel{g; Na}}right) = 0.130; mol; Na nonumber ]

Avogadro's Number Example

Convert moles to atoms

[0.130548; cancel{ mol; Na} left(dfrac{6.02214179 times 10^{23}; atoms ;Na}{1; cancel{ mol; Na}}right) = 7.8 times 10^{22} ; atoms; of; ; Na nonumber ]

Summary

The mole, abbreviated mol, is an SI unit which measures the number of particles in a specific substance. One mole is equal to (6.02214179 times 10^{23}) atoms, or other elementary units such as molecules.

Problems

How Was Avogadro's Number Determined

1. Using a periodic table, give the molar mass of the following:
   1. H
   2. Se
   3. Ne
   4. Cs
   5. Fe
2. Convert to moles and find the total number of atoms.
   1. 5.06 grams of oxygen
   2. 2.14 grams of K
   3. 0.134 kg of Li
3. Convert the following to grams
   1. 4.5 mols of C
   2. 7.1 mols of Al
   3. 2.2 mols of Mg
4. How many moles are in the product of the reaction
   1. 6 mol H + 3 mol O → ? mol H₂O
   2. 1 mol Cl + 1 mol Cl → ? mol Cl₂
   3. 5 mol Na + 4 mol Cl → ? mol NaCl

Answers

1. Question 2
   1. 1.008 g/mol
   2. 78.96 g/mol
   3. 20.18 g/mol
   4. 132.91g/mol
   5. 55.85 g/mol
2. Question 2

2. 5.06g O (1mol/16.00g)= 0.316 mol of O

0.316 mols (6.022x10²³ atoms/ 1mol) = 1.904x10²³ atoms of O

3. 2.14g K (1mol/39.10g)= 0.055 mol of K

0.055 mols (6.022x10²³ atoms/ 1mol) = 3.312x10²² atoms of K

4. 0.134kg Li (1000g/1kg)= 134g Li (1mol/6.941g)= 19.3 mols Li

19.3 (6.022x10²³ atoms/ 1mol) = 1.16x10²⁵ atoms of Li

3. Question 3
   1. 4.5 mols of C (12.011g/1mol) = 54.05 g of C
   2. 7.1 mols of Al (26.98g/1mol) = 191.56 g of Al
   3. 2.2 mols of Mg (24.31g/1mol) = 53.48 g of MG
4. Question 4
   1. 8. 6 mol H + 3 mol O → 3 mol H₂O
   2. 9. 1 mol Cl + 1 mol Cl → 1 mol Cl₂
   3. _{10. 5 mol Na + 4 mol Cl → 4 mol NaCl + 1 mol Na (excess)}

References

1. Keenan, Charles W. and Wood, Jesse H. . General College Chemistry. 4th ed. New York: Haper and Row, 1971.
2. Mortimer, Charles E. Chemistry a Conceptual Approach. 2nd ed. New York: Van Nostrand Reinhold, 1971.
3. Jones, Loretta and Atkins, Peter. Chemistry: Molecules, Matter, and Change. 4th ed. New York: W.H. Freeman, 2000.
4. Petrucci, Ralph H., Herring, Goeffrey F., Madura, Jeffrey D., and Bissonnette, Carey. General Chemistry: Principles and Modern Applications. 10th ed. New Jersey: Pearson Canada, 2011.

Contributors and Attributions

• Ryan Benoit (UCD), Michael Thai (UCD), Charlie Wang (UCD), Jacob Gomez (UCD)