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Lab 17: The Mole and Avogadro’s Number

1. A mole is also just a number, like a pair, dozen, gross. For example, one pair of shoe means, 2 shoes, 1 dozen eggs mean 12 eggs, likewise, 1 mole of iron means 6.022.10 23 iron atoms. One mole of anything contains 6.022.10 23 of that thing and always this number is constant. So, this number is also called as Avogadro’s constant.
2. Chemists use the term mole to represent a large number of atoms or molecules. Just as a dozen implies 12 things, a mole (abbreviated as mol ) represents 6.022 × 10 23 things. The number 6.022 × 10 23, called Avogadro’s number after the 19th-century chemist Amedeo Avogadro, is the number we use in chemistry to represent macroscopic amounts.
3. Published on Jun 11, 2020 This chemistry video focuses on concept of mole, molar mass,Avogadro's number (6.0221367 X 10 ^23) basic introduction and how to do the calculations.

Introduction

“Avocados” number: How many avocados and artichokes are there in a mole?
A recipe calls for two avocados and two artichokes. Would you say that equal amounts of avocados and artichokes are used? The answer to that question depends on how you define “the same amount”. If you consider the quantity, yes, there are two of each. What if instead the recipe told you to use 250 grams of artichokes and avocados? There might be one and a half avocados used for every arti‐choke—would you call this the same amount as well?

One way to solve this problem would be to ask for more specific instructions. The phrase “the same amount” is being used to describe quantity (number) in one instance and mass in another. Similar situations come up in chemistry. If you are supposed to put the same mass of two different substances into a beaker, all you would have to do is weigh equal amounts using a scale. Things become more complicated, however, when the ratio of the total number of molecules or atoms is important in an experiment—you might know the number of molecules in the reactants and products, but not the actual masses. How would you measure an exact number of NaCl molecules?

The mole is an important unit in chemistry that you will use often. The modern definition of the mole is based around the carbon‐12 (12C) atom: 12 grams of 12C is exactly one mole of substance. It turns out that 1 gram of 12C has approximately 6.02 x 1023 individual atoms—a value called Avogadro’s Number after the chemist Amedeo Avogadro. The mole is a similar concept to a dozen: one mole of a substance will always have 6.02 x 1023 atoms or molecules.

To learn more about Mole, enroll in our full course now: this video, we will learn: 0:00 Concept of Mole0:30 Definition of a.

Atomic weight is a measurement of the mass of each element, and can be easily found on most periodic tables. Atoms that have a large number of protons and neutrons have more total mass than atoms with only a few protons and neutrons, and this difference is reflected by the atomic weight. Conveniently, the mole and atomic weight are defined so that one mole of a substance will have a mass equal to the atomic weight of that substance in grams. This number is called molar mass. For instance, the atomic weight of potassium (K) is 39.098. This means that one mole of potassium will have a mass equal to 39.098 grams. Calcium (Ca) is a larger atom than potassium, and has an atomic weight of 40.078. One mole of calcium will have the same number of atoms as a mole of potassium, but the Calcium will weigh more due to its larger atomic weight.

See the next lab for more detail on atomic weight and atomic mass.
So how do you measure 1 mole of NaCl? We know that this molecule is made up of one sodium ion and one chlorine ion (chloride). Looking up sodium (Na) on the Periodic Table tells you its atomic weight is 22.99, meaning it has a molar mass of 22.99 g/mol. Chlorine, meanwhile, has a molar mass of 35.45 g/mol. Since one mole of sodium chloride consists of one mole sodium ions and one mole chlorine ions, we can add these together to find the molecular mass of NaCl.

Figure 1: You can think of avocados and artichokes in this example as two different types of molecule—each with a different
molar mass.

Concepts to explore:
Understand the importance of Avogadro’s Number
Approximate the value of Avogadro’s Number 180

What if we weighed out 1.00 grams of NaCl—how many molecules is this? We use the molar mass of NaCl, which we already
know from above, to convert from mass to a number of moles. We can then use the fact that there are 6.02 x 1023 molecules in
a mole to find the number of molecules NaCl in one gram:

Notice how the molar mass is inverted in the second term. The value is the same, but we “flip” the fraction so that the gram
units cancel. You can go through and cross out the units that cancel to verify that the resulting units are molecules. You can
use similar calculations to convert between mass, moles, and the number of molecules fairly easily.

Through this lab procedure, we will determine the experimental value for Avogadro’s number. You will float cinnamon, evenly
distributed, on the surface of water in a Petri dish. The dishwashing liquid you will use in this Lab is about 1% sodium stearate,
and a solution with a known concentration of the liquid will be dropped onto the water. The sodium stearate molecules will
form a single layer and spread out, pushing the cinnamon toward the edges of the Petri dish, allowing the surface area to be
determined. We will assume that each molecule takes up 0.210 nm2 of surface area, and that there is no space between the
molecules.
23
 22
1 mol NaCl 6.02 10 molecules
1.00 g NaCl 1.03 10 molecules NaCl
58.44 g NaCl 1 mol NaCl
1 Na = 22.99 g/mol
+ 1 Cl = 35.45 g/mol
58.44 g/mol of NaCl
This is how to determine molar mass of a compound.
1 mol NaCl x 58.44 g NaCl = 58.44 g NaCl
1 mol NaCl
Pre‐lab Questions
1. How many grams of H2O do you need to weigh out to have 1 mole of H2O?

2. How many molecules of water are there in one mole of H2O?
3. How many moles of H2O are there in 1.0 g of H2O?
4. How many molecules of H2O are there in 1.0 g of H2O?

Lab 17: The Mole and Avogadro’s Number

Experiment: Avogadro’s Number

Procedure

Part 1: Preparing the Sodium Stearate Solution

1. Measure exactly 1.50 mL of dishwashing liquid into a 10 mL graduated cylinder.
2. Fill a wash bottle with distilled water. Gently rinse the 1.50 mL of dishwashing liquid with distilled water and
pour it into a 100 mL graduated cylinder. Rinse the 10 mL graduated cylinder several times to make sure all
the dishwashing liquid has been transferred to the 100 mL graduated cylinder. HINT: Try not to create suds.
3. Add enough additional distilled water to get to the 100.0 mL.
4. Gently stir the solution with a stirring rod until it is mixed well.

Part 2: Calibrating a Dropper

1. Fill a 50 mL beaker half full with distilled water. Use a pipette to fill a 10 mL graduated cylinder to 1.00 mL
with water. HINT: Make sure the 10 mL graduated cylinder is clean of dishwashing liquid.
2. Next, draw up water from the 50 mL beaker into the pipette. Add water dropwise into the graduated cylin‐
der. Hold the pipette consistently at a 45o angle and drop at a rate of about one drop per second. Count the
drops it takes to reach the 2.00 mL mark. HINT: It should take about 25 drops. If you feel that your measure‐
ment is incorrect, repeat until you achieve consistent readings.
3. Record in the Data section the number of the drops it takes to add 1 mL water to the graduated cylinder.
4. Repeat calibration for a second trial, and record the number of drops in the Data section. Average the two
results.

Part 3: Calculating the Number of Molecules

1. Rinse and then fill a petri dish with 20 mL distilled water. Allow the water to settle and remain motionless.

Materials

Safety Equipment: Safety goggles, gloves

2. Lightly sprinkle cinnamon onto the surface of the water in the Petri dish. HINT: Add just enough to barely
cover the water.
3. Draw up the dishwashing liquid solution with the calibrated pipette. Hold the pipette at a 45o angle about 1
inch above the center of the Petri dish. Slowly deliver one drop of the solution. HINT: A clear circle should
form, spreading the cinnamon outward.
4. Quickly use a ruler to measure the diameter of the cleared circle in cm.
5. Record the diameter in the Data section. Wash out the Petri dish.
Data

Part 2: Calibrating a Dropper

1. The number of drops in 1 mL water (drops used to move from the 1.00 mL to 2.00 mL mark):
Trial 1: Trial 2:
2. The number of drops on average per one milliliter:
Part 3: Calculating the Number of Molecules
1. The diameter of the circle formed (cm):
Calculations
1. Calculate the surface area of the circle formed ( πd2 /4 ) :
2. Calculate the number of molecules on the top layer. We must convert the surface area in centimeters
squared to nanometers squared and then multiply that by the surface area of a sodium stearate molecule.
Convert the surface area of the circle formed (#1) to molecules per layer:
Surface area =

=
molecules
top layer

Lab 17: The Mole and Avogadro’s Number

3. Calculate the concentration of grams of sodium stearate per milliliter of diluted solution. To do this, multiply the
concentration of sodium stearate in the dishwashing liquid by the dilution of the solution (1.50 mL dishwashing
liquid per 100 mL solution).
4. Calculate the number of moles of sodium stearate in a single layer. To do this, first take the number of drops used
to achieve the monolayer (1 drop) and convert it to mL using the calibrated number of drops per mL. Then multi‐
ply the number of grams of sodium stearate per milliliter of solution. Finally, convert to moles through the molar
mass of sodium stearate. HINT: The molar mass of sodium stearate is 296.4 g/mol.

= g /ml
= mol / top layer
5. Finally, we can calculate the Avogadro’s number through the comparison of molecules of sodium stearate in the
top single layer to the moles of sodium stearate in the monolayer.
Avogadro’s number (experimental) =
# molecules / top layer (#2)
# moles / top layer (#4)
molecules
= mole

Post‐lab Questions

1. Why do you think that Avogadro’s number, 6.02 x 1023, was probably not the exact number you obtained?
Was your experimental value close to the actual value (i.e., was your experimental value on the order of 1023
molecules)?
2. How many moles are in 0.289 g of methane (CH4)?
3. How many moles are in 1,000,000,000 molecules of H2 02?
4. What is the mass in grams of 1,000,000,000 (109) molecules of H2O2?

Lab 17: The Mole and Avogadro’s Number

Last Updated on December 15, 2020 by

Learning Objectives

• Use Avogadro's number to convert to moles and vice versa given the number of particles of an element.
• Know the definition of the mole.
• Determine the formula mass of an ionic or molecular compound.
• Determine the percent composition of each element in a compound from the chemical formula.

When objects are very small, it is often inconvenient or inefficient, or even impossible to deal with the objects one at a time. For these reasons, we often deal with very small objects in groups, and have even invented names for various numbers of objects. The most common of these is 'dozen' which refers to 12 objects. We frequently buy objects in groups of 12, like doughnuts or pencils. Even smaller objects such as straight pins or staples are usually sold in boxes of 144, or a dozen dozen. A group of 144 is called a 'gross'.

This problem of dealing with things that are too small to operate with as single items also occurs in chemistry. Atoms and molecules are too small to see, let alone to count or measure. Chemists needed to select a group of atoms or molecules that would be convenient to operate with.

Avogadro's Number:Counting Atoms

Owing to their tiny size, atoms and molecules cannot be counted by direct observation. But much as we do when 'counting' beans in a jar, we can estimate the number of particles in a sample of an element or compound if we have some idea of the volume occupied by each particle and the volume of the container. Once this has been done, we know the number of formula units (to use the most general term for any combination of atoms we wish to define) in any arbitrary weight of the substance. The number will of course depend both on the formula of the substance and on the weight of the sample. However, if we consider a weight of substance that is the same as its formula (molecular) weight expressed in grams, we have only one number to know: Avogadro's number.

Avogadro's number

Avogadro's number is known to ten significant digits:

[N_A = 6.022141527 times 10^{23}.]

However, you only need to know it to three significant figures:

[N_A approx 6.02 times 10^{23}. label{3.2.1}]

So (6.02 times 10^{23}) of what? Well, of anything you like: apples, stars in the sky, burritos. However, the only practical use for (N_A) is to have a more convenient way of expressing the huge numbers of the tiny particles such as atoms or molecules that we deal with in chemistry. Avogadro's number is a collective number, just like a dozen. Students can think of (6.02 times 10^{23}) as the 'chemist's dozen'.

Before getting into the use of Avogadro's number in problems, take a moment to convince yourself of the reasoning embodied in the following examples.

Things to understand about Avogadro's number

• It is a number, just as is 'dozen', and thus is dimensionless.
• It is a huge number, far greater in magnitude than we can visualize
• Its practical use is limited to counting tiny things like atoms, molecules, 'formula units', electrons, or photons.
• The value of N_A can be known only to the precision that the number of atoms in a measurable weight of a substance can be estimated. Because large numbers of atoms cannot be counted directly, a variety of ingenious indirect measurements have been made involving such things as Brownian motion and X-ray scattering.

The Mole: 'A Dozen Eggs and a Mole of Sugar, Please'

The mole (symbol: mol) is the base unit of amount of substance ('number of substance') in the International System of Units or System International (SI), defined as exactly 6.02214076×10²³ particles, e.g., atoms, molecules, ions or electrons. The current definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (¹²C) (the isotope of carbon with relative atomic mass 12 Daltons by definition).

It is not obvious why eggs come in dozens rather than 10s or 14s, or why a ream of paper contains 500 sheets rather than 400 or 600. The definition of a mole—that is, the decision to base it on 12 g of carbon-12—is also arbitrary. The important point is that 1 mole of carbon—or of anything else, whether atoms, compact discs, or houses—always has the same number of objects: 6.02 × 10²³.

The Mole

Video (PageIndex{1}) How big is a mole?

Converting Between Number of Atoms to Moles and Vice Versa

We can use Avogadro's number as a conversion factor, or ratio, in dimensional analysis problems. If we are given the number of atoms of an element X, we can convert it into moles of by using the relationship

[text{1 mol X} = 6.022 times 10^{23} text{ X atoms}.]

An example on the use of Avogadro's number as a conversion factor is given below for carbon.

Example (PageIndex{1}): Moles of Carbon

The element carbon exists in two primary forms: graphite and diamond. How many moles of carbon atoms is (4.72 times 10^{24}) atoms of carbon?

What Is A Mole Avogadro

Solution

Formula Mass

One skill needed in future chapters is the ability to determine the mass of the formula of various chemical substances. This quantity is called the formula mass. The formula mass is obtained by adding the masses of each individual atom in the formula of the substance. Because a proper formula is electrically neutral (with no net electrons gained or lost), the ions can be considered atoms for the purpose of calculating the formula mass.

Let us start by calculating the formula mass of sodium chloride (NaCl). This formula mass is the sum of the atomic masses of one sodium atom and one chlorine atom, which we find from the periodic table; here, we use the masses to two decimal places:

To two decimal places, the formula mass of NaCl is 58.44 amu.

For covalent substances, the formula represents the numbers and types of atoms composing a single molecule of the substance; therefore, the formula mass may be correctly referred to as a molecular mass. Consider chloroform (CHCl₃), a covalent compound once used as a surgical anesthetic and now primarily used in the production of tetrafluoroethylene, the building block for the “anti-stick” polymer, Teflon. The molecular formula of chloroform indicates that a single molecule contains one carbon atom, one hydrogen atom, and three chlorine atoms. The average molecular mass of a chloroform molecule is therefore equal to the sum of the average atomic masses of these atoms.

For ionic compounds with polyatomic ions, the sum must include the number and mass of each atom in the formula for the polyatomic ion. as shown in the example below for aluminum sulfate, Al₂(SO₄)₃.

Example (PageIndex{2}) Formula Mass for an Ionic Compound

Aluminum sulfate, Al₂(SO₄)₃, is an ionic compound that is used in the manufacture of paper and in various water purification processes. What is the formula mass (amu) of this compound?

Solution

The formula for this compound indicates it contains Al³⁺ and SO₄²⁻ ions combined in a 2:3 ratio. For purposes of computing a formula mass, it is helpful to rewrite the formula in the simpler format, Al₂S₃O₁₂. Following the approach outlined above, the formula mass for this compound is calculated as follows:

The formula mass for Al₂(SO₄)₃, is 342.14 amu.

Exercise (PageIndex{1})

Use the atomic masses (rounded to two decimal places) to determine the formula mass for each ionic compound.

1. TiO₂
2. AgBr
3. Au(NO₃)₃
4. Fe₃(PO₄)₂

Answer

a. 79.87 amu

b. 187.77 amu

c. 383.0 amu

Percent Composition of a Compound from a Chemical Formula

The percent composition of a compound can also be determined from the formula of the compound. The subscripts in the formula are first used to calculate the mass of each element in one mole of the compound. That is divided by the molar mass of the compound and multiplied by (100%).

[% : text{by mass} = frac{text{mass of element in} : 1 : text{mol}}{text{molar mass of compound}} times 100%]

The percent composition of a given compound is always the same as long as the compound is pure.

Example (PageIndex{3})

Dichlorine heptoxide (left( ce{Cl_2O_7} right)) is a highly reactive compound used in some organic synthesis reactions. Calculate the percent composition of dichlorine heptoxide.

Solution

Percent composition can also be used to determine the mass of a certain element that is contained in any mass of a compound. In the previous sample problem, it was found that the percent composition of dichlorine heptoxide is (38.76% : ce{Cl}) and (61.24% : ce{O}). Suppose that you needed to know the masses of chlorine and oxygen present in a (12.50 : text{g}) sample of dichlorine heptoxide. You can set up a conversion factor based on the percent by mass of each element.

[12.50 : text{g} : ce{Cl_2O_7} times frac{38.76 : text{g} : ce{Cl}}{100 : text{g} : ce{Cl_2O_7}} = 4.845 : text{g} : ce{Cl}]

[12.50 : text{g} : ce{Cl_2O_7} times frac{61.24 : text{g} : ce{O}}{100 : text{g} : ce{Cl_2O_7}} = 7.655 : text{g} : ce{O}]

The sum of the two masses is (12.50 : text{g}), the mass of the sample size.

Exercise (PageIndex{2})

Avogadro's Number Moles To Atoms

Barium fluoride is a transparent crystal that can be found in nature as the mineral frankdicksonite. Determine the percent composition of barium fluoride.

Answer a:

78.32% Ba and 21.67% F

Summary

• The mole (symbol: mol) is the base unit of amount of substance ('number of substance') in the International System of Units or System International (SI), defined as exactly 6.02214076×10²³ particles, e.g., atoms, molecules, ions or electrons.
• Avogadro's number is related to moles of any substance X as follows:

[text{1 mol X} = 6.022 times 10^{23} text{ X atoms}.]

• Formula masses of ionic and molecular compounds can be determined from the masses of the atoms in their formulas.
• Processes are described for calculating the percent composition of a compound based on the chemical formula.

• Anonymous

• Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).

• Stephen Lower, Professor Emeritus (Simon Fraser U.) Chem1 Virtual Textbook

• Marisa Alviar-Agnew (Sacramento City College)

• Henry Agnew (UC Davis)

• Wikipedia