What Relationships Are Needed to Convert 1.5 Grams of Carbon to the Number of Carbon Atoms?

The Mole

Avogadro'south Number

Ascertain mole.
Define Avogadro's number.

It is often convenient to have a unit for large amounts, such as a mole

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Avogadro'south Number

It certainly is easy to count bananas or to count elephants (every bit long as yous stay out of their manner). Still, you would be counting grains of sugar from your carbohydrate canister for a long, long time. Atoms and molecules are extremely small – far, far smaller than grains of sugar. Counting atoms or molecules is non only unwise, it is absolutely impossible. One drop of water contains about 10 ²² molecules of h2o. If you counted 10 molecules every second for l years without stopping yous would accept counted merely 1.6 × 10 ¹⁰ molecules. Put another fashion, at that counting rate, it would have you lot over 30 trillion years to count the water molecules in i tiny drib.

Chemists needed a name that can stand for a very large number of items. Amedeo Avogadro (1776 – 1856), an Italian scientist, provided but such a number. He is responsible for the counting unit of measure called the mole. A mole (mol) is the amount of a substance that contains six.02 × ten ²³ representative particles of that substance. The mole is the SI unit for amount of a substance. Simply like the dozen and the gross, it is a name that stands for a number. There are therefore 6.02 × 10 ²³ water molecules in a mole of h2o molecules. In that location also would be 6.02 × 10 ²³ bananas in a mole of bananas, if such a huge number of bananas ever existed.

Figure ten.1

Italian scientist Amedeo Avogadro, whose piece of work led to the concept of the mole as a counting unit in chemistry.

The number vi.02 × 10 ²³ is called Avogadro's number , the number of representative particles in a mole. Information technology is an experimentally determined number. A representative particle is the smallest unit of measurement in which a substance naturally exists. For the majority of elements, the representative particle is the atom. Atomic number 26, carbon, and helium consist of iron atoms, carbon atoms, and helium atoms, respectively. Seven elements exist in nature equally diatomic molecules and they are H ₂ , N _ii , O _ii , F _ii , Cl ₂ , Br ₂ , and I ₂ . The representative particle for these elements is the molecule. Likewise, all molecular compounds such equally H ₂ O and CO ₂ exist every bit molecules and so the molecule is their representative particle. For ionic compounds such every bit NaCl and Ca(NO ₃ ) ₂ , the representative particle is the formula unit. A mole of whatever substance contains Avogadro'southward number (six.02 × 10 ²³ ) of representative particles.

The animal mole is very different from the unit mole

Figure 10.2

The creature mole is very different than the counting unit of measurement of the mole. Chemists nevertheless have adopted the mole as their unofficial mascot. National Mole Day is a celebration of chemistry that occurs on October 23rd (10/23) of each year.

Summary

A mole of any substance contains Avogadro'southward number (half-dozen.02 × 10 ²³ ) of representative particles.

Practice

Questions

Utilize the link beneath to answer the following questions:

http://www.scientificamerican.com/commodity.cfm?id=how-was-avogadros-number

What was Avogadro'south hypothesis?
Who first calculated this number?
Who coined the term "Avogadro'due south number"?
What contribution did Robert Millikan make to the determination for the value for the number?

Review

Questions

What is the SI unit for corporeality of a substance?
What is the representative particle for an element?
The formula unit is the representative particle for what?

Avogadro's number: The number of representative particles in a mole, 6.02 × 10 ²³ .
mole (mol): The amount of a substance that contains 6.02 × 10 ²³ representative particles of that substance.
representative particle : The smallest unit of measurement in which a substance naturally exists.

Conversions Between Moles and Atoms

Perform calculations involving conversions between number of moles and number of atoms or molecules.

Using moles allows us to avoid superscripts and subscripts

Big numbers or piddling numbers?

Do yous hate to type subscripts and superscripts? Even with a good word-processing plan, having to click on an icon to get a superscript and then remembering to click off subsequently you type the number can be a real hassle. If nosotros did not know almost moles and but knew near numbers of atoms or molecules (those big numbers that require lots of superscripts), life would be much more than complicated and we would make many more typing errors.

Conversions Between Moles and Atoms

Conversions Betwixt Moles and Number of Particles

Using our unit conversion techniques, we tin utilize the mole characterization to convert back and forth betwixt the number of particles and moles.

Sample Problem 1: Converting Number of Particles to Moles

The element carbon exists in two master forms: graphite and diamond. How many moles of carbon atoms is 4.72 × 10 ²⁴ atoms of carbon?

Footstep i: Listing the known quantities and plan the problem.

Known

number of C atoms = 4.72 × 10 ²⁴
i mole = half-dozen.02 × 10 ²³ atoms

Unknown

iv.72 × x ²⁴ = ? mol C

One conversion factor will allow us to catechumen from the number of C atoms to moles of C atoms.

Step 2: Calculate.

$4.72 times 10^{24} text{atoms C} times frac{1 text{mol C}}{6.02 times 10^{23} text{atoms C}}=7.84 text{mol C}$

Step iii: Think well-nigh your outcome.

The given number of carbon atoms was greater than Avogadro'south number, so the number of moles of C atoms is greater than ane mole. Since Avogadro'south number is a measured quantity with three significant figures, the result of the calculation is rounded to iii significant figures.

Suppose that you wanted to know how many hydrogen atoms were in a mole of water molecules. Commencement, you would need to know the chemical formula for water, which is H ₂ O. There are two atoms of hydrogen in each molecule of water. How many atoms of hydrogen would there be in 2 water molecules? There would be two × two = iv hydrogen atoms. How well-nigh in a dozen? In that case a dozen is 12 and then 12 × 2 = 24 hydrogen atoms in a dozen water molecules. To get the answers, (iv and 24) you had to multiply the given number of molecules past 2 atoms of hydrogen per molecule. Then to observe the number of hydrogen atoms in a mole of water molecules, the trouble could be solved using conversion factors.

$1 text{mol} text{H}_2text{O} times frac{6.02 times 10^{23} text{molecules} text{H}_2text{O}}{1 text{mol} text{H}_2text{O}} times frac{2 text{atoms H}}{1 text{molecule} text{H}_2text{O}}=1.20 times 10^{24} text{atoms H}$

The first conversion factor converts from moles of particles to the number of particles. The second conversion factor reflects the number of atoms contained within each molecule.

Figure ten.three

Two water molecules contain four hydrogen atoms and ii oxygen atoms. A mole of h2o molecules contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms.

Sample Problem two: Atoms, Molecules, and Moles

Sulfuric acid has the chemical formula H _two So ₄ . A sure quantity of sulfuric acid contains four.89 × 10 ²⁵ atoms of oxygen. How many moles of sulfuric acid is the sample?

Step one: List the known quantities and plan the problem.

Known

4.89 × 10 ²⁵ = O atoms
1 mole = six.02 × x ²³ molecules H ₂ SO ₄

Unknown

mol of H _ii SO ₄ molecules

Two conversion factors will be used. Starting time, convert atoms of oxygen to molecules of sulfuric acid. Then, convert molecules of sulfuric acid to moles of sulfuric acid.

Step 2: Summate.

$4.89 times 10^{25} text{atoms O} times frac{1 text{molecule} text{H}_2text{SO}_4}{4 text{atoms O}} times frac{1 text{mol} text{H}_2text{SO}_4}{6.02 times 10^{23} text{molecules} text{H}_2text{SO}4}=20.3 text{mol} text{H}_2text{SO}_4$

Step iii: Think nigh your result.

The original number of oxygen atoms was about 80 times larger than Avogadro's number. Since each sulfuric acrid molecule contains 4 oxygen atoms, in that location are about 20 moles of sulfuric acid molecules.