Avogadro’s law also means the ideal gas constant is the same value for all gases, so: constant = p 1 V 1 /T 1 n 1 = P 2 V 2 /T 2 n 2. V 1 /n 1 = V 2 /n 2. V 1 n 2 = V 2 n 1. Where p is the pressure of a gas, V is volume, T is temperature, and n is number of moles. Examples of Avogadro’s law in Real Life Applications. Avogadro's number is used in chemistry when you need to work with very large numbers. It's the basis for the mole unit of measurement, which provides an easy way to convert between moles, mass, and the number of molecules. For example, you can use the number to find the number of water molecules in a single snowflake. Avogadro's Number Avogadro’s number tells us the number of particles in 1 mole (or mol) of a substance. These particles could be electrons or molecules or atoms. The value of Avogadro’s number is approximately 6.0221 mol−1. To calculate the mass of a single atom, first look up the atomic mass of carbon from the periodic table. This number, 12.01, is the mass in grams of one mole of carbon. One mole of carbon is 6.022 x 10 23 atoms of carbon (Avogadro's number). This relation is then used to 'convert' a carbon atom to grams by the ratio. Avogadro’s law tells about the relationship between the volume of a gas and the number of molecules possessed by it. It was formulated by an Italian scientist Amedeo Avogadro in the year 1811. During a series of experiments conducted by him, he observed that an equal volume of gases contains an equal number of particles.

Chemistry

The Avogadro's number is a constant used in analytical chemistry to quantify the number of particles or microscopic entities from macroscopic measurements such as mass. It is very important to know this number in order to understand molecule composition, interactions and combinations. For example, to create a water molecule it is necessary to combine two hydrogen atoms and one oxygen atom to obtain one mole of water. The number of Avogadro is a constant that must be multiplied by the number of atoms of each element to obtain the value of oxygen (6.023 x 1023 atoms of O) and Hydrogen (2x 6.022x 1023) that form a mole of H2O.

## What is the Avogadro's number?

The Avogadro's number is a constant that represents the number of existing atoms in twelve grams of 12-pure carbon. This figure makes possible to count microscopic entities. This includes the number of elementary entities (i.e. atoms, electrons, ions, molecules) that exist in a mole of any substance. The Avogadro's number is equal to (6,022 x 10 raised to 23 particles) and is symbolized in the formulas with the letters L or NA. In addition, it is used to make conversions between grams and atomic mass unit. The unit of measure of the Avogadro's number is the mole (mol-1) but it can also be defined in lb/mol-1 and oz/mol-1.

## What is the Avogadro’s number?

The Avogadro’s number is 602,000,000,000,000,000,000,000,000 which is equal to 602,000 trillion = 6.02 x 1023. This value is found from the number of carbon atoms contained in 12 grams of carbon 12 elevated to power 23.

It is important to mention that depending on the unit of measurement used, the number may vary. In this sense, if you work with mole the number is 6.022140857 (74) x 1023 mole-1.

• If you work with pounds it will be 2.731 597 34(12) × 1026 (Lb.-mol)-1.
• If you work with ounces it will be 1.707 248434 (77) x 1025 (oz-mol)-1.

## What does the Avogadro’s number represent?

The Avogadro’s number represents the number of atoms that exist in twelve grams of carbon-12.

This number represents a quantity without an associated physical dimension, so it is considered a pure number to describe a physical characteristic without dimension or explicit unit of expression. For this reason, it has the numerical value of constant that the units of measurement have.

## How the Avogadro’s number is calculated

The Avogadro’s number can be calculated by measuring the Faraday constant (F) which represents the electrical charge carried by a mole of electrons and dividing it by the elementary charge (e). This formula is Na= F/e.

The Avogadro constant can be calculated using analytical chemistry techniques known as coulometry, which determine the amount of matter transformed during the electrolysis reaction by measuring the amount consumed or produced in coulombs.

There are also other methods to calculate it such as the electron mass method, known as CODATA or the system of measuring through crystal density using X-rays.

## History

The Avogadro’s number or Avogadro constant is named after the Italian scientist Amedeo Avogadro who in 1811 determined that the volume of a gas at a given pressure and temperature is proportional to the number of atoms or molecules regardless of the nature of the gas.

In 1909, Jean Perrin, a French physicist – winner of the Nobel Prize in physics in 1926 – proposed naming the constant in honor of Avogadro. Perrin, using several methods, proved the use of the Avogadro constant and its validity in many of his works.

Initially, it was called Avogadro’s number to refer to the number of molecules-grams of oxygen but in 1865, the scientist JohannJosef Loschmidf called the Avogadro’s number, Avogadro constant. Loschmidf estimated the average diameter of air molecules by a method equivalent to calculating the number of particles in a specific gas volume. For this reason, the particle density value of an ideal gas is known as the Loschmidt constant, which is approximately proportional to the Avogadro constant. From then on, the symbol for the Avogadro’s number or Avogadro constant can be NA (Avogadro’s number) or L (in honor of Loschmid).

A curious fact in Avogadro’s number history is that the Italian scientist Amedeo Avogadro never measured the volume of any particle in his lifetime because in his time there were no elements necessary to do so, but it is thanks to his contributions that Perrin developed this constant and therefore gave it that name.

Written by Gabriela Briceño V.

### Avogadro Number Calculations IIHow Many Atoms or Molecules?

The value I will use for Avogadro's Number is 6.022 x 1023 mol¯1.

Types of problems you might be asked look something like these:

0.450 mole of Fe contains how many atoms? (Example #1)
0.200 mole of H2O contains how many molecules? (Example #2)

0.450 gram of Fe contains how many atoms? (Example #3)
0.200 gram of H2O contains how many molecules? (Example #4)

When the word gram replaces mole, you have a related set of problems which requires one more step.

And, two more:

0.200 mole of H2O contains how many atoms?
0.200 gram of H2O contains how many atoms?

When the word gram replaces mole, you have a related set of problems which requires one more step. In addition, the two just above will have even another step, one to determine the number of atoms once you know the number of molecules. Here is a graphic of the procedure steps:

Pick the box of the data you are given in the problem and follow the steps toward the box containing what you are asked for in the problem.

Example #1: 0.450 mole of Fe contains how many atoms?

Solution:

Start from the box labeled 'Moles of Substance' and move (to the right) to the box labeled 'Number of Atoms or Molecules.' What do you have to do to get there? That's right - multiply by Avogadro's Number.

0.450 mol x 6.022 x 1023 mol¯1 = see below for answer

Example #2: 0.200 mole of H2O contains how many molecules?

Solution:

Start at the same box as Example #1.

0.200 mol x 6.022 x 1023 mol¯1 = see below for answer

### The answers (including units) to Examples #1 and #2

The unit on Avogadro's Number might look a bit weird. It is mol¯1 and you would say 'per mole' out loud. The question then is WHAT per mole?

The answer is that it depends on the problem. In the first example, I used iron, an element. Almost all elements come in the form of individual atoms, so the correct numerator with most elements is 'atoms.' (The exceptions would be the diatomic elements plus P4 and S8.)

So, doing the calculation and rounding off to three sig figs, we get 2.71 x 1023 atoms. Notice 'atoms' never gets written until the end. It is assumed to be there in the case of elements. If you wrote Avogadro's Number with the unit atoms/mol in the problem, you would be correct.

The same type of discussion applies to substances which are molecular in nature, such as water. So the numerator I would use in example #2 is 'molecule' and the answer is 1.20 x 1023 molecules.

Once again, the numerator part of Avogadro's Number depends on what is in the problem. Other possible numerators include 'formula units,' ions, or electrons. These, of course, are all specific to a given problem. When a general word is used, the most common one is 'entities,' as in 6.022 x 1023 entities/mol.

Keep this in mind: the 'atoms' or 'molecules' part of the unit is often omitted and simply understood to be present. However, it will often show up in the answer. Like this:

0.450 mol x 6.022 x 1023 mol¯1 = 2.71 x 1023 atoms

It's not that a mistake was made, it's that the 'atoms' part of atoms per mole was simply assumed to be there.

Example #3: 0.450 gram of Fe contains how many atoms?

Example #4: 0.200 gram of H2O contains how many molecules?

Look at the solution steps in the image above and you'll see we have to go from grams (on the left of the image above) across to the right through moles and then to how many atoms or molecules.

Solution to Example #3:

Step One (grams ---> moles): 0.450 g / 55.85 g/mol = 0.0080573 mol

Step Two (moles ---> how many): (0.0080573 mol) (6.022 x 1023 atoms/mol) = 4.85 x 1021 atoms

Solution to Example #4:

Step One: 0.200 g / 18.015 g/mol = 0.01110186 mol

Step Two: (0.01110186 mol) (6.022 x 1023 molecules/mol) = 6.68 x 1021 molecules

Example #5: Calculate the number of molecules in 1.058 mole of H2O

Solution:

(1.058 mol) (6.022 x 1023 mol¯1) = 6.371 x 1023 molecules

Example #6: Calculate the number of atoms in 0.750 mole of Fe

Solution:

(0.750 mol) (6.022 x 1023 mol¯1) = 4.52 x 1023 atoms (to three sig figs)

Example #7: Calculate the number of molecules in 1.058 gram of H2O

Solution:

(1.058 g / 18.015 g/mol) (6.022 x 1023 molecules/mole)

Here is the solution set up in dimensional analysis style:

 1 mol 6.022 x 1023 1.058 g x ––––––––– x –––––––––– = 3.537 x 1022 molecules (to four sig figs) 18.015 g 1 mol ↑ grams to moles ↑ ↑ moles to ↑molecules

Example #8: Calculate the number of atoms in 0.750 gram of Fe

(0.750 gram divided by 55.85 g/mole) x 6.022 x 1023atoms/mole
 1 mol 6.022 x 1023 0.750 g x ––––––––– x –––––––––– = 8.09 x 1021 atoms (to three sig figs) 55.85 g 1 mol

Example #9: Which contains more molecules: 10.0 grams of O2 or 50.0 grams of iodine, I2?

Solution:

Basically, this is just two two-step problems in one sentence. Convert each gram value to its mole equivalent. Then, multiply the mole value by Avogadro's Number. Finally, compare these last two values and pick the larger value. That is the one with more molecules.

 1 mol 6.022 x 1023 10.0 g x ––––––––– x –––––––––– = number of O2 molecules 31.998 g 1 mol
 1 mol 6.022 x 1023 50.0 g x ––––––––– x –––––––––– = number of I2 molecules 253.8 g 1 mol

Example #10: 18.0 g of H2O is present. (a) How many oxygen atoms are present? (b) How many hydrogen atoms are present?

Solution:

1) Convert grams to moles:

18.0 g / 18.0 g/mol = 1.00 mol

2) Convert moles to molecules:

(1.00 mol) (6.02 x 1023 mol¯1) = 6.02 x 1023 molecules

3) Determine number of atoms of oxygen present:

(6.02 x 1023 molecules) (1 O atom / 1 H2O molecule) = 6.02 x 1023 O atoms

4) Determine number of atoms of hydrogen present:

(6.02 x 1023 molecules) (2 H atoms / 1 H2O molecule) = 1.20 x 1024 H atoms (to three sig figs)

Notice that there is an additional step (as seen in step 3 for O and step 4 for H). You multiply the number of molecules times how many of that atom are present in the molecule. In one molecule of H2O, there are 2 atoms of H and 1 atom of O.

Sometimes, you will be asked for the total atoms present in the sample. Do it this way:

(6.02 x 1023 molecules) (3 atoms/molecule) = 1.81 x 1024 atoms (to three sig figs)

The 3 represents the total atoms in one molecule of water: one O atom and two H atoms.

Example #11: Which of the following contains the greatest number of hydrogen atoms?

(a) 1 mol of C6H12O6
(b) 2 mol of (NH4)2CO3
(c) 4 mol of H2O
(d) 5 mol of CH3COOH

Solution:

1) Each mole of molecules contains N number of molecules, where N equals Avogadro's Number. How many molecules are in each answer:

(a) 1 x N = N
(b) 2 x N = 2N
(c) 4 x N = 4N
(d) N x 5 = 5N

2) Each N times the number of hydrogen atoms in a formula equals the total number of hydrogen atoms in the sample:

(a) N x 12 = 12N
(b) 2N x 8 = 16N
(c) 4N x 2 = 8N
(d) 5N x 4 = 20N

Example #12: How many oxygen atoms are in 27.2 L of N2O5 at STP?

Solution:

1) Given STP, we can use molar volume:

27.2 L / 22.414 L/mol = 1.21353 mol

2) There are five moles of O atoms in one mole of N2O5:

(1.21353 mol N2O5) (5 mol O / 1 mol N2O5) = 6.06765 mol O

(6.06765 mol O) (6.022 x 1023 atoms O / mole O) = 3.65 x 1024 atoms O (to three sig figs)

Example #13: How many carbon atoms are in 0.850 mol of acetaminophen, C8H9NO2?

Solution:

1) There are 8 moles of C in every mole of acetaminophen:

(0.850 mol C8H9NO2) (8 mol C / mol C8H9NO2) = 6.80 mol C

(6.80 mol C) (6.022 x 1023 atoms C / mole C) = 4.09 x 1024 atoms C (to three sig figs)

Example #14: How many atoms are in a 0.460 g sample of elemental phosphorus?

Solution: Phosphorus has the formula P4

## Avogadro's Number Examples In Chemistry

. (Not P!!)

0.460 g / 123.896 g/mol = 0.00371279 mol

(6.022 x 1023 molecules/mol) (0.00371279 mol) = 2.23584 x 1021 molecules of P4

(2.23584 x 1021 molecules) (4 atoms/molecule) = 8.94 x 1021 atoms (to three sig figs)

Set up using dimensional analysis style:

 1 mol 6.022 x 1023 molecules 4 atoms 0.460 g x –––––––– x –––––––––––––––––– x ––––––––– = 8.94 x 1021 atoms 123.896 g 1 mol 1 molecule

## Avogadro's Number Of Iron Atoms

Example #15: Which contains the most atoms?

(a) 3.5 molecules of H2O
(b) 3.5 x 1022 molecules of N2
(c) 3.5 moles of CO
(d) 3.5 g of water

Solution:

Choice (a): You can't have half of a molecule, so this answer should not be considered. Also, compare it to (b). Since (a) is much less than (b), (a) cannot ever be the answer to the most number of atoms.

Choice (b): this is a viable contender for the correct answer. Since there are two atoms per molecule, we have 7.0 x 1022 atoms. We continue to analyze the answer choices.

Choice (c): Use Avogadro's number (3.5 x 1023 mol¯1) and compare it to choice (b). You should be able to see, even without the 3.5 moles, choice (c) is already larger than choice (b). Especially when you consider that N2 and CO both have 2 atoms per molecule.

Choice (d): 3.5 g of water is significantly less that the 3.5 moles of choice (c). 3.5 / 18.0 equals a bit less that 0.2 moles of water.

Bonus Example: A sample of C3H8 has 2.96 x 1024 H atoms.

(a) How many carbon atoms does the sample contain?
(b) What is the total mass of the sample?

Solution to (a):

1) The ratio between C and H is 3 to 8, so this:

 3 y ––––––– = –––––––––––––––– 8 2.96 x 1024 H atoms

2) will tell us the number of carbon atoms present:

y = 1.11 x 1024 carbon atoms

3) By the way, the above ratio and proportion can also be written like this:

3 is to 8 as y is to 2.96 x 1024

Be sure you understand that the two different ways to present the ratio and proportion mean the same thing.

Solution to (b) using hydrogen:

1) Determine the moles of C3H8 present.

2.96 x 1024 / 8 = 3.70 x 1023 molecules of C3H8

## Define Avogadro's Number With Example 