Avogadro's number. Avogadro's number is the number of particles in one mole of any substance. Its numerical value is 6.02225 × 1023. One mole of oxygen gas contains 6.02 × 1023molecules of oxygen, while one mole of sodium chloride contains 6.02 × 1023sodium ions and 6.02 × 1023 chloride ions. 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 × 10 23 as the 'chemist's dozen'.

Here is the answer for the question – b (Avogadro’s number of chemical particles of that substance). You’ll find the correct answer below

b (Avogadro’s number of chemical particles of that substance)

The Correct Answer is

A mole of a chemical represents:a the weight of the substance that will combine with 100 g of oxygenb Avogadro’s number of chemical particles of that substancec the number of chemical particles in 100 g of that substanced the number of chemical particles in 1 g of that subtance

Reason Explained

A mole of a chemical represents:a the weight of the substance that will combine with 100 g of oxygenb Avogadro’s number of chemical particles of that substancec the number of chemical particles in 100 g of that substanced the number of chemical particles in 1 g of that subtance is correct for b (Avogadro’s number of chemical particles of that substance)

Avogadro Number Calculations II
How 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 10

How Many Particles Are Equal To 1 Mole

²³atoms/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

Avogadro's Full Number

(d) 5N x 4 = 20N

(d) is the answer.

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

3) Use Avogadro's Number:

(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

2) Use Avogadro's Number:

(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. (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

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:

The correct answer is (c). Now, some discussion about each answer choice.

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

2) Divide by Avogadro's Number:

3.70 x 10²³ / 6.022 x 10²³ mol¯¹ = 0.614414 mol <--- I'll keep some guard digits

Avogadro's Number Is Number Of Particles Present In

3) Use the molar mass of C₃H₈:

Avogadro's Number Of Representative Particles Is Equal To One

0.614414 mol times 44.0962 g/mol = 27.1 g (to three sig figs)