Moles molar mass_avonumb pt1

Moles, Molar Mass, and Avogadro’s Number, Part 1

By Shawn P. Shields, Ph.D.

This work is licensed by Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

http://creativecommons.org/licenses/by-nc-sa/4.0/





A Practical Problem Concerning Atom Size…

Recall: Atomic Mass Units (amu)

One amu is equal to 1.6605 1027 kg

This is a VERY small amount of mass.

We know that the average mass of a water (H2O) molecule is 18.02 amu…

…which would be 2.992 1026 kg, and very hard to measure!

A Practical Problem Concerning Atom Size…

We can’t count them either…(too small)

Plus, we’d need a whole lot of them to be able to weigh them on a balance.

A Practical Problem…

So, how could we solve this problem?

Observe:

The ratio of atomic masses for one atom each of O and H is

The ratio of atomic masses for 100 atoms each of O and H is

!

A Practical Problem…We could keep on using larger numbers, and still get the same result, so…

Let’s go ahead and add enough atoms to equal 15.999 g O and 1.008 g H; matching the average atomic masses shown on the periodic table for O and H.)

The number of atoms required to have the mass (in g) the same as that shown on the periodic table is a very special number…

!8

O15.999

1

H1.008

Avogadro’s Number!

It takes 6.022 1023 atoms of Oxygen to have a mass of 15.999 g.

It takes 6.022 1023 atoms of Hydrogen to have a mass of 1.008 g.

How many P atoms would it take to have 30.973 g?

15

P30.973

1

H1.008

8

O15.999


It takes 6.022 1023 atoms of Oxygen to have a mass of 15.999 g.

It takes 6.022 1023 atoms of Hydrogen to have a mass of 1.008 g.

How many P atoms would it take to have 30.973 g?


15

P30.973

1

H1.008

8

O15.999

The Mole Concept(A Chemist Counting Unit)

A “mole” of atoms is 6.022 1023

atoms.

The “mole” is a counting unit directly analogous to a “dozen.”

12 pencils = 1 dozen pencils

6.022 1023 pencils = 1 mole pencils

The Mole Concept(A Chemist Counting Unit)

Here are a few other ways you’ll see this number expressed:

6.022 1023 mol-1

This just means that there are 6.022 1023 “particles” per mol. (“particles” is implied)

You’ll also see NA = 6.022 1023 mol-1 and N0 = 6.022 1023 mol-1

Remember, “particles” can be atoms, electrons, cations, anions…anything!

Avogadro’s number is just the number of particles in a mole!

Molar Mass

Molar Mass is the amount of mass (in grams) in one mole of particles (atoms, ions, etc).

A “mole” of atoms is 6.022 1023 atoms.

One mole of any element has a molar mass in grams numerically equal to the atomic mass of that element. (Look on the Periodic Table)

74

W183.84

6

C12.011

8

O15.999

Molar Mass

Look at your periodic table:

Now, the average atomic mass (atomic weight) can be interpreted in grams.

So, one mole of tungsten (W) has a mass of 183.84 g

6.022 1023 “tungsten atoms” has a mass of 183.84 g

74

W183.84

6

C12.011

8

O15.999

Calculating the Molar Mass of a Compound

To calculate the molar mass of a compound:

• Add the molar masses for all elements in the compound using the atomic mass given (in grams).

• Be sure to multiply the mass by the number of moles of that element in the compound before adding them up.1

H1.008

6

C12.011

53

I126.90

15

P30.973


Ex: Calculate the molar mass of propane (C3H8)

Molar Mass = 3(Cavg mass) + 8(Havg mass) = ? g

1

H1.008

6

C12.011

53

I126.90

15

P30.973


Ex: Calculate the molar mass of propane (C3H8)

Molar Mass = 3(Cavg mass) + 8(Havg mass) = ? g

Molar Mass = 3(12.011) + 8(1.008) = 44.097 g

1

H1.008

6

C12.011

53

I126.90

15

P30.973

Mini Quiz: Calculating the Molar Mass of a Compound

Calculate the molar mass of phosgene (COCl2)

18

Ar39.948

6

C12.011

8

O15.999

7

N14.007

17

Cl35.453

74

W183.84

Mini Quiz Solution

Calculate the molar mass of phosgene (COCl2)

Add up the molar mass of each element multiplied by the number of moles of that element in the compound:

Molar Mass = 1(12.011) + 1(15.999) + 2(35.453) = 98.916 g

18

Ar39.948

6

C12.011

8

O15.999

7

N14.007

17

Cl35.453

74

W183.84

Converting from Mass to Moles

We use the molar mass to convert from grams (which we can measure) to moles of that substance.

Example: Suppose we are going to use 35.5 g of potassium chloride (KCl) in a reaction. How moles of KCl are there is 35.5 g?

Step 1: Calculate the molar mass of KCl.

Molar Mass = 1(39.098) + 1(35.453) = 74.551 g

17

Cl35.453

6

C12.011

8

O15.999

19

K39.098



Step 1: Calculate the molar mass of KCl.Molar Mass = 1(39.098) + 1(35.453) = 74.551 g

Step 2: Use the molar mass of KCl as a conversion factor to moles…

17

Cl35.453

6

C12.011

8

O15.999

19

K39.098



Step 1: Calculate the molar mass of KCl.

Molar Mass = 1(39.098) + 1(35.453) = 74.551 g

Step 2: Use the molar mass of KCl as a conversion factor to moles…

Step 3: Write the quantity that you need to convert, then use the appropriate conversion factor (with the unit you need to cancel out on the bottom), then do the math.

17

Cl35.453

6

C12.011

8

O15.999

19

K39.098

Converting Moles to Number of Molecules (Atoms, Particles, etc.)

We use Avogadro’s number to convert from moles to number of molecules of that substance.

Example: Convert 0.267 moles of sulfur trioxide (SO3) to number to molecules.

Remember, there are 6.022 1023 “particles” (molecules) in one mole.

Written another way…

16

S32.065

7

N14.007

8

O15.999


Example: Convert 0.267 moles of sulfur trioxide (SO3) to number to molecules.

So,

You try one…

How many atoms are in 0.23 moles N atoms?

16

S32.065

7

N14.007

8

O15.999


You try one…

How many atoms are in 0.23 moles N atoms?

Did you notice that we did not need the molar mass for N ?

16

S32.065

7

N14.007

8

O15.999


Example 2: How many O atoms are in 0.82 moles of SO3?

So,

Are we done? NO!

16

S32.065

7

N14.007

8

O15.999


Example 2: How many O atoms are in 0.82 moles of SO3?

So,

Multiply the number of O atoms per molecule by the number of SO3 molecules.

remember sig figs!

16

S32.065

7

N14.007

8

O15.999


Finally, how many moles of O atoms is this?

Convert from number of atoms to moles using Avogadro’s number:

remember sig figs!

16

S32.065

7

N14.007

8

O15.999

Moles molar mass_avonumb pt1

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