# Calculations with Elements and Compounds

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Calculations with Elements and Compounds
The Mole Concept Calculations with Elements and Compounds Pisgah High School M. Jones Rev 050212

Moles?

No. Not real moles, or Whack-a-moles, or even the moles on your back.
Chemistry moles

It’s a way of measuring atoms and molecules.
What is a mole? It’s a way of measuring atoms and molecules. The “mole concept” is a lot like the “dozen concept.”

A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting. A dozen is 12. A dozen is always 12.

A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting. A dozen is 12. A dozen is always 12. A dozen donuts.

A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting. A dozen is 12. A dozen is always 12. A dozen donuts. A dozen pencils.

A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting. A dozen is 12. A dozen is always 12. A dozen donuts. A dozen pencils. A dozen Volkswagons.

A dozen is always 12.

Like we can count by dozens, or multiples of 12, we can also count by multiples of a much larger number, which we call Avogadro’s number.

So how did chemists come up with such a huge number?

He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights.

Avogadro’s law 10.0 liters of CO2 weighs 19.6 grams 10.0 liters of N2 weighs 12.5 grams 10.0 liters of Xe weighs 58.6 grams 19.6 g 12.5 g = 44.0 g 28.0 g = 1.57 1.57 Ratio of the masses of equal volumes of CO2 and N2 Ratio of the molar masses of CO2 and N2

Avogadro’s law 10.0 liters of CO2 weighs 19.6 grams 10.0 liters of N2 weighs 12.5 grams 10.0 liters of Xe weighs 58.6 grams 19.6 g 58.6 g = 0.335 44.0 g 131.3 g = 0.335 Ratio of the masses of equal volumes of CO2 and Xe Ratio of the molar masses of CO2 and Xe

See! I told you so. He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights.

I wish I knew what my number was.
But Avogadro never determined the value we know as Avogadro’s number. I wish I knew what my number was. It was called Avogadro’s number as a tribute to his pioneering work.

Equal volumes of gases at the same temperature and pressure have equal numbers of particles.

Cannizzaro was able to convince chemists of the value of standardized atomic weights.
Loschmidt (1865) was the first to determine the number of atoms or molecules in a fixed volume of gas.

Jean Perrin was the first to use the term Avogadro’s number in 1909 to describe the number of atoms in the atomic weight of an element. He was the first to determine a value of Avogadro’s number which is close to the present-day value of x 1023.

Atomic Mass We can relate Avogadro’s number to the amount of an element equal to its atomic mass measured in grams.

Atomic Mass This used to be called the “gram atomic weight”. Atomic weights are now called atomic masses. Atomic masses are given in units of “atomic mass units”, or amu. The amu is also called the dalton.

Atomic Mass The “atomic mass unit” (amu) is based on the mass of the carbon-12 isotope. It was decided that an atom of C-12 be assigned a mass of exactly amu

Atomic Mass This way, hydrogen,the lightest element (H) would have a mass very close to 1. The average atomic mass of hydrogen is amu.

Atomic Mass Instead of amu of carbon-12, which is too small to even see, we consider grams of C-12. How many atoms are in g of C-12?

Atomic Mass 1 C atom C atom x 12.000 g C 1.993 x 10-23 g C
How many atoms are in g of carbon-12? A C-12 atom has a mass of x g 1 C atom C atom x g C 1.993 x g C = x 1023 C atoms

Atomic Mass The mole is the “official” metric unit for the “quantity of matter”. A mole is the quantity of an element which has a mass equal to the atomic mass expressed in grams.

The word “mole” can be abbreviated as “mol”.

So, what is a mole? It is a word that describes a very large number of atoms. 6.022 x 1023 atoms It comes from the Latin word moles which means “quantity” 6.022 x 1023 is also called Avogadro’s Number.

A mole is … 6.022 x 1023 atoms, molecules, electrons or ions … – any particle. Can you count to a mole? Since they are so small, we must count atoms indirectly.

Suppose you wanted to know the number of marbles in a large jar.
Weigh a few marbles, weigh all the marbles, use a conversion factor.

Suppose … Like this: 10 marbles = 86.45 grams
Avg. marble = grams All the marbles = g This is a conversion factor 1 marble g x = 286 marbles 8.645 g

We can count a large number of particles by weighing them.

We can count atoms if we know the mass of an Avogadro's number of atoms.

An Avogadro's number of atoms has a mass equal to the molar mass.
6.022 x 1023 atoms of sodium have a mass of 23.0 g 6.022 x 1023 atoms of iron have a mass of 55.8 g 6.022 x 1023 atoms of aluminum have a mass of 27.0 g

Q. How many atoms are in 50.0 grams of potassium?
We know that 1 mole of K has a mass of 39.1 grams; and 1 mole is 6.02 x 1023 atoms. 6.02 x 1023 atoms K 50.0 g K x = 39.1 g K 7.70 x 1023 atoms K

The molar mass of an element is the mass of 6
The molar mass of an element is the mass of x 1023 atoms or 1 mole of that element.

FYI: We now use “molar mass” instead of.. gram atomic weight, gram molecular weight, gram formula weight.

sodium (Na) 23.0 g/mol iron (Fe) 55.8 g/mol chlorine (Cl) 35.5 g/mol
The molar mass of an element is usually rounded to one decimal place: sodium (Na) 23.0 g/mol iron (Fe) 55.8 g/mol chlorine (Cl) 35.5 g/mol phosphorous (P) 31.0 g/mol

What do the subscripts in a formula tell us?
The subscripts give the number of moles of each element in one mole of the compound. 1 mole of Fe2O3 contains … 2 moles of iron (Fe), and … 3 moles of oxygen (O)

How many moles of each kind of element are in one mole of …
CaCl2 1 mole Ca and 2 moles Cl C12H22O11 12 moles C, 22 moles H, 11 moles O Fe3(PO4)2 3 moles Fe, 2 moles P, 8 moles O

Calculating molar masses of compounds …
Sum of the molar masses of the elements Molar mass of the compound = The molar mass of an element its atomic mass

Calculate the molar mass of water:
Molar mass of H2O = (2 x 1.0) + (1 x 16.0) = 18.0 g/mol 2 hydrogen atoms 1 oxygen atom

General Equation for Molar Mass
S (atomic masses) For each element, multiply it’s atomic mass by its subscript, then add them all together.

What is the molar mass of calcium chlorate?
Start with the formula: Ca(ClO3)2 1 mol Ca, 2 mol Cl, 6 mol O (1 x 40.1) + (2 x 35.5) + (6 x 16.0) = g/mol

What are the molar masses of each of the following?
1. HCl 2. Fe2O3 3. H2SO4 4. Ca3(PO4)2 5. (NH4)2CO3 36.5 g/mol 159.6 g/mol 98.1 g/mol 310.3 g/mol 96.0 g/mol

Molar Conversions 1 mol = 1 molar mass 1 mol = 6.022 x 1023 particles
Use conversion factors to convert between moles, grams, molecules and the volumes of gases at STP. 1 mol = 1 molar mass 1 mol = x 1023 particles 1 mol = 22.4 L of any gas at STP

Convert the following:
grams of iron metal to moles. 0.314 moles Fe moles of CaCl2 to grams. 4.02 g CaCl2 x 1024 molecules of SO3 to moles. 9.05 moles SO3

Detailed solutions:

1 mole equals 22.4 L of any gas at STP
Why 22.4 L? What is STP? What has this all got to do with a mole?

Standard temperature and pressure
STP stands for Standard temperature and pressure

Standard temperature Standard pressure STP … 0 C or 273 K
…the freezing point of water 0 C or K Standard pressure … atmospheric pressure at sea level 1.00 atmosphere, kPa, 760. mm Hg, 760. Torr or lbs/in2

1 mole of any gas at STP has a volume of 22.4 L
Consider a box with a volume of 22.4L O2 1 atm C 1.00 mol 22.4 L If the box contains 1.00 mole of oxygen gas, at a temperature of 0 C, the pressure will be atm.

More molar conversions …
1. Convert 3.00 liters of N2 gas at STP to moles. 0.134 mol N2 2. Convert moles of HCl(g) to liters at STP. 10.2 L HCl 3. How many molecules are in mL of NH3 at STP? 6.72 x 1021 molecules NH3 Click for solutions

Detailed solutions: Click to return

Calculations with density…
Recall that density is the mass per unit volume … D = m V We can find the density of a gas at STP if we know the molar mass.

Sample density calculation:
What is the density of carbon dioxide at STP? We know that the molar mass of CO2 is 44.0 g/mol and the volume of 1 mole of gas is 22.4L at STP

Sample density calculation:
What is the density of carbon dioxide at STP? Mass of 1 mole of CO2 Volume of 1 mole of CO2

Additional problems: 1. Find the density of nitrogen gas (N2) at STP.

2. Find the mass of 200.0 mL of propane (C3H8) at STP.
m = V D Hint: What is the density of propane? This is the density of propane

D = ----------------------- mass of one mole volume of one mole
m = V D This is the density of propane

This concludes the presentation on moles and molar mass.