Notes on Mole­12.notebook

1

October 25, 2012

Oct 14­6:22 PM Oct 14­6:22 PM

How do chemists “count” atoms/formula units/molecules? How do we go from the atomic scale to the scale of everyday measurements (macroscopic scale)? The gateway is the mole!

But before we get to the mole, let’s review some things we have previously learned.

Can you write the chemical reaction for the synthesis of calcium sulfide from its elements? First, what is the chemical formula of calcium sulfide?

Now, what elements make it up?

Let’s write an equation for the reaction of the elements that go to make calcium sulfide:

In the reaction written above, the coefficients represent the numbers of atoms/molecules/units that react to give the number of atoms/molecules/units of products made. So we see one atom of calcium reacts with one atom of sulfur to produce one unit of calcium sufide. Don’t get hung up on the terms now but it is important you see that one calcium reacts with one sulfur!

Oct 14­6:23 PM

Now let’s put in the relative weights of the reactants:

Ca + S à CaS

What is the mass ratio in which sulfur reacts with calcium according to the above equation?

Oct 14­6:23 PM

Since calcium and sulfur react in a 1:1 ratio, this must mean that 40.0 grams of calcium contain the same number of particles as 32.0 g of sulfur. WOW! We don’t have to count atoms to see the ratio in which they react – we can weigh them!

Now let’s get more quantitative. Can you determine the percent by mass of each element in calcium sulfide?

Ca:

S:

% Ca =

% S =

What is the mass ratio as a percent in which sulfur reacts with calcium?

How does this ratio compare with the one calculated on the previous page?

Oct 14­6:23 PM

Again, this means that 40.0 grams of calcium contain the same number of particles as 32.0 grams of sulfur!

The bottom line here is that even though atoms/molecules are too small to count, we can actually count them by weighing them.

Oct 14­6:24 PM

MOLE

Key Idea ­ 1 mole of anything contains Avogadro’s number or 6.02 X 1023 particles of that thing. A mole of anything contains the same number of particles as a mole of anything else!

Let’s first consider elements

Key Idea ­ the atomic mass of an element, measured in grams (on a balance), contains one mole of atoms of that element.

Example: carbon has a mass of 12.0 amu

so, 12.0 g of C = 1 mol of C = 6.02 X 1023 atoms of C

What about Na?

What about Al?

Notes on Mole­12.notebook

2

October 25, 2012

Oct 14­6:25 PM

Key Idea ­ so now we can express masses of atoms in another unit: grams/mol or gram atomic mass (GAM)

MASS MOLE

What is the conversion factor between a given mass of an element and the equivalent moles of that element?

problem:How many moles are in 6.0 g of carbon?

How many grams are in 2.0 moles of sodium?

How many moles are in 112 g of iron?

Oct 14­6:26 PM

Next step:MOLE ATOMS

What is the conversion factor between moles and atoms?

How many aluminum atoms are there in 54.0 g of aluminum?

How many silicon atoms are there in 112.0 g of silicon?

Calculate the mass of a sample of copper containing 9.38 X 1025 atoms?

Oct 14­6:26 PM

Now let’s consider compounds

Key Idea ­ the formula mass of a compound, measured in grams (on a balance), contains one mole of formula units of the compound. Note the term formula unit is used when describing ionic compounds (metal­nonmetal) whereas the term molecules are used when dealing with molecular compounds (nonmetal­nonmetal). The mass of one mole of a compound is called the molar mass or gram formula mass (GFM)

Example: sodium hydroxide

sulfur dioxide

Oct 14­6:27 PM

problem: How many formula units of sodium nitrate are present in a 72.96 g sample of the compound?

problem: Calculate the number of molecules contained in a 100.0 mL sample of water. Assume the density of water = 1.00 g/mL.

problem: Determine the mass of nitrogen triiodide that must be massed which would contain 2.15 X 1024 molecules of nitrogen triiodide.

Oct 14­6:27 PM

Key Idea ­ a mole of a compound consists of moles of atoms comprising it. Thus, subscripts represent moles of an element as well as atoms of an element in a compound.

Example: 1 mole sodium hydrogen carbonate (or sodium bicarbonate = baking soda).

Calculate the number of moles of each element in baking soda, sodium hydrogen carbonate:

NaHCO3 Na H C O O O

Oct 14­6:28 PM

Let’s take it a step further by doing problems in which we do calculations involving atoms in compounds. Remember that the subscript in a chemical formula tells us the number of moles of atoms in one mole of the molecule/formula unit. One mole of carbon dioxide (CO2), for example, contains one mole of carbon atoms (C) and two moles of oxygen atoms (O).

O = C = O contains 1 mole C atoms2 mole O atoms

Calculate the number of moles of each element in sulfuric acid:

Now calculate the number of moles of each element in 2 moles of sulfuric acid:

Notes on Mole­12.notebook

3

October 25, 2012

Oct 14­6:28 PM

Let’s consider the diatomic molecules (BrINClHOF).

Calculate the number of moles of chlorine atoms in one moles of chlorine gas.

Cl­Cl

Calculate the number of moles of chlorine atoms in two moles of chlorine gas.

Cl­ClCl­Cl

Calculate the number of moles of iodine atoms in 5 moles of molecular iodine.

Now calculate the number of iodine atoms in 5 moles of molecular iodine.

Oct 14­6:28 PM

Now if we know the moles of atoms we can calculate the number of atoms. What is the conversion factor between moles of atoms and number of atoms?

Can you calculate the number of oxygen atoms in a 2.0 mole sample of cupric sulfate?

Calculate the number of chlorine atoms in a 25.0 g sample of aluminum chloride.

If we know the moles of atoms we can calculate the mass of the atoms. What is the conversion factor between moles and mass of an element?

Oct 14­6:29 PM

Calculate the mass of oxygen atoms in a 0.500 g sample of potassium chlorate. There are two ways you can do this problem:

“mole” way:

Can you think of another way to solve the problem? (Hint: think law of constant composition)

Oct 14­6:29 PM

Key Idea – the volume that one mole of any ideal gas occupies at standard temperature and pressure (STP) is 22.4 liters. An ideal gas is a gas that conforms to the Kinetic Molecular Theory of gases. More about that later in the year, but we can still do some problems based on this relationship. The conversion factor between moles and volume for any gas at STP is 22.4 L/mol.

MOLE VOLUME (for gases at STP)Calculate the volume that 2.50 moles carbon dioxide gas will occupy at STP.

Now calculate the volume that 50.0 g of methane gas (CH4) will occupy at STP.

A sample of oxygen gas occupies a volume of 75.0 L at STP. Calculate the mass of the sample and the number of oxygen molecules in this sample.

Oct 14­6:29 PM

Summary Diagram

MASS

MOLEGAS VOLUME AT STP

NUMBER OF PARTICLES

Oct 14­6:30 PM

You can calculate the density of any gas at STP. This is done by dividing the molar mass (aka gram formula mass, aka molecular mass, aka molecular weight) by molar volume.

Calculate the densities of the following gases at STP:

a) Helium

b) Sulfur dioxide

c) Uranium hexafluoride

Notes on Mole­12.notebook

4

October 25, 2012

Oct 14­6:30 PM

Formula Stoichiometry

Stoichiometry is the part of chemistry which studies the quantitative relationships implied by chemical formulas and equations. We will first deal with formulas.

Percentage Composition (by Mass)

% element = mass contributed by element/mass of compound X 100

Problem: Calculate the percentage composition of each element (by mass) in potassium phosphate.

Calculate the mass of sulfur atoms in a 1.50 g sample of sodium thiosulfate, Na2S2O3 (aka photograph fixer).

Oct 14­6:30 PM

II. Empirical/Molecular Formulas

Key Idea ­ to determine an empirical formula of a compound, convert the mass ratio (percentage) to a mole ratio. Then, if necessary, adjust the mole ratio (i.e. the subscripts) to simplest whole numbers. A molecular formula of a compound can also be its empirical formula or some multiple of the empirical formula depending on the molecular mass of the compound.

Oct 14­6:31 PM

Problem:

A compound was found to consist of 30% nitrogen and 70% oxygen by mass.

Determine the compounds empirical formula.

If the molecular mass of the compound is 92.0 g/mol, determine its molecular formula.

Oct 14­6:31 PM

An alternate but more direct way for getting the molecular formula (given the percentage composition and molecular mass is:

mole of element (subscript) = % of molar mass/atomic mass of element

Oct 14­6:32 PM

Problem:

A compound is composed of 7.20 g of carbon, 1.20 g of hydrogen, and 9.60 g of oxygen. The molar mass of the compound is 180 g/mol. Find the molecular formula for this compound.

Oct 14­6:32 PM

Additional Problems:

1. Determine the percent by mass of each of the elements in the compound iron(II)oxide (rust).

2. What mass of chlorine is present in a 24.51 g sample of carbon tetrachloride?

Notes on Mole­12.notebook

5

October 25, 2012

Oct 14­6:32 PM

3. There are two common oxides of sulfur. One contains 32 g of sulfur for each 32 g of oxygen. The other oxide contains 32 g of sulfur for each 48 g of oxygen. What are the empirical formulas of the two oxides?

4. A form of phosphorous called red phosphorous is used in match heads. When 0.062 g of red phosphorous burns, 0.142 g of phosphorous oxide is formed. What is the empirical formula of this oxide?

Oct 14­6:32 PM

5. A compound is composed of 19.01 g of carbon, 18.48 g of nitrogen, 25.34 g of oxygen, and 1.58 g of hydrogen. Find the empirical formula of this compound.

6. A compound containing only phosphorous and oxygen is 43.7% P by mass; the molar mass is 142.0 g/mol. What are the empirical and molecular formulas of the compound?

Oct 14­6:25 PM