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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: 3
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! Now let s put in the relative weights of the reactants: Ca + S CaS What is the mass ratio in which sulfur reacts with calcium according to the above equation? 4
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. W 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? Again, this means that 40.0 grams of calcium contain the same number of particles as 32.0 grams of sulfur! 5
MOLE Key Idea 1 mole of anything contains Avogadro s number or 6.02 X 10 23 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 What about Na? so, 12.0 g of C = 1 mol of C = 6.02 X 10 23 atoms of C What about Al? 6
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? 7
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 10 25 atoms? 8
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 (metal nonmetal) whereas the term molecules are used when dealing with molecular compounds (nonmetal nonmetal). The mass of one mole of a compound is called the molar mass or gram formula mass (GFM) Example: sodium hydroxide sulfur dioxide z 9
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 10 24 molecules of nitrogen triiodide. 10
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: NaHCO 3 Na H C O O O 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 (CO 2), for example, contains one mole of carbon atoms (C) and two moles of oxygen atoms (O). O = C = O contains 1 mole C atoms 2 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: 11
Let s consider the diatomic molecules (BrINClHOF). Calculate the number of moles of chlorine atoms in one moles of chlorine gas. Cl Cl Calculate the number of moles of chlorine atoms in two moles of chlorine gas. Cl Cl Cl Cl 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. 12
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? 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) 13
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 (CH 4) 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. 14
Summary Diagram MASS MOLE GAS VOLUME AT STP NUMBER OF PARTICLES 15
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 16
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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. 1. 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, Na 2S 2O 3 (aka photograph fixer). 18
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. 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. 19
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 20
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. 21
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? 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 a 22
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 emp 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. 23
6. A compound containing only phosphorous and oxygen is 43.7% P by mass; the molar mass is 142.0 g/mol. W hat are the empirical and molecular formulas of the compound? 24