How do you measure matter? You may count how many you have. Determine a substances mass and weight. Determine a substances volume. But how can you relate these three types of measurements to one another?
How do you measure matter? Knowing how to relate the count, mass and volume relate to a dozen apples allows you to convert between units. In chemistry we will use the mole as our common factor. The is the SI unit that measure the amount of a substance.
The Number of Particles in a Mole One way to measure the amount of a substance is to count the number of particles in the substance. What problem arises because atoms, molecules, and ions are extremely small? The number of individual particles in a sample of any substance would be
The Number of Particles in a Mole How can you solve this problem? Just as a dozen equals 12 apples, a mole represents a certain number of particles. 1 mole of a substance equals 6.02 x 10 23 particles of that substance. This number is called number = 6.02 x 10 23 Representative particle refers to the type present in a substance: Usually the for most elements
The Number of Particles in a Mole Substance Representative Particle Chemical Formula Representative particles in 1 mol Atomic nitrogen Atom N 6.02 x 10 23 Nitrogen gas Molecule N 2 6.02 x 10 23 Water Molecule H 2 O 6.02 x 10 23 Calcium ion Ion Ca 2+ 6.02 x 10 23 Calcium fluoride Formula unit CaF 2 6.02 x 10 23 Sucrose Molecule C 12 H 22 O 11 6.02 x 10 23
How to determine how many atoms are in a mole of a compound? First you must know how many atoms are in a representative particle of the compound. The number is determined from the chemical formula. A molecule of CO2 is composed of. A mole of CO2 contains Avogadro s number of CO2 molecules. Thus a mole of CO2 contains 3 times Avogadro s number of atoms. To figure out the number of atoms in a mole of a compound, you 1 st determine the number of atoms in a representative particle of that compound and then multiply that number by Avogadro s number.
Review 1 mole = 6.02 x 10 23 molecules Number of atoms = 1 molecule=6.02 x 10 23
Problems How many moles is 2.80 x 10 24 atoms of silicon? 1) Analyze Known: Number of atoms 1 mole of Si= 6.02 x 10 23 Conversion= atoms to moles Unknown: moles = moles of Si 2) Calculate 3) Evaluate Make sure unit cancel out correctly.
Problems How many molecules is 0.360 mol of water? 1) Analyze Known: Number of moles 1 mole of Water= 6.02 x 10 23 molecules of water Conversion= moles to molecules Unknown: molecules of water 2) Calculate 3) Evaluate Make sure unit cancel out correctly.
1) How many moles are equal to 2.41 x 10 24 formula units of sodium chloride (NaCl)?
2) How many moles are equal to 9.03 x 10 24 atoms of mercury (Hg)?
3) How many atoms are equal to 4.5 moles of copper (Cu)?
4) How many molecules are equal to 100.0 moles of carbon dioxide (CO 2 )?
5) How many atoms are in 1.00 moles of sucrose C 12 H 22 O 11?
6) How many atoms of C are in 2.0 moles of C 12 H 22 O 11?
7) How many atoms of H are in 2.0 moles of C 12 H 22 O 11?
8) How many atoms of O are in 3.65 moles of C 12 H 22 O 11?
The gram atomic masses of any 2 elements contains the same number of atoms, because the atomic masses of the elements are relative values. In other words. Suppose that the mass of an atom of element X is twice as great as the mass of an atom of element Y. Now suppose that you have 10 grams of element X and 10 grams of element Y. Would you expect both samples to contain the same number of atoms? Why or Why not?
Review Continue What would you have to do to get the same number of atoms in both samples? Although the mass of a single atom can be expressed in atomic mass units ( ) it isn t realistic to work with single atoms. Chemists work with large numbers of atoms (moles of atoms) for which the mass can be determined in grams. The (gam) of an element is the mass of an mole of atoms of that element expressed in grams.
The Mass of a Mole of an Element By checking the atomic masses in the periodic table you can find the gram atomic mass of the element. The gram atomic masses of any 2 elements must contain the same number of atoms. How many atoms are contained in the gram atomic mass of an element?
What is the mass of a mole of a compound? To answer you need to know: 1. (remember this tell you the number of atoms of each element in a representative particle of the compound) 2. Then you can calculate the mass of a molecule by adding the atomic masses of the atoms making up the molecule. To give you the. 3. If you substitute the unit grams for atomic mass units you will have the gram molecular mass.
Mass of a Mole of a compound The (gmm) of any molecular compound is the mass of 1 mole of that compound. The gmm equals the molecular mass expressed in grams.
Gram molecular mass may be calculated directly from gam. For each element in a compound find the number of grams of that element per mole of the compound. Then sum the masses of the elements in the compound.
Practice Find the gram molecular mass of each of the following compounds: C 2 H 6 N 2 O 5 C 3 H 7 OH
Practice What is the mass of 1.00 mol of each of the following substances? Carbon tetrabromide Silicon dioxide Chlorine
Practice Determine the mass of 1 mole of the following compounds 1. CO 2 2. SO 3 3. Br 2 4. H 2 5. N 2 6. NaOH 7. Al 2 8. Ba(NO 3 ) 2
You do not calculate the gmm of. The representative particle of an ionic compound is a, not a molecule. The mass of one mole of an ionic compound is the gram formula mass (gfm) gfm= the formula mass expressed in grams. Gfm is calculated the same way as the gmm by simply taking the sum of the atomic masses of the ions in the formula of the compound. Out of gam, gmm, and gfm gfm is the most inclusive. The term gfm can be used to refer to a mole of any substance.
Review for 7.1 1. Explain what a mole of a substance represents. 2. Demonstrate how to convert the number of atoms or molecules of a substance to moles. 3. Define atomic mass unit, and gram atomic mass, gram molecular mass and gram formula mass Determine the molar mass of As 2 (CO 3 ) 3
Molar Mass of a Substance gam, gmm, and gfm are used to represent a mole of a particular kind of substance. Gam contains a mole of atoms Gmm of a molecular compound contains a mole of molecules Gfm of an ionic compound contains a mole of formula units. We can use molar mass to refer to a mole of an element, a molecular compound, or an ionic compound because it is the mass in grams of one mole of the substance.
Review Name the units that determine the mass of a mole Which units should be used to describe the volume of a mole? Remember that unlike solids or liquids the molar volume of gases is more predictable and is affected by temperature and pressure.
Volume of a Mole of Gas How does temperature affect the volume of a gas? How does pressure affect the volume of a gas?
Volume of a Mole of gas When comparing the molar volumes of gases, it is necessary to have the gases at the same conditions of temperature and pressure. If the gasses are at 0 o C and 101.3 kpa ( ), they are a standard conditions of temperature and pressure ( ). At STP, 1 mole of any gas occupies. The of any gas at STP is 22.4 L/mole. Molar volume contains 6.02 x 10 23 particles of that gas
Volume of a Mole of Gas The density of a gas is usually measured in the
Review Density = Mass/ Volume What are densities units? If you had a mole of gas at STP, how could you calculate the density? What information do you need to calculate the molar mass of a gas?
The Mole Road Map
Check Prior Knowledge What is 73% of 150? What percent of 6.5 is 3.1? Look at figure 7.15 which compound is the better source of potassium?
Calculating the % Composition of a Compound The relative amounts of each element in a compound are expressed as the percent composition, or the percent by mass of each element in a compound. The percent by mass of an element in a compound is the number of grams of the element divided by the number of grams of the compound multiplied by 100%. % mass of element E = (grams of element E)/(grams of compound) x 100%
9.03 g Mg combine completely with 3.48 g N to form a compound. What is the percent composition of this compound? A: Known mass of Mg, Mass of N, mass of compound (9.03 + 3.48 = 12.52g) Unknown: % Mg, % N C: % Mg = mass of Mg / grams of compound x 100% = 72.2% % N = mass of N/grams of compound x 100% = 27.8%
Calculating % Composition Of a known compound % mass = (grams of element in 1 mole of compound) / molar mass of compound x 100%
Calculate the percent composition of these compounds: Ethane (C 2 H 6 ) Ethane % C= mass of C / grams of compound x 100% % H= mass of H / grams of compound x 100% Mass of C = 2 * 12= 24 Mass of H = 6 *1= 6 Mass of compound = 30 %C = 24/30 x 100% = 80% % H = 6/30 x 100%= 20%
% Composition Practice 1) Fe 2 O 3 2) HgO 3) Ag 2 O 4) Na 2 O
Using % as a Conversion Factor You can use the percent composition to calculate the number of grams of an element contained in a specific amount of a compound. For example if you know that the %C in the compound is 81.8% and you have a 82.0 g sample 82.0g of compound x 81.8grams C/ 100 g of compound= 67.1 g C
Calculating Empirical Formulas What is an Empirical Formula? Why do we need it? Suppose you are given a sample of a substance that contains hydrogen and oxygen. You are told that the ratio of moles of hydrogen to moles of oxygen is 1:1. What is the formula of the substance?
Calculating Empirical Formula % composition can be used to calculate the empirical formula of a compound. The empirical formula gives the lowest whole-number ratio f the atoms of the elements in a compound.
Calculate the empirical formula of 94.1% O, 5.9% H A: Known- % O, % H Unknown- empirical formula C: In 100.0 g of the compound, there are 94.1g of O and 5.9 g H. These values are used to convert to moles. 94.1 g O x 1 mol O / 16 g O = 5.88 mol O 5.9 g H x 1 mol H/ 1 g H = 5.9 mol H Next you divide each by the smaller mole number. 5.88/5.88= 1.00 5.9/5.88= 1.00 OH is the empirical formula
25.9% N and 74.1 % O what is the empirical formula? A: known % N and % O Unknown empirical formula C: 25.9 g N x 1 mol N/ 14 g N = 1.85 mol N 74.1 g O x 1 mol O / 16 g O = 4.63 mol O Then divide each by the smaller mole number 1.85/1.85 = 1 mol N 4.63/1.85= 2.5 mol O However we can not have NO2.5 So we multiply both by 2 to get N2O5
Calculating Molecular Formulas Look at table 7.2 on page 194 Both ethyne and benzene have the same empirical formula of CH. But each of these have different molar masses. The molecular formula is either the same as the empirical formula or a simple whole-number multiple of it.
Calculating Molecular Formula You can determine the molecular formula of a compound if you know the and its. From the empirical formula you calculate the empirical formula mass (efm). Or the molar mass of the empirical formula. Then the known molar mass is divided by the efm.
Calculate the molecular formula of the compound whose molar mass is 60.0g and empirical formula is CH 4 N. A: Known empirical formula; molar mass C: Unknown molecular formula Empirical formula efm molar mass/efm molecular formula CH4N 30 60/30=2 C 2 H 8 N 2
When you known the % composition and gram molecular mass, you must first use the % composition to calculate the empirical formula. Then you can calculate the empirical formula mass, and compare it to the gram molecular mass to determine the molecular formula.