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.
13 Avogadro’s number is 6.022 x 1023. Avogadro’s number is much larger… So how did chemists come up with such a huge number?
14 It began with Amedeo Avogadro about a 150 years ago. He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights.
15 Avogadro’s law10.0 liters of CO2 weighs 19.6 grams10.0 liters of N2 weighs 12.5 grams10.0 liters of Xe weighs 58.6 grams19.6 g12.5 g=44.0 g28.0 g=1.571.57Ratio of the masses of equal volumes of CO2 and N2Ratio of the molar masses of CO2 and N2
16 Avogadro’s law10.0 liters of CO2 weighs 19.6 grams10.0 liters of N2 weighs 12.5 grams10.0 liters of Xe weighs 58.6 grams19.6 g58.6 g=0.33544.0 g131.3 g=0.335Ratio of the masses of equal volumes of CO2 and XeRatio of the molar masses of CO2 and Xe
17 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.
18 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.
19 After Avogadro’s death, Stanislao Cannizzaro published an explanation of Avogadro’s law. Equal volumes of gases at the same temperature and pressure have equal numbers of particles.
20 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.
21 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.
22 Atomic MassWe can relate Avogadro’s number to the amount of an element equal to its atomic mass measured in grams.
23 Atomic MassThis 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.
24 Atomic MassThe “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
25 Atomic MassThis way, hydrogen,the lightest element (H) would have a mass very close to 1.The average atomic mass of hydrogen is amu.
26 Atomic MassInstead 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?
27 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 g1 C atomC atomxg C1.993 x g C= x 1023 C atoms
28 Atomic MassThe 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.
30 So, what is a mole?It is a word that describes a very large number of atoms.6.022 x 1023 atomsIt comes from the Latin word moles which means “quantity”6.022 x 1023 is also called Avogadro’s Number.
31 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.
32 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.
33 Suppose … Like this: 10 marbles = 86.45 grams Avg. marble = gramsAll the marbles = gThis is a conversion factor1 marbleg x =286 marbles8.645 g
34 We can count a large number of particles by weighing them.
35 We can count atoms if we know the mass of an Avogadro's number of atoms.
36 An Avogadro's number of atoms has a mass equal to the molar mass. 6.022 x 1023 atoms of sodiumhave a mass of 23.0 g6.022 x 1023 atoms of ironhave a mass of 55.8 g6.022 x 1023 atoms of aluminumhave a mass of 27.0 g
37 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; and1 mole is 6.02 x 1023 atoms.6.02 x 1023 atoms K50.0 g Kx =39.1 g K7.70 x 1023 atoms K
38 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.
39 FYI: We now use“molar mass” instead of..gram atomic weight,gram molecular weight,gram formula weight.
40 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/moliron (Fe)55.8 g/molchlorine (Cl)35.5 g/molphosphorous (P)31.0 g/mol
41 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)
42 How many moles of each kind of element are in one mole of … CaCl21 mole Ca and 2 moles ClC12H22O1112 moles C, 22 moles H, 11 moles OFe3(PO4)23 moles Fe, 2 moles P, 8 moles O
43 Calculating molar masses of compounds … Sum of themolar masses of the elementsMolar mass of the compound=The molar mass of an element its atomic mass
44 Calculate the molar mass of water: Molar mass of H2O =(2 x 1.0) + (1 x 16.0) =18.0 g/mol2 hydrogen atoms1 oxygen atom
45 General Equation for Molar Mass S (atomic masses)For each element, multiply it’s atomic mass by its subscript, then add them all together.
46 What is the molar mass of calcium chlorate? Start with the formula:Ca(ClO3)21 mol Ca, 2 mol Cl, 6 mol O(1 x 40.1) + (2 x 35.5) + (6 x 16.0)= g/mol
47 What are the molar masses of each of the following? 1. HCl2. Fe2O33. H2SO44. Ca3(PO4)25. (NH4)2CO336.5 g/mol159.6 g/mol98.1 g/mol310.3 g/mol96.0 g/mol
48 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 mass1 mol = x 1023 particles1 mol = 22.4 L of any gas at STP
49 Convert the following: grams of iron metal to moles.0.314 moles Femoles of CaCl2 to grams.4.02 g CaCl2x 1024 molecules of SO3 to moles.9.05 moles SO3
51 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?
52 Standard temperature and pressure STP stands forStandard temperature and pressure
53 Standard temperature Standard pressure STP … 0 C or 273 K …the freezing point of water0 C or KStandard pressure… atmospheric pressure at sea level1.00 atmosphere, kPa,760. mm Hg, 760. Torror lbs/in2
54 1 mole of any gas at STP has a volume of 22.4 L Consider a box with a volume of 22.4LO21 atm C1.00 mol22.4 LIf the box contains 1.00 mole of oxygen gas, at a temperature of 0 C, the pressure will be atm.
55 More molar conversions … 1. Convert 3.00 liters of N2 gas at STP to moles.0.134 mol N22. Convert moles of HCl(g) to liters at STP.10.2 L HCl3. How many molecules are in mL of NH3 at STP?6.72 x 1021 molecules NH3Click for solutions