Chemical Quantities

Chemical Quantities Unit 6 Chapter 10, Section 10.1 The Mole: A Measurement of Matter

Objectives • When you complete this presentation, you will be able to: • describe methods of measuring the amountof something. • define Avogadro’s number, N0, as it relates to a moleof a substance. • distinguish between the atomic mass of an element and its molar mass. • describe how the mass of a moleof compound is calculated.

Measuring Matter • We live in a world of quantities, of measurement. • What was your grade on the 1st Semester Exam? • How many friends do you have on Facebook? • How big is a “tall” cup of coffee at Starbucks? • Chemists have similar kinds of quantitative questions. • How many kg of iron can we get from 100 kg of ore? • How many grams of N2(g) and H2(g) must be combined to give us 200 g of NH3(g)? • What volume of CO2(g) is produced when we burn one gallon of gasoline?

Measuring Matter • To solve chemists’ problems we need to measure the amountof matter we have. • What do we mean by the “amount” of matter? • For chemists, this is not a trivial question.

Measuring Matter • When we measure matter, do we mean … • the numberof atoms or molecules? • How many oxygen molecules combine with each methane molecule when we burn natural gas? • the massof the elements or compounds? • How many grams of oxygen (as O2 gas) combines with ten grams of methane (as CH4 gas) when we burn natural gas? • the volumesof the matter? • How many liters of oxygen (as O2 gas) combines with one liter of methane (as CH4 gas) when we burn natural gas?

Measuring Matter • Some units for measuring indicate a specific number of items. • A pairalways means two. • A dozenalways means twelve.

Measuring Matter • For example, apples are measured in three different ways. • At a fruit stand, they may be sold by the count (3 for $2.40). • In a supermarket, you buy apples by the weight ($1.29/lb) or mass ($2.79/kg). • At an orchard, you buy apples by the volume ($12.00/bushel).

Measuring Matter • For example, apples are measured in three different ways. • At a fruit stand, they may be sold by the count (3 for $2.40). • In a supermarket, you buy apples by the weight ($1.29/lb) or mass ($2.79/kg). • At an orchard, you buy apples by the volume ($12.00/bushel). • Each of these may be equated to a dozen apples.

Measuring Matter • For example, apples are measured in three different ways. • At a fruit stand, they may be sold by the count (3 for $2.40). • By count: 1 dozen apples = 12 apples

Measuring Matter • For example, apples are measured in three different ways. • At a fruit stand, they may be sold by the count (3 for $2.40). • By count: 1 dozen apples = 12 apples • In a supermarket, you buy apples by the weight ($1.29/lb). • By mass: 1dozen apples = 2.0 kg apples

Measuring Matter • For example, apples are measured in three different ways. • At a fruit stand, they may be sold by the count (3 for $2.40). • By count: 1 dozen apples = 12 apples • In a supermarket, you buy apples by the weight ($1.29/lb). • By mass: 1dozen apples = 2.0 kg apples • At an orchard, you buy apples by the volume ($12.00/bushel). • By volume: 1dozen apples = 0.20 bushel apples

Measuring Matter • Knowing how the count, mass, and volume of apples relates to a dozen apples allows us to convert between these units. • For example, we could calculate the mass of … • a bushel of apples or • 90 average sized apples • … by using the following conversion factors 1 dozen apples 2.0 kg apples 1 dozen apples 12 apples 1 dozen apples 0.20 bushel apples

Sample Problem 10.1 What is the mass of 90 average-sized apples if 1 dozen apples has a mass of 2.0 kg? Known: # of apples = 90 apples 12 apples = 1 dozen apples 1 dozen apples = 2.0 kg apples Unknown: mass of 90 apples = ? kg Process: # of apples → dozens of apples → mass of apples 1 dozen apples 2.0 kg apples 12 apples 1 dozen apples mass of 90 apples = 90 apples × ×

Sample Problem 10.1 What is the mass of 90 average-sized apples if 1 dozen apples has a mass of 2.0 kg? Known: # of apples = 90 apples 12 apples = 1 dozen apples 1 dozen apples = 2.0 kg apples Unknown: mass of 90 apples = ? kg Process: # of apples → dozens of apples → mass of apples 90 × 1 × 2.0 mass of 90 apples = kg apples = 15 kg apples 12 × 1

What is a Mole? • Counting things as big as apples is a reasonable way to measure the amount of something. • Would counting the grains of sand on a beach be a reasonable way to measure the amount of sand? • Would counting individual atoms in a kilogram of a compound be a reasonable way to measure the amount of matter?

What is a Mole? • Counting individual small things (such as atoms or molecules) can be difficult. • It is much easier if the things are grouped into convenient units. • Counting individual eggs could be tedious. • Unless they are grouped by dozens.

What is a Mole? • Chemists use a similar kind of unit to measure amounts of matter (atoms and molecules). • The unit for the amount of matter is a mole, abbreviated as mol. • 1 mole of any thing is defined as 6.02 × 1024 pieces of that thing. • That is 6,020,000,000,000,000,000,000,000 pieces. • This number is called Avogadro’s number, N0.

What is a Mole? • Just to be sure you understand this … • 1 mol of hydrogen atoms is 6.02 × 1024atoms • 1 mol of hydrogen molecules is 6.02 × 1024molecules • 1 mol of glucose molecules is 6.02 × 1024molecules • 1 mol of pencils is 6.02 × 1024pencils • 1 mol of students is 6.02 × 1024students • 1 mol of grains of sand is 6.02 × 1024grains • Thereareonly 7.005 × 1020grains of sand on earth. • 1 mol of stars is 6.02 × 1024stars • Thereareonly 9 × 1021stars in ouruniverse.

What is a Mole? • Let’s look at a couple of compounds a little more closely. • 1 mole of hydrogen moleculesis 6.02 × 1023 molecules. • Each hydrogen molecule, H2, is composed of two atoms of hydrogen. • That means there are 2 × 6.02 × 1023 = 12.04 × 1023 hydrogen atoms in 1 mole of hydrogen molecules.

What is a Mole? • Let’s look at a couple of compounds a little more closely. • 1 mole of glucose moleculesis 6.02 × 1023 molecules. • Each glucose molecule, C6H12O6, is composed of 6 atoms of carbon, 12 atoms of hydrogen, and 6 atoms of oxygen • That means there are 6 × 6.02 × 1023 = 36.12 × 1023 carbon atoms in 1 mole of glucose molecules. • That means there are 12 × 6.02 × 1023 = 72.24 × 1023hydrogen atoms in 1 mole of glucose molecules. • That means there are 6 × 6.02 × 1023 = 36.12 × 1023oxygen atoms in 1 mole of glucose molecules.

What is a Mole? • Let’s practice converting fromnumber of particlestonumber of mols. • The conversion looks like this: • Let’s try Sample Problem 10.2 (page 291). 1 mole # of moles = # of representative particles × 6.02 × 1023 representative particles

Sample Problem 10.2 • Magnesium is a light metal used in the manufacture of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 × 1023 atoms of magnesium? Known: # of atoms = 1.25 × 1023 atoms 1 mol Mg = 6.02 × 1023 atoms Mg Unknown: mols = ? mol Mg 1 mole 6.02 × 1023 representative particles Process: atoms → mols # of moles = # of representative particles ×

Sample Problem 10.2 • Magnesium is a light metal used in the manufacture of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 × 1023 atoms of magnesium? Known: # of atoms = 1.25 × 1023 atoms 1 mol Mg = 6.02 × 1023 atoms Mg Unknown: mols = ? mol Mg 1 mole Mg 6.02 × 1023 atoms Mg Process: atoms → mols # of moles = 1.25 × 1023atoms Mg ×

Sample Problem 10.2 • Magnesium is a light metal used in the manufacture of aircraft, automobile wheels, tools, and garden furniture. How many moles of magnesium is 1.25 × 1023 atoms of magnesium? Known: # of atoms = 1.25 × 1023 atoms 1 mol Mg = 6.02 × 1023 atoms Mg Unknown: mols = ? mol Mg 1.25 × 1023 × 1 6.02 × 1023 Process: atoms → mols # of moles = moles Mg = 0.208 moles Mg

What is a Mole? • Let’s practice converting fromnumber of molsto number of particles. • The conversion looks like this: • Let’s try Sample Problem 10.3 (page 292). 6.02 × 1023 representative particles # of particles = # of mols × 1 mol

Sample Problem 10.3 • Propane gas is used for cooking and heating. How many atoms are in 2.12 mol of propane (C3H8)? Known: # of mols = 2.12 mols 1 mol C3H8 = 6.02 × 1023 molecules C3H8 1 molecule C3H8 = 11 atoms (3 C + 8 H) Unknowns: # atoms = ? atoms # of atoms 6.02 × 1023molecules 1 molecule 1 mol Process: mols → molecules → atoms # of atoms = # of mols × ×

Sample Problem 10.3 • Propane gas is used for cooking and heating. How many atoms are in 2.12 mol of propane (C3H8)? Known: # of mols = 2.12 mols 1 mol C3H8 = 6.02 × 1023 molecules C3H8 1 molecule C3H8 = 11 atoms (3 C + 8 H) Unknowns: # atoms = ? atoms 11 atoms 6.02 × 1023molecules 1 molecule 1 mol Process: mols → molecules → atoms # of atoms = 2.12 mols × ×

Sample Problem 10.3 • Propane gas is used for cooking and heating. How many atoms are in 2.12 mol of propane (C3H8)? Known: # of mols = 2.12 mols 1 mol C3H8 = 6.02 × 1023 molecules C3H8 1 molecule C3H8 = 11 atoms (3 C + 8 H) Unknowns: # atoms = ? atoms 2.12 × 6.02 × 1023 × 11 1 × 1 Process: mols → molecules → atoms # of atoms = atoms = 1.40 × 1025 atoms

The Mass of a Mole • What is so special about Avogadro’s Number? • Why do we use “6.02 × 1023” any way?

The Mass of a Mole • If we measure out 6.02 × 1023 atoms of an element, the mass is equal to the atomic mass of that element. • For 6.02 × 1023 atoms of H, mass = 1.01 g • For 6.02 × 1023 atoms of C, mass = 12.01 g • For 6.02 × 1023 atoms of O, mass = 16.00 g • If we measure out 6.02 × 1023molecules of a compound, the mass is equal to the molar mass of that compound. • For 6.02 × 1023molecules of CO2, mass = 44.01 g • For 6.02 × 1023molecules of C6H12O6, mass = 180.16 g

The Mass of a Mole • The atomic mass of an element is the mass of 1 mol of that element. • The molar mass of a compound is the mass of 1 mol of that compound.

The Mass of a Mole • To calculate the molar mass of a compound • find the number of grams of each element in one mole of the compound • add the masses of the elements in the compound • For example: • for glucose, C6H12O6: • mass of C = 6 × 12.01 g = 72.06 g • mass of H = 12 × 1.00794 g = 12.09528 g • mass of O = 6 × 16.00 g = 96.00 g • mass of C6H12O6 = (72.06 + 12.10 + 96.00) g = 180.16 g

The Mass of a Mole • To calculate the molar mass of a compound • find the number of grams of each element in one mole of the compound • add the masses of the elements in the compound • For example: • for water, H2O: • mass of H = 2 × 1.00794 g = 2.01588 g • mass of O = 1 × 16.00 g = 16.00 g • mass of H2O = (12.02 + 16.00) g = 18.02 g

The Mass of a Mole • To calculate the molar mass of a compound • find the number of grams of each element in one mole of the compound • add the masses of the elements in the compound • For example: • for methane, CH4: • mass of C = 1 × 12.01 g = 12.01 g • mass of H = 4 × 1.00794 g = 4.03177 g • mass of CH4 = (12.01 + 4.03) g = 16.04 g

The Mass of a Mole • Try some on your own: find the molar mass of … NH3 CO2 NaCl H2SO4 KOH Fe2O3 17.02 g/mol 44.01 g/mol 58.44 g/mol 98.08 g/mol 56.11 g/mol 159.69 g/mol

Summary • When chemists measure matter, they measure … • the numbers of atoms or molecules • the mass of the elements or compounds • the volumes of the matter • The unit for the amount of matter is a mole. • 1 mole of any thing is defined as 6.02 × 1023 pieces of that thing. • This number is called Avogadro’s Number, N0.

Summary • To convert from numbers of particles to number of mols, we use the conversion… • To convert form number of mols to number of particles, we use the conversion … # of moles = # of representative particles × 1 mole 6.02 × 1023 representative particles 6.02 × 1023 representative particles 1 mol # of particles = # of mols ×

Summary • The atomic mass of an element is the mass of 1 mol of that element. • The molar mass of a compound is the mass of 1 mol of that compound. • To calculate the molar mass of a compound find the number of grams of each element in one mole of the compound and add the masses of the elements in the compound.

Chemical Quantities