Atomic Mass and The Mole

Topic: AMU’s & Atomic Mass Objectives: Day 1 of 3 To learn how we define 1 amu (atomic mass unit) To learn how we derive atomic mass from amu (atomic mass unit) To learn how atomic mass is calculated using the average natural abundance of isotopes Unit: The Mole and Atomic Mass

Quickwrite Answer one of the questions below 1-2 sentences: 1 light year (the distance light travels in a year) is equal to 9.5 trillion kilometers!!!!!!!!!! Why do you think we measure distances to nearby stars in light years and not kilometers????? Consider the reaction below, In order to make one molecule of CO 2 (g), each carbon atom needs how many molecules of oxygen gas???? C (s) + O 2 (g)  CO 2 (g)

Atomic Mass The balanced Chemical equation for the reaction of solid carbon and gaseous oxygen to form gaseous carbon dioxide is as follows: Now suppose you have a small pile of carbon, and you want to know how many oxygen molecules are required to convert all this carbon into carbon dioxide The balanced equation tells us that one oxygen molecule (O 2 ) is required for each carbon atom (C) C (s) + O 2 (g)  CO 2 (g) 1 Atom reacts with 1 Molecule to yield 1 Molecule

Atomic Mass To determine the number of oxygen molecules required, we must know how many carbon atoms are present in the pile of carbon But individual atoms are to small to see We can easily count things like jelly beans and pennies, but atoms are far too small to be counted C (s) + O 2 (g)  CO 2 (g) 1 Atom reacts with 1 Molecule to yield 1 Molecule

Atomic Mass The mass of one proton in a carbon atom is 1.66 x grams You can’t exactly put a carbon proton on a scale and weigh it To simplify things, and to avoid using very small complex numbers like 1.66 x grams, scientists have defined a unit of mass called the atomic mass unit or amu for short 1 AMU = 1.66 x grams or 1/12 the mass of a carbon atom

Atomic Mass The mass of one carbon proton is equal to 1 AMU or 1.66 x grams Neutrons and protons weigh the same and electrons virtually have no mass or weight So how many protons and neutrons does carbon have? That’s right, 12, so carbon has 12 atomic mass units Or, we say carbon has an average atomic mass of AMU

What is Atomic Mass Unit (amu)? A unit of mass equal to _____the mass of a carbon atom 1 amu = 1/12 the mass of a ______ atom or 1.66 x grams It is a way to _______ the mass of a proton or ________ Answer Bank average 1/12 simplify Carbon abundance neutron carbon 1/12 simplify neutron

Atomic Mass A hydrogen atom is composed of one proton or 1 amu Remember, neutrons and protons weigh the same and electrons virtually have no mass or weight A helium has 2 protons and 2 neutrons What is the average atomic mass for Helium? That’s right, 4!

What is the average atomic mass for some common elements? Element Average Atomic Mass Hydrogen1.008 Helium4.00 Carbon12.01 Nitrogen14.01 Oxygen16.00 Aluminum26.98 Sodium22.99

Atomic Mass The average atomic mass for carbon is amu Where does the 0.01 come from? 0.01 is the percent abundance in nature of the carbon isotopes For example, if we weighed 12 grams of carbon, 0.01 percent is the amount of Carbon 14 and carbon 13 isotopes that exist in nature

Atomic Mass Atomic Mass is the weighted average mass of the atoms in a naturally occurring element It is based on AMU’s and the natural abundance of an elements isotopes

What is atomic mass? The weighted _______ mass of the atoms in a naturally occurring element It is based on AMU’s and the natural _________ of an elements isotopes Answer Bank average 1/12 simplify Carbon abundance neutron average abundance

Atomic Mass Now that we know the average mass of a carbon atom, we can count carbon atoms by weighing samples of natural carbon For example, let’s say you want to count out 100 carbon atoms Because amu is the average atomic mass, Mass of 100 natural carbon atoms = 100 atoms amu 1 carbon atom = 1,201 amu

Atomic Mass Now let’s assume that when we weigh the pile of natural carbon mentioned earlier, the result is 3.00 x amu How many carbon atoms are present? We know that carbon has an average atomic mass of amu, so we can compute the carbon atoms using the following conversion factor 1 carbon atom = amu or 1 carbon atom amu 3.00 x amu 1 carbon atom amu = 2.50 x carbon atoms

Practice: 75 aluminum atoms amu 1 aluminum atom = 2,024 amu Calculate the mass or weight in amu of a sample of aluminum that contains 75 atoms

Practice: 2,024 amu amu 1 aluminum atom = 75 atoms How many aluminum atoms are present in a sample of aluminum that has a mass of 2,024 amu?

Practice: Zagot Lab 150 atoms 1 atom 2 grams = 300 grams 1 zagot is equal to 150 atoms or 1 zagot = 150 atoms. If one atom has a mass of 2 grams, what is the mass or weight of one zagot?

Practice: Zagot Lab 150 atoms 1 atom 0.2mL = 300 grams 1 zagot is equal to 1.5x10 2 atoms or 1 zagot = 150 atoms. If one atom has a volume of 0.2 mL, what is the mass or weight of one zagot? Instead of counting out 150 atoms and weighing them, We can simply continuously add atoms on a scale until The weight is 300 grams. When the mass reads 300g, You know you have 300 atoms!!!!

Summarize: Why do scientist’s use AMU’s and light years??? What is the mass, in AMU of one nitrogen atom??? 1 amu = 1/12 the mass of a _____ nucleus or _________ grams ______ _____ is the weighted average mass of the atoms in a naturally occurring element It is based on AMU’s and the natural ______ of elemental isotopes

Topic: The Mole Objectives: Day 2 of 3 To understand the quantity of a mole To understand the huge quantity of Avogadro’s number To understand the mole mass relationship Unit: The Mole and Atomic Mass

Quickwrite Answer one of the questions below 1-2 sentences: Your pencil uses graphite (pure carbon) to write with; how many atoms do you think are in 12 grams of graphite or carbon???????? How many items make up a dozen????? How many items make up a half dozen???? How many items are in two dozen??

The Mole In the previous section we used atomic mass units for mass, but these are extremely small units In a laboratory, the gram is the preferred and more convenient unit for mass Remember our sample of carbon? It weighs gram But how many atoms are in a sample of carbon that weighs grams?

The Mole Lets look at the periodic table What is the atomic mass of carbon? That’s right, A sample of carbon with a mass of has x10 23 atoms! The number of atoms present in grams of carbon is called the mole

Element Number of Atoms Present Average Atomic Mass in grams Hydrogen6.022 x Helium6.022 x Carbon6.022 x Nitrogen6.022 x Oxygen6.022 x Aluminum6.022 x Sodium6.022 x How many atoms does grams of hydrogen contain? x10 23 How many atoms does 4.00 grams of helium contain? How many atoms does grams of carbon contain? How many atoms does grams of nitrogen contain? x10 23 The point is, a sample Of any element that weighs A number of grams equal To the average atomic mass of that element contains x10 23 atoms!

What is a Mole? The _____ of a substance that contains __________ particles of a substance It is also the number equal to the amount of carbon atoms in _____ grams of carbon Answer Bank Atoms 24 Amount x (2) amount x

The Mole As it turns out, one mole of anything contains x10 23 units of that substance Just as a dozen eggs is 12 eggs, a mole of eggs is x10 23 eggs The mole is an incredibly large number to imagine - 602,000,000,000,000,000,000,000!!!!!!!!!!!!!!!!! We use scientific notation to simply this number We call this unbelievably large number Avogadro’s number

The Mole If I have a dozen eggs how many eggs do I have? If I have 2 dozen eggs, how many eggs do I have? If I have a mole of eggs, how many eggs do I have? If I have a 2 mole of eggs, how many eggs do I have? (2) x (6.022 x )

What is Avogadro’s Number? The amount of _____ in 1 mole of a substance which is ________ Just as two dozen is (2) x (12), or ____eggs, a mole of atoms is equal to (2) x (6.022 x ) atoms Answer Bank Atoms 24 Amount x (2) atoms x

The Mole Consider the following sample of hydrogen atoms below (symbolized by red dots) which contains one mole (6.022 x ) of hydrogen atoms Now consider another sample in which the number of hydrogen atoms is unknown Sample A = gramsSample B = grams

The Mole We know sample A has x10 23 hydrogen atoms But how many atoms are in sample B? We know the mass is grams Sample A = gramsSample B = grams

The Mole Let’s consider what we know We know that 1 mol of hydrogen atoms has a mass of grams Sample B has a mass of grams which is exactly half the mass of a mole of hydrogen atoms Sample A = gramsSample B = grams

The Mole Let’s consider what we know We know that 1 mol of hydrogen atoms has a mass of grams Sample B has a mass of grams which is exactly half the mass of a mole of hydrogen atoms Sample A = gramsSample B = grams

The Mole Let’s do the math! Sample A = gramsSample B = grams Our conversion factor is: 1mol hydrogen grams grams of hydrogen 1 mol hydrogen = mol of hydrogen in sample B grams of hydrogen We know we have grams of hydrogen

The Mole Now that we have moles, we can compute the number of atoms by using our conversion factor Sample A = grams Contains x10 23 Atoms Sample B = grams Contains ???? Atoms 1 mol of hydrogen x10 23 hydrogen atoms = 2.99 x10 23 hydrogen atoms in sample B mol of hydrogen We solved for moles In the last example Our conversion factor is: x mol

Practice: Your chicken laid 562 eggs. How many dozen eggs do you have? 12 eggs 1 dozen = 46 dozen 562 eggs

Practice: How many moles are in a 42 gram sample of aluminum? grams Al 1 mol aluminum = 1.56 mol of Aluminum 42 grams Al molesgrams

Practice: How many atoms are in 1.56 mol of aluminum? 1 mol Al x10 23 Al atoms = 9.39 x10 23 Aluminum Atoms 1.56 mol Al number of atomsmoles

Practice: Calculate the mass of 1.56 mol of Aluminum: 1 mol Al grams Al = 42 grams Aluminum 1.56 mol Al gramsmoles

Practice: How many atoms are in a 18 gram sample of carbon? 1 mol C6.022 x10 23 C atoms 18 grams C grams C 1 mol C = 9.07 x10 23 Carbon Atoms gramsnumber of atomsmoles

Summarize: If I have a _____of something I have_______ particles Avogadro number is ___________ A mole of carbon atoms weighs(mass) ______grams and contains ______ atoms 2 moles of carbons atoms weighs _____ grams Review: An ______ is atom with a different amount of neutron than protons

Topic: Molar Mass/Molecular Weight Objectives: Day 3 of 3 To learn how to calculate Molar Mass To learn how to convert between moles and grams To learn how to calculate % composition Unit: The Mole and Atomic Mass

Quickwrite Answer one of the questions below 1-2 sentences: Let’s say you want to find the weight of your dog, which is too big to stand on your bathroom scale; how could you find his weight??? Together, you and your dog weigh 100 kilograms, you know that you weigh 75 kilograms, what percent by weight does your dog weigh????

Molar Mass/Molecular Weight A chemical compound such as methane (CH 4 ) is a collection of atoms Methane contains 1 carbon atom and 4 hydrogen atoms But how do we calculate the mass of one mol of methane? In other words, what is the mass of x10 23 C methane molecules?

Molar Mass/Molecular Weight Because each methane molecule (CH 4 ) contains one carbon atom and 4 hydrogen atoms, 1 mol (CH 4 ) molecules consists of 1 mol carbon atoms and 4 mol of hydrogen atoms So the mass of 1 mol of (CH 4 ) is equal to: Mass of 1 mol of carbon (C) = 1 x 12.01g = g Mass of 4 mol of hydrogen (H) = 4 x = 4.032g _______ Mass of 1 mol of (CH 4 ) = g

1 C atom 4 hydrogen atoms 1 CH 4 molecule 10 CH 4 molecule 10 C atoms 40 hydrogen atoms 1 mol of CH 4 molecules ( x10 23 CH 4 molecules) 1 mol of C atoms ( x10 23 C atoms) 4 mol of H atoms 4 ( x10 23 H atoms)

What is molar mass or molecular weight? It is the mass in grams of one _____ of a substance or compound It is found by _______ the atomic ________that make up a compound or molecule Ex: methane Mass of 1 mol of carbon (C) = 1 x 12.01g = g Mass of 4 mol of hydrogen (H) = 4 x = 4.032g _______ Mass of 1 mol of (CH 4 ) = g Answer Bank Total Percent Element adding mole masses mole adding masses

Practice: Calculate the molar mass of sulfur dioxide: Mass of 1 mol of sulfur (S) = 1 x g = g Mass of 2 mol of oxygen (O) = 2 x g = g _______ Mass of 1 mol of (SO 2 ) = g

Practice: A sample of calcium carbonate (chalk) contains 4.86 mol. What is the mass in grams of this sample: 1 mol CaCO grams CaCO 3 = 486 grams CaCO mol CaCO 3 First calculate the molar mass of CaCO 3 : Mass of 1 mol of Calcium (Ca)=1 x g = g Mass of 1 mol of Carbon (C) =1x g = g Mass of 3 mol of Oxygen (O) =3 x g = g _______ Mass of 1 mol of (CaCO 3 ): = g

20.56 gms H 2 O gms H 2 O Practice: A sample of water weighs grams. How many water molecules are in a sample of water that weighs grams? =6.87 x molecules 1 mol of H 2 O x10 23 H 2 O molecules 1 mol H 2 O

Percent Composition Chemists often need to know a chemical’s composition in terms of the masses of it’s elements We can obtain this information from the formula of the compound by comparing the mass of each element present in 1 mol of the compound to the total mass of 1 mol of the compound

Percent Composition The mass fraction for each element is calculated as follows: Mass for a given = element Mass of the element present in 1 mol of compound Mass of 1 mol of compound

For example, lets consider ethanol (C 2 H 6 O): We calculate the mass of each element present and the molar mass of ethanol as follows: 1 mol C grams C = g C x100 = % C g C 2 H 6 O Mass of C = 2 mol C 1 mol H grams H = g H x100 = 13.13% H g C 2 H 6 O Mass of H = 6 mol H 1 mol O grams O = g O x 100 = 34.73% O g C 2 H 6 O Mass of O = 1 mol O Mass of 1 mol of C 2 H 6 O ethanol = g = molar mass

The mass percent of carbon in ethanol can be computed by comparing the mass of carbon in 1 mol of ethanol with the total mass of 1 mol of ethanol and multiplying the result by 100% Mass % of C = Mass of C in 1 mol C 2 H 6 O Mass of 1 mol C 2 H 6 O g x 100% = 52.14% = g Mass % of H = Mass of H in 1 mol C 2 H 6 O Mass of 1 mol C 2 H 6 O g x 100% = 13.13% = g Mass % of O = Mass of O in 1 mol C 2 H 6 O Mass of 1 mol C 2 H 6 O g x 100% = 34.73% = g

Percent Composition To review, by weight, ethanol contains 52.14% carbon, 13.13% hydrogen, and 34.73% Oxygen Or, 52.14% % % = 100%

What is Mass Percent? The ________by mass of an ________ in a compound or molecule Mass % is calculated by comparing the mass of a single element to the _____ mass (molar mass) of the compound Answer Bank Total Percent Element adding mole masses percent element total

Practice: Find the weight percent of oxygen in water H 2 O:

Practice: First calculate the molar mass of H 2 O: A sample of water weighs grams. How many moles of water are in grams of water? grams H 2 O 1 mol of H 2 O = 1.14 mol H 2 O grams H 2 O Mass of 2 mol of hydrogen (H)= 2 x g = g Mass of 1 mol of oxygen (O) = 1 x g = g _______ Mass of 1 mol of (H 2 O): = g

Summarize: _____ _____is the mass in grams of one mole of a substance To calculate Molar mass, you would add up the ____ ______for each element that make up a molecule The percent by mass of an element in a compound is called it’s ______ ______ Calculate the percentage of nitrogen in nitrogen dioxide NO 2