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THE MOLE

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What is the Mole? 6.02 x 1023 OR

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What is a dozen? 1 dozen = 12

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Why don’t we just say 12? It is often easier to group objects when counting them 2 dozen = dozen = 36 …and it doesn’t matter what the objects are… a dozen means 12 whether it is a dozen eggs, a dozen roses, or a dozen ugly hats

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So what is a mole? A mole is a counting unit. It tells us how many objects there are. A pair and a dozen are also counting units. Pair means 2 objects Dozen 12 objects Mole 6.02x1023 objects

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**So what is a mole? It is just a term used to represent a number**

2 = pair = 1 dozen x 1023 = 1 mole …and we call 6.02 x Avagadro’s number

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Avogadro’s number = 6.02 x = Avogadro - He didn’t actually identify the number – but it was named after him to honor his many contributions to chemistry

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**So why is it such a big number?**

What counting unit would you use for these objects? PAIR

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**So why is it such a big number?**

What counting unit would you use for these objects? DOZEN

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**So why is it such a big number?**

What counting unit would you use for these objects? MOLE Since atoms and molecules are very small, the quantity used to measure them needs to be a very large number

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**So why is it such a big number?**

Since a mole is such a large number, it is useful only for counting very small objects like atoms and molecules. A mole of donuts is too many to eat. Like a pair (2) or a dozen (12), the quantity of a mole (6.02 x 1023) never changes, but unlike a pair or a dozen, its value is very, very large

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**Avogadro’s Number as Conversion Factor**

6.02 x 1023 particles 1 mole or 1 mole Note that a particle could be an atom OR a molecule!

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**Practice Number of atoms in 0.500 mole of Al**

a) Al atoms b) x 1023 Al atoms c) x 1023 Al atoms a) Al atoms b) x 1023 Al atoms c) x 1023 Al atoms 0.500 mole Al | *1023 atoms = |1 mole 2. Number of moles of S in 1.8 x 1024 S atoms a) mole S atoms b) mole S atoms c) x 1048 mole S atoms a) mole S atoms b) mole S atoms c) x 1048 mole S atoms 1.8 *1024 atoms S | 1 mole = | *1023 atoms

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**REPRESENTATIVE PARTICLES & MOLES**

ATOMIC NITROGEN ATOM N 6.02x1023 NITROGEN GAS MOLEC. N2 WATER H20 CALCIUM ION ION Ca2+ CALCIUM FLUORIDE FORMULA UNIT CaF2 CHEMICAL REP. PARTICLE SUBTANCE REPRESENTATIVE PARTICLE FORMULA IN 1 MOL

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**What if I asked you how many atoms are in a mole of a compound?**

you must know how many atoms are in a representative particle or cluster of the compound. To do this you must know the chem formula For example, each molecule of CO2 is composed of 1 C + 2 O’s = 3 atoms 1 mole of carbon dioxide molecules contains avogadro’s number of carbon dioxide molecules. Thus a mole of CO2 contains three times avogadro’s number of atoms

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**How many atoms of carbon are in 2.12 mols of propane molecules (C3H8)?**

To find the # of atoms in a mol of a compound, You 1st determine the # of atoms in a representative particle of that compound And then multiply that # of atoms by avogadro’s # How many atoms of carbon are in 2.12 mols of propane molecules (C3H8)? Useful Info: 1 mol C3H8 = 6.02x1023 molecules C3H8 1molecule C3H8 = 3 atoms of C

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**(1molecC3H8)(X)=(1.276x1024molec•molsC3H8)**

1st we need to see how many molecules of propane we have if we have 2.12 moles. 1 mole C3H8 2.12 moles C3H8 = 6.02x1023molec C3H8 X molec C3H8 (1molecC3H8)(X)=(1.276x1024molec•molsC3H8) (1 molec C3H8) (1 molec C3H8) X = 1.276x1024 molecules of C3H8

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**(1molec C3H8)(X)=(3.83x1024molec • atoms C)**

2nd we need to see how many atoms of C if we have 1.276x1024 molecs of C3H8. 1 molecule C3H8 1.276x1024 molec C3H8 = 3 atoms of C X atoms C (1molec C3H8)(X)=(3.83x1024molec • atoms C) (1 molec C3H8) (1 molec C3H8) X = 3.83x1024 atoms of Carbon

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**So the mole can be used to measure any kind of particle – atoms, ions, molecules, formula units**

It is possible to have a mole of iron atoms, a mole of water molecules and a mole of sodium chloride – all contain 6.02 x 1023 particles But do 1 mol of iron, 1 mol of water and 1 mol of sodium chloride all have the same mass? NO!!

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**Do a dozen donuts, a dozen books and a dozen bricks weigh the same?**

NO, so neither do a mole of different atoms, ions or molecules

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**Each sample contains 1 mol (6.02 x 1023 atoms)**

12.0g carbon 32.0g sulfur 65.38g zinc Which element do you think has the heaviest atoms?

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**So now that we know what a mole of atoms looks like…where did the number come from?**

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**CARBON!! 6.02 x 1023 atoms Guess how many there were?**

Scientists took 12g of pure carbon-12 (composed of 6 protons + 6 neutrons; mass number = 12) and counted how many carbon atoms were in the sample Guess how many there were? 6.02 x 1023 atoms Why use 12 grams? They wanted the mass of one mole to be the same as the mass number

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6.02 x1023 atoms of Carbon This pile of carbon-12 weighs 12.0 grams and contains 6.02 x 1023 carbon atoms This is one mole of carbon

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**This pile of sulfur contains 6.02x1023 atoms of sulfur.**

This is one mole of sulfur. Review: A mole is a simple way of saying we have 6.02x1023 objects.

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**Atomic molar mass of an element = is the average mass (g) of one mole of atoms of that element**

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Back to carbon…. 12.01 g/mol atomic molar mass of an element = mass (g) of one mole of atoms of that element Here is one mole of carbon which weighs 12.0 g The atomic molar mass of carbon on the periodic table is…. Which means there are g for every mol of carbon

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**Here is 65. 38 grams of the element zinc**

Here is grams of the element zinc. How many moles of zinc do we have? 1 mole . atomic molar mass of an element = mass (g) of one mole of atoms of that element

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**What is the mass, in grams, of this sample of sulfur?**

This pile of sulfur contains 6.02x1023 atoms of sulfur (or 1 mole of sulfur) What is the mass, in grams, of this sample of sulfur? 32.06 g atomic molar mass of an element = mass (g) of one mole of atoms of that element

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**Here is 0.50 moles of copper. How many grams of copper do we have?**

0.50 moles x (63.55 g/mole) = 31.8g 0.50 moles | g= 31.8g | 1 mole)

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**This pile of powdered iron contains 3.01x1023 atoms. What is its mass?**

27.9 g 3.01x1023 atoms| 1 mole Fe | g = 27.9g Fe | *1023 atoms Fe | 1mole Fe 3.01x1023 atoms| 1 mole = moles | 6.02 *1023 atoms moles | g Fe = 27.9 g Fe | 1 mole

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**Molar mass = the mass of one mole of a substance**

So now we’re not talking about individual elements but molecules and compounds I.e. What is the molar mass of water? The formula for water is: H2O , so one molecule contains hydrogen atoms and 1 oxygen atom

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**Molar mass = the mass of one mole of a substance**

Atomic molar mass of H = 1.01g/mol x 2 = 2.02 g/mol Atomic molar mass of O = 16.00g/mol x 1 = 16.00g/mol Molar mass of water H2O is g/mol

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**Other Names Related to Molar Mass**

Molecular Mass/Molecular Weight: If you have a single molecule, mass is measured in amu’s instead of grams. But, the molecular mass/weight is the same numerical value as 1 mole of molecules. Only the units are different. (This is the beauty of Avogadro’s Number!) Formula Mass/Formula Weight: Same goes for compounds. But again, the numerical value is the same. Only the units are different. THE POINT: You may hear all of these terms which mean the SAME NUMBER… just different units

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**Molar mass Now you try it… What is the molar mass of methane CH4(g) ?**

C = g/mol x 1 = g/mol H = 1.01g/mol x = 4.04 g/mol Molar mass of methane = g/mol

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**Molar mass Now you try it… What is the molar mass of methanol CH3OH?**

C = g/mol x 1 = g/mol H = 1.01g/mol x 4 = g/mol O = g/mol x = g/mol Molar mass of methanol = g/mol

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**Find the molar mass of SnBr**

Practice Find the molar mass of SnBr = g/mole 1 mole of Br atoms 1 mole of Sn atoms 1 mole of SnBr formula units = g/mole = g/mole

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**Converting between mass, molar mass and moles**

m = quantity of matter (mass) in grams n = quantity of matter in moles M = molar mass m = n x M So if you wanted to know the mass of 2 mol of carbon m = (2 mol) x (12.01g/mol) or 2 mol C | g C | 1 mole C = g C

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**Molar Mass of Molecules and Compounds**

Mass in grams of 1 mole equal numerically to the sum of the atomic masses 1 mole of CaCl2 = g/mol 1 mole Ca x 40.1 g/mol + 2 moles Cl x 35.5 g/mol = g/mol CaCl2 1 mole of N2O4 = 92.0 g/mol

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**Practice Molar Mass of K2O = ? Grams/mole**

B. Molar Mass of antacid Al(OH)3 = ? Grams/mole Al= 1*26.98 =26.98 O =3 *16. = 48.0 H= 3*1.008 = g/mol

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Practice Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. Find its molar mass.

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**Converting Moles and Grams**

Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al? 3.00 moles Al ? g Al

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**1. Molar mass of Al 1 mole Al = 27.0 g Al**

2. Conversion factors for Al 27.0g Al or mol Al 1 mol Al g Al 3. Setup 3.00 moles Al | g Al 1 mole Al Answer = 3.00* 27 g Al = 81.0 g Al

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Practice The artificial sweetener aspartame (Nutra-Sweet) formula C14H18N2O5 is used to sweeten diet foods, coffee and soft drinks. How many moles of aspartame are present in 225 g of aspartame?

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**Atoms/Molecules and Grams**

Since 6.02 X 1023 particles = 1 mole AND 1 mole = molar mass (grams) You can convert atoms/molecules to moles and then moles to grams! (Two step process) You can’t go directly from atoms to grams!!!! You MUST go thru MOLES. That’s like asking 2 dozen cookies weigh how many ounces if 1 cookie weighs 4 oz? You have to convert to dozen first!

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**Everything must go through Moles!!!**

Calculations molar mass Avogadro’s number Grams Moles particles Everything must go through Moles!!!

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**Atoms/Molecules and Grams**

How many atoms of Cu are present in 35.4 g of Cu? 35.4 g Cu mol Cu X 1023 atoms Cu g Cu mol Cu = 3.4 X 1023 atoms Cu

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Practice How many atoms of K are present in 78.4 g of K?

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Practice What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)?

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**Practice How many atoms of O are present in 78.1 g of oxygen?**

78.1 g O2 1 mol O X 1023 molecules O2 2 atoms O g O mol O molecule O2

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**X = 12.2 L of CO 1 mole CO .500 mol CO = X L CO**

*Remember* 1 mol CO = 22.4 L CO 1 mole CO .500 mol CO = 22.4 L CO X L CO (1mol CO)(X L CO)= (.500 mol CO)(22.4 L CO (1mol CO) (1mol CO) X = 12.2 L of CO

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atomic 1 mole mass Mass 22.4 L Representative Particles Volume of Gas at STP 6.02x10 23 Mole

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Practice If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are in this piece of metal? You are given mass and asked for number of particles Set it up as a factor label problem

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atomic 1 mole mass Mass 22.4 L Representative Particles Volume of Gas at STP 6.02x10 23 Mole

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**Representative Volume of Gas Particles at STP 23 6.02x10 22.4 L Mole**

atomic 1 mole mass Mass 22.4 L Representative Particles Volume of Gas at STP 6.02x10 23 Mole We are given a mass

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**Representative Volume of Gas Particles at STP 23 6.02x10 22.4 L Mole**

atomic 1 mole mass Mass 22.4 L Representative Particles Volume of Gas at STP 6.02x10 23 Mole We are asked for atoms It’s going to take us 2 conversions, we just need to follow the arrows We are given a mass

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**1st we must convert our given mass of Chromium to moles of Chromium**

So we need to use the periodic table to calculate the mass of 1 mole of Chromium 1 mole Cr X mol Cr = 51.996g Cr 35.67g Cr (51.996gCr)(X mol Cr) = (35.67gCr)(1 mol Cr) X = mol Cr

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**2nd we must convert our newly found moles of Cr to atoms of Cr**

So we need to remember that 1 mole of anything there are 6.02x1023 particles 6.02x1023 atoms Cr X atoms Cr = 1 mole Cr .6860 mol Cr (1 mol Cr)(X atoms Cr) = (6.02x1023 atoms Cr) (.6860 mol Cr) X = 4.13x1023 atoms Cr

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**Factor label one step method**

Given: 35.67g Cr Want: atoms Cr Conversions: 1 mole Cr = 6.02*1023 atoms 1 mole Cr = g Cr Set up 35.67g Cr | 1 mole Cr |6.02*1023 atoms | g Cr | 1 mole Cr = *1* 6.02*1023 atoms= 2.148*1025 atoms = 4.131*10 23 atoms

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Percent Composition Atomic weights can be found by using the Periodic Table of the Elements. Find the atomic weight of each element. Multiply the number of atoms by the atomic weight, and add all of these weights per compound together. Divide each atom (or ion's) individual atomic mass by the total chemical mass *100

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**Percent Composition FeO = Fe = 55.845g/mol O = 15.999 g/mol**

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**Percent Composition FeO = 71.844 Fe = 55.845g/mol /71.844 = 0.777**

= 0.223

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Percent Composition Fe = 0.777*100= % 0 = *100 = %

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**Percent Composition Li3P - Lithium Phosphide Li = P = 3* 6.941 =**

20.823 / = 0.402 30.97 1* = / = 0.598 51.793

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**Percent Composition C=5*12.01 = 60.050 C= 60.050 / 145.140 = 0.411**

What is the percent carbon in C5H8NO4 (the glutamic acid used to make MSG monosodium glutamate), a compound used to flavor foods and tenderize meats? a) %C b) %C c) %C C=5*12.01 = H= 8*1.01 = 8.080 N = 1*14.01 = 14.01 O= 4* =64.0 C5H8NO4 = C= / = 0.411 0.411*100 = 41.1%

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**Chemical Formulas of Compounds**

Formulas give the relative numbers of atoms or moles of each element in a formula unit - always a whole number ratio (the law of definite proportions). NO atoms of O for every 1 atom of N 1 mole of NO2 : 2 moles of O atoms to every 1 mole of N atoms If we know or can determine the relative number of moles of each element in a compound, we can determine a formula for the compound.

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**Types of Formulas Empirical Formula**

The formula of a compound that expresses the smallest whole number ratio of the atoms present. Ionic formula are always empirical formula Molecular Formula The formula that states the actual number of each kind of atom found in one molecule of the compound.

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**Simplest and molecular formulae**

Consider NaCl (ionic) vs. H2O2 (covalent) Cl Na Cl H O Na H O H O Cl Cl Na Na Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular”. Ionic compounds are always expressed as simplest formulas. Covalent compounds can either be molecular formulas (I.e. H2O2) or simplest (e.g. HO)

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**Simplest and molecular formulae**

Consider NaCl (ionic) vs. H2O2 (covalent) Cl Na Cl H O Na H O H O Cl Cl Na Na Q - Write simplest formulas for propene (C3H6), C2H2, glucose (C6H12O6), octane (C8H14) Q - Identify these as simplest formula, molecular formula, or both H2O, C4H10, CH, NaCl

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**Answers Q - Write simplest formulas for propene (C3H6),**

C2H2, glucose (C6H12O6), octane (C8H14) Q - Identify these as simplest formula, molecular formula, or both H2O, C4H10, CH, NaCl A - CH2 A - H2O is both simplest and molecular C4H10 is molecular (C2H5 would be simplest) CH is simplest (not molecular since CH can’t form a molecule - recall Lewis diagrams) NaCl is simplest (it’s ionic, thus it doesn’t form molecules; it has no molecular formula) CH CH2O C4H7

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**To obtain an Empirical Formula**

1. Determine the mass in grams of each element present, if necessary. 2. Calculate the number of moles of each element. 3. Divide each by the smallest number of moles to obtain the simplest whole number ratio. If whole numbers are not obtained* (in step 3), multiply through by the smallest number that will give all whole numbers * Be careful! Do not round off numbers prematurely

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**A sample of a brown gas, a major air pollutant, is found to contain 2**

A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance. require mole ratios so convert grams to moles moles of N = 2.34g of N = moles of N 14.01 g/mole moles of O = g = moles of O 16.00 g/mole Formula:

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**A sample of a brown gas, a major air pollutant, is found to contain 2**

A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance. moles of N moles of O /0.167 =1 =2 /0.167 NO2 N1O2

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**Empirical Formula from % Composition**

A substance has the following composition by mass: % Na ; % B ; % H What is the empirical formula of the substance? 2.645 / 2.645 = 1 Na = g / = B = g / = 2.645 / 2.645 = 1 H = g / = 10.516 / 2.645 = =4 NaBH4

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**Calculation of the Molecular Formula**

Molecular formula is actual formula of the compound. To determine the molecular formula from the empirical formula you must have the mass of the molecular formula. (Always Given to you) Divide the mass of molecular formula by the mass of the empirical formula. This will give you a whole number that you must multiply the subscripts in the empirical formula by.

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**Calculation of the Molecular Formula**

CH2O is the empirical formula for a compound with a molecular mass of g. CH2O = = 30.02g/mol Divide by 30.03 180.18/30.03 = 6 6 (CH2O) = C6H12O6

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**Calculation of the Molecular Formula**

A compound has an empirical formula of NO2. The colourless liquid, used in rocket engines has a molar mass of 92.0 g/mole. What is the molecular formula of this substance? N2O4

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**CO2 H5N = Empirical CO2 H5N = 63.050g/mol 252.3 / 63.050 = 4**

A compound contains 0.80 mol C, 4.0 moles H and 1.60 mol O, and 0.80 mol of N, and has a molecular mass of g/mol. What is the molecular formula for the compound? CO2 H5N = Empirical CO2 H5N = g/mol 252.3 / = 4 4(CO2 H5N) = C4O8H20N4

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