Unit 12 Mass and Moles

Avogadro’s Hypothesis–Under the same conditions of

temperature and pressure, equal volumes of two different gases will have the same number of particles regardless of mass.

–At STP, this number of particles is Avogadro’s number or 6.02 x 1023 or 1 mole

This number can be used to express the mass, volume or number of particles for any gas sample. The conversion from one to another involves this equivalency:

1mole = 6.02 x 1023 particles = gram formula mass = 22.4 liters of space

*YOU MUST MEMORIZE THIS*

Determining mass using formulasAtomic Mass Unit (amu)

• 1 amu = 1/12 the mass of a C-12 atom

Gram Atomic Mass• The mass of 1 mole of atoms• Numerically equal to atomic mass number • The unit used is (g) gram

Gram Molecular Mass• The mass of 1 mole of molecules• Found by adding up the atomic mass

numbers of each element in the molecule

• The unit used is (g) grams

Gram Formula Mass• The mass of 1 mole of an ionic

substance• *remember that ionic substances are

not composed of molecules!• Determine the gram formula

mass/gram molecular mass of the following:

• NaCl

• H2O

• 1 mole of H2 gas

Avogadro’s Number and Mole Map Problems

What we know:• At STP and in the gaseous phase:• 1 mole = 6.02 x 1023 particles of a

substance• 1 mole takes up 22.4 L of space• 1 mole has a mass equal to the gram

formula/gram molecular mass

We could convert from moles to mass to volume using a Mole Map

to set up a proportion• Example: What is the mass of 3.01 x 1023

molecules of NH3(g) at STP?

• What is the mass of 5 moles of O2 gas at STP?

• How many molecules of NH3 would take up 44.8 L at STP?

• What is the mass of 9.03 x 1023 atoms of neon gas at STP?

Density

• The mass per unit volume of a substance.• The density of a substance DOES NOT change

for that substance!• Formula: Density = Mass/Volume

3 ways for the Regents to ask Density problems

• Table S: What is the density of one mole of N2?

• Question will give 2 variables, you must use the formula to solve for the 3rd_: What is the density of a solid having a mass of 75g and a volume of 3 cm3?

• Given the density, the Regents can ask for the molecular mass at STP: Remember that at STP, the molecular mass or 1 mole of a gas has what volume? 22.4L

• What is the gram molecular mass of a gas having a density of 2g/L at STP?

Percent Composition• To determine the percentage by

mass of a particular element in a compound.

•Determine the gfm•Take the mass of individual element and divide by gfm

•Multiply by 100%

Examples• What percent by mass of CaCO3 is

made up of calcium?• What is the percent by mass of

nitrogen in NH4NO3

• What is the percent by mass of water in copper sulfate pentahydrate?

Empirical Formula from Percent Composition• Using the percent composition, one can

determine the smallest whole number ratio of atom to atom in a compound (empirical formula). **Remember that since ionic substances do not have true molecules, they are always expressed in empirical formulas**

Follow the steps:• Divide the percent by the atomic mass• Take the answer to step 1 and divide it by the

smallest answer to step 1.

Examples• What is the empirical formula of a compound

containing 40% calcium, 12% carbon and 48% oxygen by mass?

• What compound contains 56.58% potassium, 8.68% carbon and 34.73% oxygen by mass?

Special Rule• if the answer to step 2 ends in .1 or .9 you can

round off, BUT if it ends in .3 or .5, this is a significant portion of a number. You cannot round away this number, instead you must adjust all numbers accordingly by following the formula:

• If the number ends in .3 _multiply everything by 3____

• If the number ends in .5 __multiply everything by 2___

Example

• Give the empirical formula of a compound containing 90.7% lead and 9.3% oxygen by mass.

Molecular Formula from Empirical FormulaTo determine the molecular formula from

the empirical formula follow the steps:*Calculate the empirical mass.*Divide the mass of the compound by the

mass of the empirical formula.*Multiply all subscripts by the answer in

step 2.

Example

• A compound has a molecular mass of 42 amu and an empirical formula of CH2. What is the molecular formula?

Moles in Balanced Equations• A chemical equation usually represents a

chemical reaction. The equation will identify:

• The reactants and products• The molar ratio of each of these.• Phases of matter for each substance.• Possibly some reference to energy

changes in the reaction.

Example

• 2H2(g) + O2(g) → 2H2O(l) + heat

• When using equations to solve conversion problems, one must remember the proportions the original substances are in. One can determine how many grams of a reactant are needed to produce a set volume by using the following rules:

Mass is the ONLY part of Avogadro’s hypothesis that CAN NOT be used directly in a proportion!!You must convert grams to moles–Table TFollow these steps:read and underlinecross out what is not involvedset up a proportion coefficients/known informationcross multiply and divide

Example

• What volume of CO2(g) is produced when 15 liters of O2(g) are consumed in the reaction:

• C2H4(g) + 3 O2(g) → 2 CO2(g) + 2H2O(g)

• Given the reaction:• 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(g)

• What number of carbon dioxide molecules are produced when 6.02x1023 molecules of ethane are consumed?