Dimensional Analysis “Unit Factor Method”

» How to convert 6 in to cm?

» Desired factor = cm, so you multiply it so that the units of inches cancel out » Start off with the number with only 1 unit, and not two units.

» How many seconds are in 2 years

» Desired factor is seconds, you can multiply multiple factors but be sure that the factors cancel out!!!

Dim. Analysis in Chemistry» (6) How many atoms of hydrogen can be found in 45 g of ammonia, NH3?

We will need three unit factors to do this calculation, derived from the following information:

» 1 mole of NH3 has a mass of 17 grams.

» 1 mole of NH3 contains 6.02 x 1023 molecules of NH3.

» 1 molecule of NH3 has 3 atoms of hydrogen in it.

Molarity Island

When in doubt how to convert a measurement, convert it to moles first!

“The Conversion Triangle”

moles

volume

mass

representative particles

(22.4 L /mol)* (moles)

(liters)(22.4 L /mol)

(moles) *

(6.022 x 102

3 )

(6.022 x 1023 )

(moles)

(moles) *

(MW

g/mol) (G

ram

s)(M

W g

/mol

) Representative Particles:element (contains) atoms

ionic compound (contains) ions

molecular cmpd (contains) molecules

The following three examples use “The Conversion Triangle” only once to solve the question.

One Step Conversions

Example Problem #1a

How many moles are in 232.6 grams of C6H12O6?» Steps to solving this problem:

˃ 1. Find the molecular weight (MW) of the compound + use a periodic table to find the molecular weights of the

individual elements (MW are listed in “grams/mole”)– C = 12 grams/mole– H = 1 gram/mole– O = 16 grams/mole

» 6 C*12.0107 g/mol = 72 g/mol» 12 H*1.007 g/mol = 12 g.mol» 6 O*15.99 g/mol = 96 g/mol

Total MW = 180.0882 g/mol C6H12O6

˃ 2. Convert grams to moles (using “The Conversion Triangle”)

Example Problem #1a

» Step 1 gave us:˃ MW of C6H12O6 = 180.0882 g/mol

» Step 2: Now to convert grams of C6H12O6 to moles (from “conversion triangle”)

+ (grams C6H12O6 /MW C6H12O6) = moles C6H12O6

» With significant figures, the answer is 1.3 moles of C6H12O6 ˃ This is because the initial grams of C6H12O6 has only one significant

figure

Example Problem #1b

How many grams are in 3.2 moles of NaCl?» Steps to solving this problem:

˃ 1. Find the molecular weight (MW) of the compound + use a periodic table to find the molecular weights of the

individual elements (MW are listed in “grams/mole”)– 1*Na = 1*23 g/mol– 1*Cl = 1*35.5 g/mol

» Total Mw = 58.5 g/mol˃ 2. Convert moles to grams (using “Conversion Triangle”)

+ grams (mass) NaCl = moles NaCl * MW NaCl

» Answer only has 1 significant figure because initial value of moles has only 1 significant figure

Example Problem #2

How many representative particles are in 1.65 moles of Calcium (Ca)?» Steps to solving this problem:

˃ 1. We already have moles of Ca, all we need to do is convert them to representative particles (or atoms)

+ atoms Ca = moles Ca * 6.022x1023 atoms*» With significant figures: 9.93x1023 atoms

˃ Two significant figures in final answer are because of two significant figures in initial moles of Ca

Example Problem #2b

How many moles are in 1.32x1024 ions of compound “XYZ”?» Steps to solving this problem:

˃ We don’t need MW of compound XYZ to solve for how many moles are in it, all we need is Avagodro’s number and the Conversion Triangle

+ moles XYZ = ions (representative particles) XYZ / 6.022x1023 ions

» With significant figures, the answer is 2.19 moles of XYZ˃ Since the initial ions have only 2 significant figures, the answer must also

Example Problem #3a

How many liters are in 4.32 moles of O2?» Equation from Conversion Triangle:

˃ liters O2 = moles of O2 * 22.4 L

» With significant Figures, the answer is 96.8 L of O2˃ Since the number of significant figures from 22.4 L is 1, the answer

must also contain 1 significant figure

Example Problem #3b

How many moles of N2 are in 150.2 L?» Equation from Conversion Triangle:

˃ Moles of N2 = liters of N2 / 22.4 L

» With significant Figures, the answer is 6.7 moles of N2˃ Since the number of significant figures from 22.4 L and 150.2 L are

both 1, the answer must also contain 1 significant figure

The next two examples use “The Conversion Triangle” twice to solve the question.

Two Step Conversions

Example Problem #1

How many liters (L) are in 28.3 g of Ne?» Steps to solve this problem:

˃ 1. Convert grams of Ne to moles of Ne+ get MW from periodic table then use Conversion Triangle to convert to

grams moles˃ 2. Convert moles of Ne to L of Ne

» Solution:˃ 1. moles of Ne = grams of Ne / MW of Ne

+ MW of Ne = 20.1797 g/mol

˃ 2. liters of Ne = moles of Ne * 22.4 L of Ne

» Answer with significant figures: 31.4 L of Ne˃ Because initial grams of Ne and 22.4 L both have only one significant figure

thus the answer should have only one significant figure

Example Problem #2

How many grams are in 2.65x1020 ions of BaCl2?» Steps to solve this problem:

˃ 1. convert ions to moles˃ 2. convert moles to grams

+ get MW from periodic table then use Conversion Triangle to convert to moles grams

» Solution:˃ 1. moles of BaCl2 = ions of BaCl2 / 6.022x1020 ions

˃ 2. grams of BaCl2 = moles of BaCl2 * MW of BaCl2

» With significant figures, the answer is 456.7 g BaCl2