Dimensional Analysis “Unit Factor Method”

How many seconds are in 2 years 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) (6.022 x 1023) (moles) (moles) * (6.022 x 1023) (liters) (22.4 L /mol) Representative Particles: element (contains) atoms ionic compound  (contains) ions molecular cmpd  (contains) molecules (moles) * (MW g/mol) (Grams) (MW g/mol) “The Conversion Triangle”

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

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

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 232.6 𝑔 𝐶6𝐻12𝑂6 1 ∗ 𝑚𝑜𝑙𝑒 180.0882 𝑔 =1.2915 𝑚𝑜𝑙𝑒𝑠 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 #1a

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 3.2 𝑚𝑜𝑙𝑒𝑠 𝑁𝑎𝐶𝑙 1 ∗ 58.5 𝑔 𝑁𝑎𝐶𝑙 𝑚𝑜𝑙𝑒 =187.2 𝑔 𝑁𝑎𝐶𝑙 Answer only has 1 significant figure because initial value of moles has only 1 significant figure Example Problem #1b

1.65 𝑚𝑜𝑙𝑒𝑠 𝐶𝑎 1 * 6.022𝑥 10 23 𝑎𝑡𝑜𝑚𝑠 1 𝑚𝑜𝑙𝑒 =9.9336𝑥 10 23 𝑎𝑡𝑜𝑚𝑠 𝐶𝑎 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 1.65 𝑚𝑜𝑙𝑒𝑠 𝐶𝑎 1 * 6.022𝑥 10 23 𝑎𝑡𝑜𝑚𝑠 1 𝑚𝑜𝑙𝑒 =9.9336𝑥 10 23 𝑎𝑡𝑜𝑚𝑠 𝐶𝑎 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 #2

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 1.32𝑥 10 24 𝑖𝑜𝑛𝑠 𝑜𝑓 𝑋𝑌𝑍 1 ∗ 𝑚𝑜𝑙𝑒𝑠 6.022𝑥 10 23 𝑖𝑜𝑛𝑠 =2.192 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑋𝑌𝑍 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 #2b

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 4.32 𝑚𝑜𝑙𝑒𝑠 𝑂2 1 ∗ 22.4 𝐿 𝑚𝑜𝑙𝑒 =96.768 𝐿 𝑂2 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 #3a

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 150.2 𝐿 𝑂2 1 ∗ 𝑚𝑜𝑙𝑒𝑠 22.4 𝐿 =6.705 𝑚𝑜𝑙𝑒𝑠 𝑁2 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 Example Problem #3b

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

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 28.3 𝑔 𝑁𝑒 1 ∗ 𝑚𝑜𝑙𝑒 20.1797 𝑔 =1.402399441 𝑚𝑜𝑙𝑒𝑠 𝑁𝑒 2. liters of Ne = moles of Ne * 22.4 L of Ne 1.402399441 𝑚𝑜𝑙𝑒𝑠 𝑁𝑒 1 ∗ 22.4 𝐿 𝑚𝑜𝑙𝑒𝑠 =31.4137 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 #1

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 2.65𝑥 10 20 𝑖𝑜𝑛𝑠 1 ∗ 𝑚𝑜𝑙𝑒𝑠 6.022𝑥 10 23 𝑖𝑜𝑛𝑠 =4.4005𝑥 10 −4 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓BaCl2 2. grams of BaCl2 = moles of BaCl2 * MW of BaCl2 4.4005𝑥 10 −4 𝑚𝑜𝑙𝑒𝑠 BaCl2 1 ∗ 208.3 𝑔BaCl2 𝑚𝑜𝑙𝑒𝑠 =456.737 𝑔 BaCl2 With significant figures, the answer is 456.7 g BaCl2 Example Problem #2