Dimensional Analysis “Unit Factor Method”

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## Dimensional Analysis “Unit Factor Method”

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**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!!!**(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. Dim. Analysis in Chemistry**Molarity Island**When in doubt how to convert a measurement, convert it to moles first!**volume**representative particles (6.022 x 1023) (moles) (22.4 L /mol)* (moles) moles (moles) * (6.022 x 1023) (liters)(22.4 L /mol) Representative Particles:element (contains) atomsionic compound (contains) ionsmolecular cmpd (contains) molecules (moles) * (MW g/mol) (Grams)(MW g/mol) mass “The Conversion Triangle”**The following three examples use “The Conversion**Triangle” only once to solve the question. One Step Conversions**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/molC6H12O6 • 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 C6H12O6has only one significant figure Example Problem #1a**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 #1b**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 #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 • 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**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 #3a**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 Example Problem #3b**The next two examples use “The Conversion Triangle”**twice to solve the question. Two Step Conversions**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 #1**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 Example Problem #2