Dimensional Analysis A way of changing units

Advantages to Using Dimensional Analysis The steps are the same for all problems, regardless of how different the problems may be. The steps follow a pattern; no memorization is necessary.

Advantages for Using Dimensional Analysis This also means that you can use the process to solve problems you haven’t encountered yet….. Again, NO NEED TO MEMORIZE the individual steps of all 9 types of problems we will use. NOTE: there are an infinite number of types of problems

Advantages to Using Dimensional Analysis Comparing it to cross-multiplication, there is less to write down. ? L H 2 = 20.0g Na X 1 mol Na x 1 mol H 2 x 22.4 L H 2 = 9.74 L H g Na 2 mol Na 1 mol H 2 Versus….. X mol Na = 1 mol Na X L H 2 = 22.4 L H g Na g Na mol H 2 1 mol H 2 X = mol Na X = 9.74 L H 2 X mol H 2 = 1 mol H mol Na 2 mol Na X = mol H 2

Advantages to Using Dimensional Analysis You will be graded on your ability to understand and use this method. AND this method will be used for at least the next 1.5 months (the next 3 assessments)

Conversion Factors When two things that are equal to each other …. 2 = 2

Conversion Factors Are put on opposite sides of a fraction (one side of the equation in the numerator and one side of the equation in the denominator) …

Conversion Factors The result…… 2 = 1 2 …… is 1

Therefore… Any two values that are equal, will equal 1 in a fraction…. 1 yd = 3ft 1yd = 13 ft = 1 3 ft1 yd These fractions are called “conversion factors”

Conversion Factors Labeling units is IMPORTANT! 2.02 lb = 1 1 kg BUT 2.02 ≠ 1 1

Your turn…. Make conversion factors using the following information… 1 kg = 2.02 lbs 1 lb = 16 ounces

Answers 2.02 lb 1 kg 1 kg 2.02 lb 16 oz 1 lb 1 lb16 oz

Conversion Factors 32 mi/hr Is stating that for every 32 miles, 1 hr passes In other words 32 mi= 1hr

Your turn… Make conversion factors using the following g/mol

Answers g 1 mol 1 mol g

Thinking Back… What is “ g/mol” an example of? (Hint: look at the units) How are these calculated?

Thinking back (answers) g/mol is an example of a “molar mass” or the mass of 1 mole of a substance, in this case water. Molar masses are calculated using the Periodic Table. (The atomic mass of each element in the formula is multiplied by how many of that element exist in the formula) H 2 X = O 1 x = ( = g/mol H 2 O

Converting with Conversion Factors Multiplying anything by 1 does not change the value…. 35 g x 1 x 1 = 35 g

Converting with Conversion Factors AND because “conversion factors” are equal to 1……

Converting with Conversion Factors they can be used to change units. 123 lb x 1 kg = kg 2.02 lb In other words, 123 lbs = kg

NOTE although the number and units change the value remains the same.

Using Conversion Factors In order to determine Which conversion factor to use, and What position to put it in….. You have to look at where you are starting, and Where you want to end.

Using Conversion Factors Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this?

STEP 1: Identify what you are looking for, and set it up after a “?”

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? STEP 2: Set it equal to what you are given (something that is conditional to this problem only). For example 3 tsp = 1 tbsp is NOT a “given” value because it never changes.

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp = 355 mL

Note: Once you use the given in your equation, you can’t use it again for the same problem. So for this problem, the units “mL” may be used again, but the “355 mL” can not.

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? STEP 3: If the units on the left of the equal sign are not the same as the units on the right of the equal sign (tbsp ≠ mL), Then, get ready to use a conversion factor……

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp = 355 mL x _______

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? STEP 4: The units that are “undesired” (in this case, we don’t want mL), go into the denominator of the conversion factor

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp = 355 mL x ________ mL

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? STEP 5: Consider what you know and/or any provided information

Reference Conversions 3 tsp = 1 tbsp 1 gal = L 2 pints = 1 quart 2 cups = 1 pint 1 tsp = 4.93 mL 1 lb = 454 g 1 in = 2.54 cm 1 dram = 30 mL 20 drops = 1 mL

STEP 6: Chose units that directly relate to the units you placed in the denominator, and can eventually lead to your “desired units”

There is nothing that relates tbsp directly to mL…. 3 tsp = 1 tbsp 1 gal = L 2 pints = 1 quart 2 cups = 1 pint 1 tsp = 4.93 mL 1 lb = 454 g 1 in = 2.54 cm 1 dram = 30 mL 20 drops = 1 mL The only thing that has tbsp is 3 tsp = 1 tbsp So, that is used….

? tbsp = 355 mL x ________ mL But WAIT… We are starting with mL… When we look back at what we know…..

Using the Reference 3 tsp = 1 tbsp 1 gal = L 2 pints = 1 quart 2 cups = 1 pint 1 tsp = 4.93 mL 1 lb = 454 g 1 in = 2.54 cm 1 dram = 30 mL 20 drops = 1 mL We see that we CAN relate mL to tsp 1 tsp = 4.93 mL

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp = 355 mL x _ 1 tsp mL

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? STEP 7: Cancel out any units that are on opposite sides of the fraction.

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp = 355 mL x _ 1 tsp mL

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? ? tbsp = 355 x _ 1 tsp 4. 93

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? STEP 8: Repeat steps 3-7 until the units that remain match the “desired units”

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? (tsp ≠ tbsp so the “undesired units” (tsp) go into the denominator of a new fraction) ? tbsp = 355 x _ 1 tsp x _____ tsp

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? (tsp can be directly related to tbsp, so tbsp is put in the numerator) ? tbsp = 355 x _ 1 tsp x _1 tbsp tsp

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? (“tsp” occurs in both the numerator and in the denominator, so they cancel out) ? tbsp = 355 x _ 1 tsp x _1 tbsp tsp

Jenny is instructed to take medication by the tablespoon. If Jenny is given a 355 mL bottle, how many tablespoons is this? (the units in the numerator of the last conversion factor match the “desired units” so no more conversion factors are needed) ? tbsp = 355 x _ 1 x _1 tbsp

Type into the calculator STEP 9: Solve. (It can be treated like one big fraction so everything on the top is multiplied, then divided by everything on the bottom) 355 ÷ 4.93 ÷ 3 = 24.0 tbsp or 4.93 x 3 = Then 355 ÷ = 24.0 tbsp

Your turn.. How many drops are in 1 pint of blood?

Reference Conversions 3 tsp = 1 tbsp 1 gal = L 2 pints = 1 quart 2 cups = 1 pint 1 tsp = 4.93 mL 1 lb = 454 g 1 in = 2.54 cm 1 dram = 30 mL 20 drops = 1 mL

Solution ? drops = 1 pint x 1 quart x 1 gal x L x 1000 mL x 20 drops 2 pints 4 quarts 1 gal 1 L 1 mL drops of blood

Your Turn…. For amoxicillin, the pediatric dosage is 80mg amoxicillin/kg child. The strength of liquid amoxicillin is 250 mg medication/tsp. If a child weighs 23lbs, how many mL will the child take?

Analyze the problem 80 mg medication = 1 kg child 250 mg medication = 1 tsp medication 23 lb child NOTE! Both mass & object are written because 80 mg ≠ 1 kg BUT 80 mg medication does equal 1 kg child (it also helps guide you when trying to solve)

Solution ? mL med = 23 lb child x 454 g x 1 kg x 80 mg med x 1 tsp x 4.93 mL 1 lb 1000 g 1 kg child 250mg med 1 tsp Answer: ≈ 16.5 mL medication

Your Turn…. The human body is approximately 60% water by mass. If water has a density of 1 g/mL, how many milliliters of water are in a person who weighs 135 lbs?

The human body is approximately 60% water by mass. How many milliliters of water are in a person who weighs 135 lbs? Analyze the problem 100 lb person = 60 lb H 2 O or 100 g person = 60 g H 2 O or 100 kg person = 60 kg H 2 O or 100 mg person = 60 mg H 2 O 1 g H 2 O = 1 mL H 2 O 135 lb person

The human body is approximately 60% water by mass. How many milliliters of water are in a person who weighs 135 lbs? ? mL H 2 O = 135 lb person x 60 lb H 2 O x 1 kg H 2 O x 1000 g H 2 O x 100 lb person 2.02 lb H 2 O 1 kg H 2 O 1 mL H 2 O 1 g H 2 O

The human body is approximately 60% water by mass. How many milliliters of water are in a person who weighs 135 lbs? ? mL H 2 O = 135 lb person x 60 lb H 2 O x 1 kg H 2 O x 1000 g H 2 O x 100 lb person 2.02 lb H 2 O 1 kg H 2 O 1 mL H 2 O 1 g H 2 O Solve: 135 x 60 x 10 ÷ 2.02 = mL ≈ 4.01 x 10 4 mL

The human body is approximately 60% water by mass. How many milliliters of water are in a person who weighs 135 lbs? OR…… ? mL H 2 O = 135 lb person x 454 g person x 60 g H 2 O x 1 mL H 2 O x 1 lb person 100 g person 1 g H 2 O Solve: 135 x 454 x 60 ÷ 100 = mL ≈ 3.68 x 10 4 mL

????? Why are the answers to the same question different? 1 lb = g (not exactly 454) AND 1 kg = lb (not exactly 2.02)

Squared and Cubed When dealing with units that are squared or cubed (ex. m 3 or cm 2 ), you need to use extra conversion factors (1 conversion factor per exponent)

Squared & Cubed What is 35in 3 in cm 3 ? ? cm 3 = 35 in 3 x 2.54 cm x 2.54 cm x 2.54 cm 1 in 1 in 1 in cm 3 Answer = cm 3 ≈ 570 cm 3 You use the conversion factor 3 times because the exponent on cm is 3

Squared and cubed How many L are equal to 3.75ft 3 ? (1 mL = 1 cm 3 )

How many L are equal to 3.75ft 3 ? ? L = 3.75ft 3 x 12 in x 12 in x 12 in x 2.54 cm x 2.54 cm x 2.54 cm 1 ft 1 ft 1 ft 1 in 1 in 1 in 1 mL x 1 L = L ≈ 106 L 1 cm mL

Rates If your “desired units” contain both a numerator AND a denominator….. You need to solve for both “desired units”; usually one at a time.

Rates How many m/s is a car traveling if the speedometer reads 75mph?

Solve for the numerator 1st ? m = 75 mi x 5280 ft x 12 in x 2.54 cm x 1 m x s hr 1 mi 1 ft 1 in 100 cm

Solve for the numerator 1st ? m = 75 mi x 5280 ft x 12 in x 2.54 cm x 1 m x s hr 1 mi 1 ft 1 in 100 cm The units you now have are m/hr… You want m/s. So…..

You now solve for the denominator ? m = 75 mi x 5280 ft x 12 in x 2.54 cm x 1 m x s hr 1 mi 1 ft 1 in 100 cm 1 hr x 1 min = 60 min 60 s

You now solve for the denominator ? m = 75 mi x 5280 ft x 12 in x 2.54 cm x 1 m x s hr 1 mi 1 ft 1 in 100 cm 1 hr x 1 min = 60 min 60 s You are left with m/s. Now, we solve.

How many m/s is a car traveling if the speedometer reads 75mph? Multiply everything on the top & Divide by everything on the bottom… Type into calculator 75 x 5280 x 12 x 2.54 ÷ 100 ÷ 60 ÷ 60 =

How many m/s is a car traveling if the speedometer reads 75mph? 75 x 5280 x 12 x 2.54 ÷ 100 ÷ 60 ÷ 60 = Answer = m/s ≈ 34 m/s

Your turn… Your car's gas tank holds 18.6 gallons and is one quarter full. Your car gets 16 miles/gal. You see a sign saying, "Next gas 73 miles." Your often- wrong brother, who is driving, is sure you'll make it without running out of gas. You're not so sure and do some quick figuring: Will you make it to the gas station?

Identify what you’re looking for ? mi = quarter-tank

Identify what you’re given ? mi = 16 mi quarter-tank gal

Solution ? mi = 16 mi x 18 gal x 1 tank quarter-tank gal tank 4 (¼ tank)

Answer the question ? mi = 16 mi x 18 gal x 1 tank quarter-tank gal tank 4 (¼ tank) = 72 mi/ (1/4 tank) In other words, you have enough gas to drive 72 miles. Answer: if the next gas station is 73 miles away, you don’t have enough gas to make it.

Your Turn… Viscosity is the resistance to flow. One type of oil has a viscosity of 46 mm 2 /s. How many cm 2 will flow in 1 hour?

Solution ? cm 2 = 46 mm 2 x 10 cm x 10 cm x 60 s x 60 min hr s 1 mm 1 mm 1 min 1 hr

Solution ? cm 2 = 46 mm 2 x 10 cm x 10 cm x 60 s x 60 min hr s 1 mm 1 mm 1 min 1 hr Answer 1,656,000 cm 2 /hr

Using Dimensional Analysis in Stoichiometry The coeffients in a balanced chemical equation represent the ratio in which compounds and/or elements react.

Coefficients For example, In the equation 3CaCl 2(aq) + 2Na 3 PO 4(aq)  Ca 3 PO 4(s) + 6NaCl For every 3 molecules of CaCl 2 that reacts, 6 molecules of NaCl are produced. To make 1 molecule of Ca 3 PO 4, 2 molecules of Na 3 PO 4 are needed Etc.

Coefficients Due to the fact that molecules are SO small and cannot be directly measured, Moles are used instead. The mole is x molecules, No matter what the substance is.

In the equation 3CaCl 2(aq) + 2Na 3 PO 4(aq)  Ca 3 PO 4(s) + 6NaCl 3 mol CaCl 2 = 2 mol Na 3 PO 4 3 mol CaCl 2 = 1 mol Ca 3 PO 4 3 mol CaCl 2 = 6 mol NaCl 2 mol Na 3 PO 4 = 1 mol Ca 3 PO 4 2 mol Na 3 PO 4 = 6 mol NaCl 1 mol Ca 3 PO 4 = 6 mol NaCl

Mole Ratios A conversion factor that only contains moles, is called a “mole ratio”. They are created the same way other conversion factors are created… 3CaCl 2(aq) + 2Na 3 PO 4(aq)  Ca 3 PO 4(s) + 6NaCl 3 mol CaCl 2 = 2 mol Na 3 PO 4 Mole ratios: 3 mol CaCl 2 2 mol Na 3 PO 4 2 mol Na 3 PO 4 3 mol CaCl 2

Your turn…. For the equation: C 3 H 8( l ) + 5O 2(g)  4H 2 O (g) + 3CO 2(g) Please write all the possible mole ratios

Answers C 3 H 8( l ) + 5O 2(g)  4H 2 O (g) + 3CO 2(g) 1 mol C 3 H 8 5 mol O 2 4 mol H 2 O 3 mol CO 2 5 mol O 2 1 mol C 3 H 8 1 mol C 3 H 8 1 mol C 3 H 8 1 mol C 3 H 8 5 mol O 2 4 mol H 2 O 3 mol CO 2 4 mol H 2 O 4 mol H 2 O 5 mol O 2 4 mol H 2 O 1 mol C 3 H 8 5 mol O 2 4 mol H 2 O 3 mol CO 2 3 mol CO 2 3 mol CO 2 3 mol CO 2 5 mol O 2

Reflection Why is it important to label all numbers with units? Why is it important to label all numbered units with a compound (or element) formula?

Reflection (answers may vary) Labeling all numbers with units helps you determine what comes next in the equation (and when to stop). It also shows where the numbers come from It is important to label the formula as well because in these equations, you will have 2 different molar masses, 2 different mole values, etc. Labeling the formula informs you of which numbers to use. It also shows where the numbers come from.

Stoichiometry Stoichiometry is the process by which 2 different substances (compounds or elements) are related, using dimensional analysis. The “mole ratio” is always present as a bridge from one substance to another substance.

Stoichiometry Problems Examples of types of Stoichiometric problems  Moles of X to moles of Z  Moles of X to mass of Z  Mass of X to moles of Z  Mass of X to mass of Z  Moles of X to volume of Z  Volume of X to moles of Z  Mass of X to volume of Z  Volume of X to mass of Z  Volume of X to volume of Z

Do NOT be alarmed Remember: Using the process of dimensional analysis, there is NO NEED to memorize the individual types of stoichiometric problems listed on the previous slide.