Dimensional Analysis DHS Chemistry ferrer

Setting Up Ratios 100 centimeters = 1 meter can be written as 100 cm OR 1 m___ 1 m 100 cm 8 slices = 1 pizza can be written as 1 pizza OR 8 slices___ 8 slices 1 pizza

The Format # x # x # x # = 1 # # # OR # # # = 1 # # 1 # # # OR # # # = 1 # # Note: Unless you are using 1 as a spot filler, all numbers should ALWAYS include units

Understanding order of operations & typing in calculator keys correctly Solve. 10 13 6 = 2 4 Method 1: 10 X 13 X 6 = 780 then divide 97. 5 2 x 4 = 8 Method 2: 10 X 13 X 6 / 2 / 4 = 97.5 130 780 390 97.5 Method 3: 10 X 13 / 2 X 6 / 4 = 97.5 130 65 390 97.5

Try It 15 2 3 1.2 4 = 1 4 5 14 5 0.308

Canceling out units Just as numbers are multiplied and divided, units are too. Cancel out all units that are located in both the numerator and denominator to reveal the left over units. cm in feet yard = yard cm in feet

Try It week day hr min sec = sec 1 week day hr min

Putting the numbers & units together 3 weeks 7 day 24 hr 60 min 60 sec = 1 1 week 1 day 1 hr 1 min =1814400 sec Rules?

I. One-Step Conversions

I. One- Step Conversions EX 1: Determine the number of slices in 282 I. One- Step Conversions EX 1: Determine the number of slices in 282.3 pizzas Step 1) what are you given? Step 2) What are you trying to get? Step 3) List your relationships (remember from pg 1 of the notes) Step 4) Set up your problem 282.3 pizzas Number of slices 1 pizza = 8 slices 282.3 pizzas 8 slices =2258.4 slices 1 1 pizza

EX 2: Determine the number of dozen eggs in 3.8 x 103 eggs. Step 1) what are you given? 3.8 X 103 eggs Step 2) What are you trying to get? Dozen eggs Step 3) List your relationships 12 eggs = 1 dozen Step 4) Set up your problem These should match 3.8 X 103 eggs 1 dozen =317 Dozen of eggs 1 12 eggs

Practice Relationship 1 foot = 12 inches 2821 in 1 foot = 235 feet 1 Determine the number of feet in 2821 inches. Relationship 1 foot = 12 inches want given Start with what’s given 2821 in 1 foot = 235 feet 1 12 in

Practice Relationship 1000g = 1kg 0.03455 kg 1000 g = 34.6 g 1 1 kg 2. Determine the number of g in 0.03455 kg Relationship 1000g = 1kg want given Start with what’s given 0.03455 kg 1000 g = 34.6 g 1 1 kg

Relationships 1 mi = 1609.3 meter given want Relationships 1 mi = 1609.3 meter 1 mi = 1.6093 km Start with what’s given 37 mi 1.6093 km = 59.5 km 1 1 mi 99 mi 1.6093 km = 159 km 1 1 mi

Solving the same problem, but in a different way

Relationships 1 mi = 1609.3 meter given want Relationships 1 mi = 1609.3 meter 1 km = 1000 m Start with what’s given 37 mi 1609.3 m 1 km = 59.5 km 1 1 mi 1000 m

For every problem, start with: Given: Want: Relationships:

II. Multi-Step Conversions

Given: Want: Relationships: Ex. 1 Convert 0.115 km to cm 0.115 km 100 cm = 1 m 1 km = 1000 m

Ex. 1 Convert 0.115 km to cm Relationships 1km = 1000m 100cm = 1m given want Start with what’s given 0.115 km 1000 m 100 cm 1 1 km 1 m cm = 1.15 x 104

Given: Want: Relationships: Ex. 2 Convert 323 mL to cups 323 mL 1000 mL = 1 L 1 L = 1.06 quarts 1 quart = 4 cups

Ex. 2 Convert 323 mL to cups Relationships 1000 mL = 1L 4 cups 323 mL 1L = 1.06 quarts 1 quart = 4 cups given want Start with what’s given 4 cups 323 mL 1 L 1.06 qt. 1 1000 mL 1 L 1 qt. = 1.37 cups

Practice 1: Convert 7.005 ft to mm Given: Want: Relationships: 7.005 ft ____ mm 1 foot = 12 inches 1 inch = 2.54 cm 100cm = 1 m 1m = 1000mm

Practice 1: Convert 7.005 ft to mm Relationships 1 foot = 12 inches 2.54cm = 1 in 100 cm = 1 m 1 m = 1000 mm given want Start with what’s given Use this slide as a template for others 7.005 ft 12 in 2.54 cm 1 m 1000 mm 1 1 ft 1 in 100 cm 1 m = 2135 mm

Practice 2: calculate the number of seconds in 2 years Given: Want: Relationships: 2 years ____ seconds 1 year = 365.25 days 24hrs = 1 day 60 min = 1 hr 1 min = 60 sec

Practice 2: calculate the number of seconds in 2 years Relationships 1 year = 365.25 days 1 day = 24 hours 1 hr = 60 min 1 min = 60 sec given want Start with what’s given Use this slide as a template for others 60 sec 2 years 24 hrs 60 min 365.25 days 1 1 year 1 day 1 hr 1 min = 6.31 X 10 7 seconds

What does that price mean? $1.99 = 1lb

III. Combination Unit Conversions

Writing Clean Fractions Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem. 36.0 m/s 36.0 m OR s ___ s 36.0m 722 mi/hr 722 mi OR hr__ hr 722mi

Writing clean fractions from the denominator Remember from algebra, that a fraction in the denominator can be multiplied by its reciprocal. Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem. 52m to 52m s = 0.0715 s 727m/s 1 727m 46mi to 46 mi hr = 0.767 hr 60mi/h 1 60mi

EX 1: Convert 0.083 km/hr to m/s Given: Want: Relationships: 0.083 km/hr ____ m/s 1 km = 1000m 1 hr = 60 min 1 min = 60 sec

EX 1: Convert 0.083 km/h to m/s 0.083km 1000m 1 hr 1 min 1hr 1 km Relationships 1km = 1000m 1h = 60 min 1 min = 60 s given want Start with what’s given Use this slide as a template for others 0.083km 1000m 1 hr 1 min 1hr 1 km 60 min 60 s m/s = 2.31 X 10-2

EX 2: Convert 2.85 g/mL to lb/gal Given: Want: Relationships: 2.85 g/mL ____ lbs/gal 454g = 1lbs 1 gal = 4 quarts 1.06 qts = 1L 1 L = 1000mL

EX 2: Convert 2.85 g/mL to lb/gal Relationships 454 g = 1lb 1000mL = 1 L 1.06qt = 1 L 4 qt = 1 gal given want Start with what’s given Use this slide as a template for others 1 L 4 qt 2.85 g 1lb 1000mL 1mL 1 L 454 g 1.06 qt 1 gal = 23.7 lb/gal

Given: Want: Relationships: 3.56 cm/s ____ ft/hr 1 ft = 12 in 1. Convert 3.56 cm/s to ft/hr Given: Want: Relationships: 3.56 cm/s ____ ft/hr 1 ft = 12 in 2.54 cm = 1 in 1 hr = 60 min 1 min = 60 sec

3.56 cm 1 in 1 ft 60 s 60 min 1 s 2.54 cm 12 in 1 min 1 hr = 420 ft/hr 1. Convert 3.56 cm/s to ft/h Relationships 2.54 cm = 1 in 12 in = 1 ft 60 s = 1 min 1 hr = 60 min want given Start with what’s given Use this slide as a template for others 3.56 cm 1 in 1 ft 60 s 60 min 1 s 2.54 cm 12 in 1 min 1 hr = 420 ft/hr

2. Convert $25.00/feet to cents/cm Given: Want: Relationships: $25.00/ft ____ cents/cm $1.00 = 100 cents 1 ft = 12 inches 2.54 cm = 1 in

2. Convert $25.00/feet to cents/cm Relationships $1 = 100 cents 2.54 cm = 1 in 12 in = 1 ft given want Start with what’s given Use this slide as a template for others 1 in $ 25.00 100 cents 1 ft 1 ft 12 in $1 2.54 cm = 82.0 cents/cm

Solving Word Problems using Dimensional Analysis

If you are given multiple numbers in a problem, only one number will be your starting point. The other numbers are relationships that you will use in your problem. If you are given multiple numbers and one of them involves a “/” (e.g. m/s), then always use the “/” as a relationship and start with the other number.

If it helps, change any combination unit into a relationship ex If it helps, change any combination unit into a relationship ex. 0.05mL/s 0.05mL = 1 s

Given: Want: Relationships: 0.05mL/s 1 day ____ Liters 0.05mL = 1 sec EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day? Given: Want: Relationships: 0.05mL/s 1 day ____ Liters 0.05mL = 1 sec 1000mL = 1 L 60 sec = 1 min 1 day = 24 hr 1 hr = 60 min

1 L 1 day 24 hr 60 min 60 s 0.05 mL 1 1 hr 1000 mL 1 day 1 min 1 s Relationship EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day? want given Relationships 0.05 mL = 1 s 60 min = 1 hr 1000mL = 1 L 24 hr = 1 day 60s = 1 min Start with what’s given Use this slide as a template for others 1 L 1 day 24 hr 60 min 60 s 0.05 mL 1 1 hr 1000 mL 1 day 1 min 1 s = 4.32 L

Finally, note dimensional analysis can be used anytime you can say something is equal to something else. It does not have to involve standard conversion factors.

Given: Want: Relationships: 2.5 hours ____ feet 24 frames = 1 sec EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in ft) for a 2 ½ hr movie? Given: Want: Relationships: 2.5 hours ____ feet 24 frames = 1 sec 1 hr = 60 min 1 in = 2.54cm 1 frame = 1.9cm 1 min = 60 sec 1 ft = 12 in

2.5 hr 60 min 60 s 24 frames 1in 1 ft 1 1 min 1 hr 1 s 12 in 1 frame EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in feet) for a 2 ½ hour movie? Relationship relationship want want given Relationships 24 frames = 1 s 1 frame = 1.9cm 1 hr = 60 min 60 s = 1 min 1in = 2.54 cm 1 ft = 12 in Use this slide as a template for others Start with what’s given 2.5 hr 60 min 60 s 24 frames 1.9 cm 1in 1 ft 1 1 min 1 hr 1 s 12 in 1 frame 2.54 cm = 13464.6 ft

Given: Want: Relationships: 10 gallons ____ trips 60 mi = 1 gal 1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas? Given: Want: Relationships: 10 gallons ____ trips 60 mi = 1 gal 1 trip = 3.5km 1000m = 1km 1 mile = 1609.3 m

10gal 60 mi 1609.3 m 1 km 1 trip 1 1 mi 1 gal 1000m 3.5 km = 276 trips 1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas? Relationship relationship want given Relationships 60 miles = 1 gal 1 trip = 3.5 km 1 mi = 1609.3m 1000m = 1km Start with what’s given 10gal 60 mi 1609.3 m 1 km 1 trip Use this slide as a template for others 1 1 mi 1 gal 1000m 3.5 km = 276 trips

Given: Want: Relationships: 1 day ____ kg 1 sec = 2500g 1kg = 1000g 2. Every second 2500 g of sulfuric acid flows out of a pipe. How many kg of sulfuric acid will flow in 1 day? Given: Want: Relationships: 1 day ____ kg 1 sec = 2500g 1kg = 1000g 60 s = 1 min 60 min = 1 hr 24 hrs = 1 day

1 day 24 hr 60 min 60 s 2500g 1 kg 1 1 hr 1 day 1 min 1 s 1000g 2. Every second 2500 g of sulfuric acid flows out of a pipe. How many kg of sulfuric acid will flow in 1 day? Relationship want given Relationships 1 s = 2500g 60s = 1 min 1000g = 1kg 60 min = 1 hr 24 hr = 1 day Start with what’s given 1 day 24 hr 60 min 60 s 2500g 1 kg Use this slide as a template for others 1 1 hr 1 day 1 min 1 s 1000g = 216000 kg

Tips for studying Try doing the review without using the conversion sheet Quiz yourself with the conversions Do extra practice problems (your textbook may have some)