Ch 4 Problem Solving in Chemistry Dimensional Analysis

Ch. 4 Problem Solving in Chemistry Dimensional Analysis conversion • Used in ________ problems. *Example: How many seconds are there in 3 weeks? • A method of keeping track of the_______. units Conversion Factor ratio of units that are _________ equivalent • A ____ to one another. *Examples: 1 min/ ___ 60 sec (or ___ 60 sec/ 1 min) 7 days/ 1 week (or 1 week/ ___ 7 days) ___ 1000 m/ ___ 1 km (or ___ 1 km/ 1000 m) • Conversion factors need to be set up so that when multiplied, the unit of the “Given” cancel out and you are left with the “Unknown” unit. top and the • In other words, the “Unknown” unit will go on _____ bottom “Given” unit will go on the ______ of the ratio.

How to Use Dimensional Analysis to Solve Conversion Problems • Step 1: Given Identify the “____”. This is typically the only number given in the problem. This is your starting point. Write it down! Then write “x _____”. This will be the first conversion factor ratio. • Step 2: Identify the “______”. This is what are you trying to Unknown figure out. • Step 3: Identify the ______ Sometimes you will conversion _____. factors simply be given them in the problem ahead of time. • Step 4: By using these conversion factors, begin planning a solution to convert from the given to the unknown. • Step 5: When your conversion factors are set up, _____ multiply all the divide numbers on top of your ratios, and ______ by all the numbers on bottom. If your units did not ____ cancel ______ out correctly, you’ve messed up!

Practice Problems: (1)How many hours are there in 3. 25 days? 3. 25 days x 24 hrs = 78 hrs 1 day (2) How many yards are there in 504 inches? 504 in. x 1 ft 12 in. x 1 yard = 14 yards 3 ft (3) How many days are there in 26, 748 seconds? 26, 748 sec x 1 min x 1 hr x 1 day 60 sec 60 min 24 hrs = 0. 30958 days

• Converting Complex Units numerator A complex unit is a measurement with a unit in the _______ and _______. denominator *Example: 55 miles/hour 17 meters/sec 18 g/m. L • To convert complex units, simply follow the same procedure as top first. Then convert the before by converting the units on ______ bottom next. units on _____ Practice Problems: (1) The speed of sound is about 330 meters/sec. What is the speed of sound in units of miles/hour? (1609 m = 1 mile) 330 m x 1 mile x 3600 sec = 738 miles/hr sec 1609 m 1 hr (2) The density of water is 1. 0 g/m. L. What is the density of water in units of lbs/gallon? (2. 2 lbs = 1 kg) (3. 78 L = 1 gal) 1. 0 g x 1 kg x 2. 2 lbs x 1000 m. L x 3. 78 L = 8. 3 lbs/gal m. L 1000 g 1 kg 1 L 1 gal (3) Convert 33, 500 in 2 to m 2 (5280 ft = 1609 m) (12 inches = 1 foot) 2 2 2 33, 500 in x 1 ft x 1609 m = 21. 6 m 2 12 in. 5280 ft