Problem Solving in Chemistry Dimensional Analysis Used in _______________ problems. *Example: How many seconds are there in 3 weeks? A method of keeping track of the_____________. Conversion Factor A ________ of units that are _________________ to one another. *Examples: 1 min/ ___ sec (or ___ sec/ 1 min) ___ days/ 1 week (or 1 week/ ___ days) 1000 m/ ___ km (or ___ 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. In other words, the “Unknown” unit will go on _____ and the “Given” unit will go on the ___________ of the ratio. conversion units ratio equivalent 60 60 7 7 1 1 top bottom

If your units did not ________ ______ correctly, you’ve messed up! How to Use Dimensional Analysis to Solve Conversion Problems Step 1: 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 figure out. Step 3: Identify the ____________ _________. Sometimes you will 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, __________ all the numbers on top of your ratios, and ____________ by all the numbers on bottom. Given Unknown conversion factors multiply divide If your units did not ________ ______ correctly, you’ve messed up! cancel out

How many hours are there in 3.25 days? Practice Problems: How many hours are there in 3.25 days? (2) How many yards are there in 504 inches? (3) How many days are there in 26,748 seconds? 24 hrs 3.25 days 78 hrs x = 1 day 1 ft 1 yard 504 in. 14 yards x x = 12 in. 3 ft 1 min 1 hr 1 day 26,748 sec 0.30958 days x x x = 60 sec 60 min 24 hrs

Converting Complex Units A complex unit is a measurement with a unit in the _____________ and ______________. *Example: 55 miles/hour 17 meters/sec 18 g/mL To convert complex units, simply follow the same procedure as before by converting the units on ______ first. Then convert the units on __________ next. 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) (2) The density of water is 1.0 g/mL. What is the density of water in units of lbs/gallon? (2.2 lbs = 1 kg) (3.78 L = 1 gal) (3) Convert 33,500 in2 to m2 (5280 ft = 1609 m) (12 inches = 1 foot) numerator denominator top bottom 330m 1 mile 3600 sec 738 miles/hr x x = sec 1609 m 1 hr 1.0 g 1 kg 2.2 lbs 1000 mL 3.78 L 8.3 lbs/gal x x x x = mL 1000 g 1 kg 1 L 1 gal 1 ft 2 1609 m 2 33,500 in2 21.6 m2 x x = 12 in. 5280 ft