LS 6.1 : 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) Sometimes the conversion factors are provided to you, and other times, the conversion factors are determined by reading the information given in the problem. (See practice problems for examples.) conversion units ratio equivalent 60 60 7 7 1 1

If the 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 ____________ _________. Step 4: By using these conversion factors, plan 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 the 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) Convert 55 miles per hour into miles per minute? 24 hrs 3.25 days 78 hrs x = 1 day 1 ft 1 yard 504 in. 14 yards x x = 12 in. 3 ft 55 miles 1 hr x 0.9166666 miles/min ≈ 0.92 miles/min = 1 hr 60 min Round off your answers!!

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

Find the conversion factors in each of the following word problem. If we want to buy a single head of cabbage that weighs 12 ounces. How many dollars will the head of cabbage cost if the price is 5 cents per pound? (16 ounces = 1 pound) Jane is buying pizza for class. Each person will get 2 pieces of pizza. There are 30 kids in the class. Each pizza costs $5 and the pizza will be cut into 8 slices. How many pizzas will Jane need to buy?