1 Chapter 3 Problem Solving and Conversion Factors

2 Word Problems n The laboratory does not give you numbers already plugged into a formula n You have to decide how to get the answer. n Like word problems in math. n The chemistry book gives you word problems.

3 Problem solving 1 Identify the unknown. Both in words and what units it will be measured in. Both in words and what units it will be measured in. May need to read the question several times. May need to read the question several times. 2 Identify what is given Write it down if necessary. Write it down if necessary. Unnecessary information may also be given Unnecessary information may also be given

4 Problem solving 3 Plan a solution The “heart” of problem solving The “heart” of problem solving Break it down into steps. Break it down into steps. Look up needed information. Look up needed information. Tables Tables Formulas Formulas Constants Constants Equations Equations

5 Problem solving 4 Do the calculations – math (algebra) 5 Finish up Sig Figs Sig Figs Units Units Check your work Check your work Reread the question, did you answer it Reread the question, did you answer it Is it reasonable? Is it reasonable? Estimate Estimate

6 Dimensional Analysis n Dimension = unit n Analyze = solve n Using the units to solve the problems. n If the units of your answer are right, chances are you did the math right.

7 Initial and Final Units 1. A person has a height of 2.0 meters. What is that height in inches? Initial unit = mFinal unit = _______ Initial unit = mFinal unit = _______ 2) Blood has a density of 0.05 g/mL. If a person lost 0.30 litres of blood at 18°C, how many grams of blood would that be? Initial = litresFinal unit = _______

8 Conversion factors n “A ratio of equivalent measurements” n Start with two things that are the same one meter is one hundred centimeters one meter is one hundred centimeters n write it as an equation 1 m = 100 cm 1 m = 100 cm n can divide by each side to come up with two ways of writing the number 1

9 Conversion factors n Called conversion factors because they allow us to convert units. n really just multiplying by one, in a creative way.

10 Conversion factors 100 cm1 m= 100 cm = 1

11 Conversion factors 1 1 m= 100 cm

12 Conversion factors 1 1 m= 100 cm =1 m

13 Conversion factors 1 1 m= 100 cm = 1 m 1

14 Conversion Factors The units of measurement are not always convenient dimensions and it may become necessary to change units. In a lab the distance could only be measured in cm. To calculate the speed the cm must be converted to m without changing the value of the measurement. Distance in cm x [conversion factor] = distance in m

15 Conversion Factors The only number that can multiply any other number without changing the number’s value is 1. The conversion factor is a ratio. The value of the ratio is 1. For the ratio to have a value of one the top term has to equal the bottom term. Start with 1255cm, want to find the number of m, then: By definition 1m = 100 cm 1 m = 1 100cm 1255 cm x1 m = 12.55m 100cm The conversion factor must cancel the present unit and introduce the desired unit

16 Conversion factors n A unique way of writing the number 1 n In the same system they are defined quantities so they have unlimited significant figures n Equivalence statements always have this relationship n big # small unit = small # big unit n 1000 mm = 1 m

17 Write the conversion factors for the following n kilograms to grams n feet to inches (1 foot = 12 inches) n qt. = 1.00 L

18 How many minutes are in 2.5 hours? n Initial unit n 2.5 hr n Conversion Final n factor unit n 2.5 hr x 60 min = 150 min n 1 hr n cancel Answer (2 SF)

19 Learning Check n A rattlesnake is 2.44 m long. How long is the snake in cm? n 1) 2440 cm n 2)244 cm n 3)24.4 cm

20 Solution n A rattlesnake is 2.44 m long. How long is the snake in cm? n 2)244 cm n 2.44 m x 100 cm = 244 cm n 1 m

21 Learning Check n How many seconds are in 1.4 days? n Unit plan: days hr min seconds 2 SF Exact 1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min 1 day 1 hr 1 min = 1.2 x 10 5 sec = 1.2 x 10 5 sec

22 Unit Check n What is wrong with the following setup? n 1.4 day x 1 day x 60 min x 60 sec n 24 hr 1 hr 1 min

23 Steps to Problem Solving n Read problem n Identify data n Write down a unit plan from the initial unit to the desired unit n Select conversion factors n Change initial unit to desired unit n Cancel units and check n Do math on calculator n Give an answer using significant figures

24 Learning Check n If the ski pole is 3.0 feet in length, how long is the ski pole in m? 2.54 cm = 1.00 inch12 inches = 1 foot

25 Solution unit plan ft in cm m n 3.0 ft x 12 in x 2.54 cm x 1m = 0.91m n 1 ft 1 in. 100 cm

26 The solutions for some problems contain multi-steps (require more than one calculation to solve). Using Dimensional Analysis can solve this type of problem. Dimensional Analysis 1. Identify the given or known data (information). 2. Identify the unknown. 3. Plan the solution or calculations by either: i.setting up a series of conversion factors OR ii.using a formula. 4. Check your work by canceling out units. 1. Calculate the number of seconds of Chemistry class there is in a week. 1. Calculate the number of seconds of Chemistry class there is in a week. 2. The density of gold is 19.3g. cm 3 cm 3 What is the density of gold expressed inkg? m 3 m 3

27Practice Use conversation factors to solve the following: A pain relief tablet contains 325 mg of ASA. There are 80 tablets in the package of tablets. (a) What is the mass of ASA in grams for each tablet? (b) What is the total mass, in grams, of ASA in the package? (c) A person is permitted to take 1950 mg of ASA per day. How many days will this package last?

28 n T n H n E n N n D

29 What are they good for? n We can multiply by one creatively to change the units. n 13 inches is how many yards? n 36 inches = 1 yard. n 1 yard = 1 36 inches n 13 inches x 1 yard = 36 inches

30 What are they good for? n We can multiply by one creatively to change the units. n 13 inches is how many yards? n 36 inches = 1 yard. n 1 yard = 1 36 inches n 13 inches x 1 yard =0.36 inches 36 inches

31 Dimensional Analysis n A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm) n in meters? n A race is 10.0 km long. How far is this in miles? – 1 mile = 1760 yds – 1 meter = yds) n Pikes peak is 14,110 ft above sea level. What is this in meters?

32 Example of Problem Solving n How much heat is needed to raise the temperature of 56.8 g of iron by 65ºC? 1 Identify the unknown Heat - calories. Heat - calories. 2 Knowns Mass, Change in temperature Mass, Change in temperature

33 Example of Problem Solving 3 Plan a solution Formula Heat = SH x mass x  T Formula Heat = SH x mass x  T look up SH of Iron = cal/gºC look up SH of Iron = cal/gºC 4 Do the calculations heat = cal/gºC x 56.8 g x 65ºC heat = cal/gºC x 56.8 g x 65ºC heat = cal/gºC x g x ºC heat = cal/gºC x g x ºC heat = 390 cal heat = 390 cal 5 Check your work.

34 Dimensional Analysis n Another measuring system has different units of measure. 6 ft = 1 fathom 100 fathoms = 1 cable length 10 cable lengths = 1 nautical mile 3 nautical miles = 1 league n Jules Verne wrote a book 20,000 leagues under the sea. How far is this in feet?