Chemistry: Unit 2 Chapter 3 Problem Solving in Chemistry

Three-step Problem Solving Approach Analyze – determine how you will find the solution Calculate – perform the calculation, this may involve measurements Evaluate – does the answer make sense, and did you use correct units and significant digits

Ex. What is the mass, in grams, of a piece of lead that has a volume of 19.84 cm3? Analyze: list the knowns and the unknown. Volume = 19.84 cm3 Density = mass/ volume Density = 11.4 g/cm3 Mass = ? Calculate: solve for the unknown. D = m / V so… m = D x V Mass = 19.84 cm3 x 11.4 g/cm3 = 226 g Evaluate: does the result make sense? Would a piece of lead that is about the size of an eraser have a mass of 226 grams? Yes!

Practice: Solve the following using correct significant figures. 7.823 x 15.76 = 892 + 173 + 56 = 123.3 28459

Practice What is the mass, in grams of a piece of lead that has a volume of 8.73 cm3? Knowns V = 8.73 cm3 D = 11.4 g/cm3 m = VD Unknowns m = ? To solve: m = (8.73 cm3)(11.4 g/cm3) m = 99.522 g = 99.5 g

Practice: What is the volume, in cm3, of a sample of cough syrup that has a mass of 20.0g and a density of 11.4 g/cm3? Knowns M = 20.0 g D = 11.4 g/cm3 V = M / D Unknowns V = ? To Solve V = 20.0 g 11.4 g/cm3 V = 1.75 cm3

Dimensional Analysis To convert from one unit to another, we will use a problem solving method called dimensional analysis. This method uses equalities or conversion factors to change one unit into another. Example: If someone gives you 32 quarters, how many dollars do you have? How did you know this?

How many inches are there in 4 ft? What did you have to know in order to figure that out? 1 ft = 12 inches 1 ft = 12 inches is a conversion factor. It can be written as a fraction where the numerator and the denominator are equivalent but have different units. For example, we can use the following conversion factors for changing between inches and feet: 12 inches 1 foot 1 foot or 12 inches

Some Handy Conversions Let’s look at a meter stick and list all the conversions we can get from it. We can say that one meter is equal to… 10 dm 100 cm 1000 mm Now let’s use those prefixes to figure out how we can modify units for liters. A liter should contain _____ deciliters A liter should contain _____ centiliters A liter should contain _____ milliliters Hand out metersticks so that students can discuss.

Practicing with Dimensional Analysis 70 kg = ____ g 63 cm = ____ mm   2.5 L = _____ mL 1 m2 = _____ cm2 Work out each one with students. Have them list out conversion factors before you begin, then let them arrange them so that units are cancelled.

Practice: How many atoms are in 7. 00g of gold. (1 atom of gold = 3 Practice: How many atoms are in 7.00g of gold? (1 atom of gold = 3.271 x 10-22 g) 7.00 g gold 1 atom gold = 2.14 x 1022 atoms gold 3.271 x 10-22 g gold

Bellwork, Thursday, September 12, 2012 Complete the following conversion: (Show you work using dimensional analysis) 45.00 m = _____________ mm 5.34 x 10-5 L = ______________ mL 7.00 x 105 g = ______________ mg

Wednesday’s Homework Write at least five conversion factors using the following equalities. 1000 mg = 1 g = 1 ml water = 0.001 L water Use a meter stick to fill in the following: _1_meter = ______ cm = _______ km = ______mm A filled flask that can hold 158.238 g of water at 4°C can hold only 127.339 g of ethanol. What is the density of ethanol at 4°C? (hint: water’s density is 1.0 g/mL. You may need to use a proportion!) If 100 cm = 1 m, how many cm3 are in 1 m3? Find the mass of a 5.3 mL sample of lead in kilograms if the density of the sample is 11. 34 g/mL.

Some dimensional analysis problems require several steps  How many seconds are in 5.0 days? 5.0 days 24 hours 60 min 60sec = 430,000 sec 1 day 1 hour 1 min How many students are in a 10 room building if each classroom contains 25 students? 10 rooms 25 students = 250 Students 1 room

Convert 423 m/sec to km/min. An example of this would be the conversion of speed in miles per hour to meters per second.  An object was traveling at 400. m/min. What was its speed in cm/s? 400. m 100 cm 1 min = 667 cm/sec 1 min 1 m 60sec Convert 423 m/sec to km/min. 423 m 1 km 60sec = 25.4 km/min 1 sec 1000 m 1 min

The density of manganese is 7. 21 g/cm3 The density of manganese is 7.21 g/cm3. What is the density of manganese expressed in units of kg/m3? 7.21 g 1 kg 1003 cm3 = 7210 kg/m3 1 cm3 1000g 13 m3

Bellwork: Friday, September 13 A cheetah can run 112 km/h over a 100 m distance. What is this speed in meters per second? The density of dry air measured at 25oC is 1.19 x 10-3g/cm3. What is the volume of 50.0g of air?

Thursday Homework Which gas is cheaper based on the sales prices below? (show your calculations!) 1 L = 0.261 gal Gas A: $2.53/gallon Gas B:$0.45/ liter Set up the equalities for the story and solve. Marie Currie wanted to research an unknown radioactive element (Sneezium Sz) that cost $534 per gram. Sneezium has a density of 55.67g/cm3, if Marie needs 0.35 L of Sneezium, how much money should she need? (hint: 1 cm3 = 1 mL and this will be a 4 step problem)

Bellwork: Monday, September 16 Earth is approximately 1.5 x 108 km from the sun. How many minutes does it take light to travel from the sun to Earth? The speed of light is 3.0 x 108m/s. Convert 7.86 g/cm2 to milligrams per square millimeter

Bellwork: Tuesday, Septmeber 17 The density of water is 1.0g/mL. How many deciliters will fill a 0.5 L bottle? Fill in the following table: mg g cg kg 28.3 6.6 x 103 2.8 x 10-4

Monday’s Homework Fill-in the following equalities Anna wants to buy a one carat diamond. One carat equals 200 mg. If a diamond is 0.600 carat, what is the mass of the diamond in ounces? 1 kg = 2.205 pounds 1 pound = 16 ounces The speed of a rocket is measured and found to be 145.3 m/sec. What is the rocket’s speed in km/hr? The moon is 250,000 miles away. How many feet is it from earth? _________ m = 1 km _________ cL = 1 L _________ mg = 1 g _______ sec = 1 min _______ cm3 = 1 ml _______ cm3 = 1 m3