Chapter 1 Introduction: Matter and Measurement.

Transcription

1 1.1 The study of chemistry What is chemistry? Chapter 1 Introduction: Matter and Measurement. Briefly define the following terms: Matter. Element. Atom. Molecule. 1.2 Classifications of Matter By state: Property / State Solid Liquid Gas Shape Volume Compressibility By composition (see the handout): Pure substances Matter Mixtures Elements Compounds Homogeneous Heterogeneous 1

2 1.3 Properties of Matter What are properties and where do they come from? Properties can be Physical or Chemical (does the identity change?). Properties can also be Extensive or Intensive (does size matter?). Types of changes: Physical vs Chemical (does the identity change in the process?). Concepts we need from Math Scientific Notation D. DD 10 n [Just one digit before the decimal 10 n ] 1 D. DD < 10 ; n (the power) can be positive or negative Standard Format Q Write in scientific notation x x 10-3 Scientific Notation Q Write as a regular number (standard notation) x x x 10-3 What do we need to do to compare numbers in scientific notation? Q Which number is larger on each pair? 5.22x10-7 vs 9.87x10-8 ; 9.87x10-3 vs 1.43x10 2 ; 6.31x10-5 vs 9.87x10-5 2

3 Exponent Rules (See Appendix A.1) a n a m = a n+m ; = 2 7 = 128 ; a n b n = (a b) n ; = (3 4) 2 = 144 a n a m = an m ; = 25 3 = 2 2 = 4 ; a n b n = (a b ) n ; 4 3 /2 3 = (4/2) 3 = 8 (b n ) m = b n m ; (2 3 ) 2 = 2 6 = 64 ; b n = 1 b n ; 2 3 = = b 0 = 1 ; b 1 = b ; 1 n = 1 Simplifying Scientific Notation ( ) ( )( ) = (2.6)(10 5 )(9.2)(10 13 ) = (2.6)(9.2)( ) = (2.6)(9.2)(10 8 ) = = ( )(10 8 ) = ( ) = Simplifying Scientific Notation ( ) ( ) ( ) = ( )( ) = (0.43)( ) = = ( )10 1 = Your turn. Q. Without using your calculator, find:

4 Addition and Subtraction To add (or subtract) two numbers in scientific notation, be sure that the exponents in each number are the SAME. In general: (a 10 n ) + (b 10 n ) = (a + b) 10 n ; (a 10 n ) (b 10 n ) = (a b) 10 n Changing the Exponent (smaller) = = = 5, = 51, = 514,000 Changing the Exponent (larger) = = = = = Example ( ) + ( ) = ( ) + ( ) = ( ) 10 4 = = Example ( ) ( ) = ( ) ( ) = (3 0.22) 10 2 = Example (backwards) ( ) ( ) = ( ) ( ) = (30 2.2) 10 3 = = Your turn. Q. Without using your calculator, find: Why do we need to know this if the calculator does it for us? Avoid writing just whatever the calculator displays on the screen without thinking If your answer is outrageously wrong, you won t get points for it Why? 4

5 Q. Estimate the answer to: 1.4 Units of Measurement What is the difference between a qualitative and a quantitative observation? Which are the two ingredients a measurement must possess? The Equation of the Line Length L [cm] L(cm) = ml(in) + b m = y 2 - y 1 x 2 - x cm - 0cm = = 1in - 0in 2.54 cm in b = 0cm y 2 = 2.54 P 2 (1in, 2.54cm) L(cm) = 2.54 cm in L(in) b = 0 y 1 = 0 P 1 (0cm, 0in) x 1 = 0 x 2 = 1 L [in] 1 in = 2.54 cm The slope of a line is an equivalency (or ratio). 5

6 Example: How many cm are there in 5 inches? How many in are there in 100 cm? L(cm) = cm 2.54 in L(in) 1 in = 2.54 cm 1 in 100cm 2.54cm = 39.4 in L(cm) = 2.54cm 5(in) L(cm) = 12.7cm 1 in Factor label method. Temperature T [ F] y 2 = 212 P 2 (100 C, 212 F) m b = T( F) = mt( C) + b 212 F - 32 F = = 100 C - 0 C 32 F F C 1.8 F C 0 C = 32 F y 1 = 32 P 1 (0 C, 32 F) T( F) = 1.8 F C T( C) + 32 F b x 1 = 0 x 2 = 100 T [ C] Units of Measurement Système International d Unités (an agreement). A different base unit is used for each quantity (Check Table 1.4). Prefixes from the Metric System (Why do we use them in the first place?). Memorize Micro to Giga! See the Handout. Table 1.5. Using Prefixes: 1 km = 1000 m 1 cm = 0.01 m or 1 m = 100 cm 1 mm = m or 1 m = 1000 mm 1 μm = 1x10-6 μm or 1 m = 10 6 μm 1 nm = 1x10-9 nm or 1 m = 10 9 μm 6

7 Measuring Length 1 m = 100 cm (1 m 1 yard ) 1 inch = 2.54 cm (Come from equations ) What is the difference between mass and weight? Which one do we measure with a beam balance and a top balance (or analytical balance)? Define Temperature (at the microscopic level): What is the difference between absolute and empirical temperature scales? Empirical Absolute T( ) = T( ) = T(K) 273 K 100 K Volume 1 m 3 = 1000 dm 3 1 dm 3 = 1000 cm 3 = 1 L (1 L 1.06 qt) 1 cm 3 = 1 ml Density Density = Mass (g) Volume (ml or cm 3 ) 7

8 1.5 Uncertainty in Measurements Why is uncertainty ever present? How do we account for it? See the handout on significant figures to get acquainted with the rules you need to follow when working with numbers that have uncertainty and exact numbers; also, follow the rounding rules given. Remember this!! The Last digit written in a measurement is the number that is considered uncertain g A mass between g and g (±0.01 g) g A mass between g and g (± g) Unless it is explicitly given, consider the uncertainty as ± 1 at the relative position of the last significant figure. Q. In each measurement determine: A. # of sig. figs. B. the uncertainty. a lb d g b. 51 ml e g c. 150 m f in Q. Round up each number to the marked digit. 1. 7, , , , Problem 1 Round to the correct number of significant figures. 1) = 2) = 3) = 4) = 8

9 Problem 2 What is the answer using the proper number of significant figures? Accuracy versus Precision, what is the difference? (More about this topic will be addressed at the lab.) 1.6 Dimensional Analysis Factor-Label Method: (Starting quantity) (Conversion factor) = Equivalent quantity given unit desired unit given unit 54 cm = desired unit ; in (2. ) = 183 cm 1 in Conversion factor Conversion factor Treat units as constants in an algebraic expression. 3a 4a = 12a 2 ; 3 in 4 in = 12 in 2 16a 3 4a 2 = 4a ; 16 ft 3 4 ft 2 = 4 ft Be careful! Keep in mind that you cannot add apples and oranges : 2a + 4b = 2a + 4b ; 2 lb + 4 kg = 2 lb + 4 kg If you want to do it, first you need to convert one type of unit into the other: 1 kg = 2.20 lb 2.20 lb 2 lb + 4 kg ( 1kg ) = 2 lb lb = 1 1 lb 10 lb 2 lb ( 1kg 2.20 lb ) + 4 kg = kg + 4 kg = kg 5 kg 9

10 Q. What are the units of "X in the following equations? grams[=](x)(ml) Joules[=](X)(grams)( ) Systematic Approach to Problem Solving 1. Read the problem carefully; you MUST understand the question: What are you trying to find? Identify all quantities given (# s and units). Identify all relationships (explicit and implicit) in the problem. 2. Sketch a strategy (conceptual map) to solve the problem (you don t need to write it!). Each step involves an equation or conversion factor (you may need to work backwards ) 3. Solve the problem following the outlined strategy. Check that units cancel properly. 4. Check your final answer (two ways): Perform a rough estimate (simple problems) Double check your calculations (more complex) You will not get points for answers that are impossible/make no sense. Remember: You must double check what your calculator displays as an answer Using Density in Calculations d = m V (relates two properties) ; V = m d = md 1 ; m = dv Olive oil has a density of 0.92 g/ml. Conversion factors: 0.92 g d = or d 1 = 1 ml 1 ml 0.92 g Q. a. What is the volume of 50 0 g of olive oil? b. What is the mass of 20 0 ml of olive oil? 10

11 Problem 3 Convert 1.76 yd to centimeters. (1 m = yd) Problem 4 Mercury has a density of g/ml it is the densest liquid at room temperature. How many quarts will lbs (mass of the average man) of mercury occupy? ( g = 1 lb; 1 qt = ml) Problem 5 Dextrose is a form of glucose (sugar). Dextrose 5% in water is injected into a vein through an IV to replace lost fluids and provide carbohydrates to the body; therefore, it is used to treat hypoglycemia (low blood sugar), insulin shock, or dehydration. It also given for nutritional support to patients who are unable to eat because of illness, injury or other medical condition. An order reads: Infuse 1.00 L of dextrose 5% in water over 12 hours. With a tubing set of drop factor of 10 (the drop factor is the number of drops per milliliter), what is the rate in drops per minute the tubing should be set up to? 11

12 Problem 6 You have a patient on a Dopamine drip ordered at 10 mcg/kg/min (mcg stands for micrograms). The drip comes as 400 mg/250 ml D5W (D5W stands for a 5% solution of dextrose in water). The patient weighs 75 kg. What is the rate in ml/hr? Round your answer to the nearest tenth. Converting Squared/Cubed units To convert squared or cubed units, we have to square or cube the entire conversion factor (# and unit). Problem 7 How many cubic centimeters are there in a box that measures 2.23 in by in by in? Problem 8 A 2.50 cm x 2.50 cm square piece of platinum (Pt) has a mass of g. Pt has a density of g/cm 3. What is the thickness of the Pt sheet in mm? 12

13 Problem 9 A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 7.50 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm 3. Assume that the wire is a cylinder with volume V = πr 2 h, where r is its radius and h is its height or length. (1 lb = g ; 1 in = 2.54 cm (exactly!) ; 1 ft = 12 in ; 1 m = 100 cm ; 1 m = 1000 mm) Density (a word of caution ) Volumes are not necessarily additive (i.e. the final density may not be the addition of the individual densities). g d Gold = 19.3 cm 3 ; d g Earth = 5.52 cm 3 Problem 10 Brass is an alloy (mixture) principally used for decoration due to its bright gold-like appearance. It is made of copper and zinc, but their proportions can be varied to create a range of brasses with varying properties. Consider a sample of brass that weighs 9.85g and has a volume of 1.13 cm 3. The densities of copper and zinc are 8.94 g/cm 3 and 7.14 g/cm 3, respectively. If the total volume of the piece of brass is the sum of the volumes of the copper and zinc that it contains, calculate the percentage of copper (by mass) in the sample. 13