Chapter 2: Measurements and Problem Solving

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1 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e 1 Chapter 2: Measurements and Problem Solving Read Chapter 2, work problems. Look over the lab assignments before the lab. Keep up with the online MasteringChemistry assignments and due dates. Measurements: Scientific measurements need to be understood by many and must include significant number values with units. If the temperature outdoors is 32, would you consider that hot or cold? That depends on the unit: 32 C is equivalent to 90 F which is a hot day, while 32 F is the freezing temperature of water to ice. Significant numbers include all the numbers that are know with certainty plus one more estimated number. The last reported digit is uncertain or estimated. Reporting a global warming of 0.6 C, really means 0.6 C + or 0.1 (between 0.5 C to 0.7 C) If you solve for the density (mass/volume) of a liquid that you measure to have a mass of 2.0 g while occupying 3.0 ml how many numbers should the answer have? a) 0.7 g/ml, b) 0.67 g/ml, c) g/ml, d) g/ml Scientific Notation: Writing Large and Small Numbers Scientific Notation removes the place holding zeros. Move the decimal to obtain a number between 1 to 10 (one digit) followed by a decimal and include only the significant numbers Multiply the number by 10 raised to an exponent. #.### x 10 # 141,000 sec = 1.41 x 10 5 sec m = 5.61 x m

2 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e 2 Uncertainty in Measurement: Inexact (has uncertainty, last digit is estimated) Exact (definitions i.e. 1 ft = 12 in, 1 in. = 2.54 cm, or whole items i.e. number of students enrolled) Precision (measurements agree with each other) Accuracy (measurement agrees with true value) Significant Figures: Significant Figures-only the last digit is uncertain, others known with certainty. When recording experimental measurements you always want to include all known numbers plus one estimated digit. Do not round off known measured values. Rules for significant figures: Exact numbers Numbers 1 through 9 (nonzero) Leading zero Captive zero between nonzero Trailing zero with decimal Trailing zero without decimal Unlimited significance Significant Never significant Significant Significant Uncertain 1000mm = 1 m g kg x 10 8 atoms x 10 4 s 1400 miles Significant Figures in Calculations: 1. Addition and Subtraction-minimum significant decimal places to the right taken 2. Multiplication and Division-least number of significant numbers 3. Follow order of operations you have learned in math courses Rounding Numbers: Remove all nonsignificant numbers. Less than 5 round down (drop it), when 5 or more round up. When calculating multiple steps, do not round until the final answer.

3 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e 3 Units of Measurement: SI Units (Systeme International d Unites) chosen by international agreement in 1960 based on the metric system. This has become the standard system for scientific measurements Important SI Base Units Physical Quantity Unit Abbreviation Mass kilogram kg Length meter m Time second s Temperature Kelvin K Amount mole mol Volume is derived by cubing a length; milliliter ml = cm 3 cubic centimeter SI Prefix Multipliers; Bold ones are common in Chemistry Prefix Abbrev. Meaning Example Tera T Terabyte = 1 x bytes Giga G Gigabyte = 1 x 10 9 bytes Mega M Megameter = 1 x 10 6 meter kilo k km = 1 x 10 3 m unit - 1 deci d dm = 1 m centi c cm = 1 m milli m mm = 1 m or 1 mm = m micro m = 1 m or 1 m = 1 x10-6 m nano n nm = 1 m pico p pm = 1 m femto f fm = 1 m

4 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e 4 Common Conversions; more in textbook Length 2.54cm = 1 inch 1 km = mi Mass g = 1 pound (lb) 1 kg = pounds (lbs) Volume 1 ml = 1 cm 3 = 1 cc 946 ml = 1 qt Temperature C = K -273 F = 1.8( C) + 32 K = ( C) C = [ F 32]/(1.8 ) Energy J = 1 calorie 1 food Calorie = 1 kcal Dimensional Analysis: Aids problem solving using conversion factors/definitions A conversion factor or equivalence is multiplied as 1, changing the number and units, without changing the real value. Units are multiplied, divided, and canceled like any other algebraic quantities. Using units as a guide to solving problems is called dimensional analysis. Always write every number with its associated unit. Always include units in your calculations, dividing them and multiplying them as if they were algebraic quantities. Do not let units disappear. Units must flow logically from beginning to end. Multiple Step Conversions and Conversions taken to a Power (squared, cubed): At times a problem may use several conversion factors in one problem. In this case continue the solution map and solve it as one problem. When squared, must square both the number and unit When cubed, number and unit must be cubed

5 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e 5 Problem Solving: Try this: 1) Identify the starting point (Write given quantity and units) 2) Identify the end point (Write down units to find) 3) Devise a way to get from the starting point to the end point using what is given as well as what you already know or can look up (Write down appropriate conversion factors or equations) 4) You can use a solution map to diagram steps and solve the problem 5) Round the answer to correct significant digits 6) Check/Estimate the answer, does it make sense? 1) Convert ml to quarts 2) The Earth s surface area is 197 million square miles. What is the value in square kilometers? Density: Density = Mass/Volume For liquids/solids: units are generally g/ml or equivalently g/cm 3 For gases: density units are generally g/l Calculate volume as l x w x h or by displacement of a liquid Density can be used as a conversion factor to solve for mass or volume given the other.

6 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e 6 Try this: A titanium bicycle frame contains the same amount of titanium as a titanium cube measuring 6.8 cm on a side. Use the density of titanium to calculate the mass in kilograms of titanium in the frame. What would be the mass of a similar volume frame composed of iron? More Practice Problems: 1. One lead (Pb) atom has a mass of g. Express this in proper scientific notation. 2. Round to 3 significant digits a) g b) 8,973,641 ml c) x 10-5 moles 3. Perform the calculations a) (4.62)(75.234) ( ) = b) ( ) 2 x ( 4.29 x 10 4 ) = 4. Convert 486 m to km 5. Convert 8.22 x 10 2 nanoliters/min into units of quarts/year. 6. A student finds that the weight of an empty beaker is g. She places a solid in the beaker to give a combined mass of g. To how many significant figures is the mass of the solid known? 7. A 3.00 quart container weighs 302 grams when empty. When it is filled with liquid, the container weighs kilograms. What is the density of the liquid in g/ml? 8. Describe the difference between experimental data which is accurate and data which is precise. Give examples. 9. What is the volume of 50.0 grams of an object whose density is g/ml?

7 C h 2 : M e a s u r e m e n t s a n d P r o b l e m S o l v i n g P a g e Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics industry. A particular alloy with a density of 8.70 g/cm 3 and containing 0.024% silicon by mass is used to make a rectangular plate that is 30.0 cm long, 17.0 cm wide and 0.30 cm thick. a) What is the volume of the alloy? b) What is the mass of the alloy? c) What is the mass of just the silicon in the sample? 11. In 1999, NASA lost a $94 million Mars orbiter because two groups of engineers failed to communicate to each other the units that they used in their calculations. Consequently, the orbiter descended too far into the Martian atmosphere and burned up. Suppose that the Mars orbiter was to have its orbit at 155 km and one group of engineers specified this distance as m and a second group of engineers programmed the orbiter to go to ft. a) Convert ft to kilometers and determine how low in km units the probe was mistakenly programmed to orbit? b) Solve for the difference in kilometers between the two altitudes? Practice Problems: (ANSWERS) x g 2. a) 3.50 g b) 8.97 x 10 6 ml c) 1.68 x 10-5 moles 3. a) 14.1 b) 3.96 x km quarts/year g; answer has 4 significant figures g/ml 8. Precision (measurements agree with each other). Accuracy (measurement agrees with true value). You may want to check the weight of a suitcase so you will not be charged extra for too much baggage before going on an airline flight. You may weigh your suitcase on the same bathroom scale several times and find the numbers agree with each other (Precision). If the bathroom scale always reads 5 pounds lighter that the true value you will not be accurate ml 10. a) 153 cm 3 volume b) 1330 g mass of the whole alloy c) 0.32 g mass of just the silicon 11. a) 4.72 x 10 4 km b) 1.08 x 10 5 km