CHEM 1305: Introductory Chemistry Basic Science Skills From Chapter 1, PSS and 2 Textbook Introductory Chemistry: Concepts and Critical Thinking Seventh Edition by Charles H. Corwin
Measurements In chemistry, the metric system is used to express a measurement Unit of length: centimeter (cm) Unit of mass: gram (g) Unit of volume: milliliter (ml) Measurements require the use of an instrument, every measurement has a degree of uncertainty 2
Length Measurements Ruler A: ten 1-cm divisions Ruler B: ten 1-cm divisions AND ten 0.1-cm subdivisions Ruler A has more uncertainty: candy cane is 4.2 cm Ruler B has less uncertainty: candy cane is 4.25 cm 3
Mass Measurements The mass of an object is a measure of the amount of matter it contains The term weight is often used instead of mass, but the two terms are different weight is affected by gravity and mass is not The measurement of mass always has uncertainty and varies with the balance An electronic balance (c) may weigh a sample to 0.001 of a gram, thus its mass has an uncertainty of ±0.001 g 4
Volume Measurements The amount of space occupied by a solid, gas, or liquid is its volume There are several instruments for measuring volume, including: Graduated cylinder Syringe Buret Pipet Volumetric flask 5
Significant Digits In a recorded measurement, all numbers are significant digits, which can be referred to as significant figures or sig. figs. that express the uncertainty in the measurement To determine the number of significant digits, count the numbers from left to right, starting with the first nonzero digit two significant digits three significant digits four significant digits 6
Exact Numbers All measurements have uncertainty, so a measurement is never an exact number We can obtain exact numbers when counting items For example, in the photo there are exactly seven coins this is not a measurement, thus the concept of significant digits does not apply 7
Placeholder Zeros A measurement may contain a placeholder zero to properly locate the decimal point if the number is less than 1, a placeholder zero is never significant Example: 0.5 cm, 0.05 cm, and 0.005 cm each contain only one significant digit If the number is whole (no decimal point seen) and greater than 1, we assume that placeholder zeroes are not significant Example: 50 cm, 500 cm, and 5000 cm each contain only one significant digit With a decimal point, the zeros become significant: 50.0 cm has three significant digits, 50.0 cm is an exact reading (it is not 49.9 cm) 8
How Many Significant Digits in Each Example? 760 ml...2 final zero is a placeholder 4.3267 cm 12.920 s...5...5 final zero is NOT a placeholder 0.0000862 ml...3 placeholder zeroes, properly locates decimal 5.555 min...4 1.0000002 cm...8 zeroes are significant, not placeholders 99 balloons...(exact number) 5000 km 3.00 cm...1 final zeroes are placeholders...3 final zeroes are NOT placeholders 12,345.67 g...7 9
Rounding Off Nonsignificant Digits All numbers from a measurement (except placeholder zeroes) are significant. However, we often generate nonsignificant digits when performing calculations. We eliminate nonsignificant digits through a process of rounding off We round off nonsignificant digits by following three simple rules: 1. If the first nonsignificant digit is less than 5, drop all nonsignificant digits 2. If the first nonsignificant digit is greater than or equal to 5, increase the last significant digit by 1 and drop all nonsignificant digits 3. If a calculation has several multiplication or division operations, retain nonsignificant digits in your calculator display until the last operation. Not only is it more convenient, it is also more accurate. 10
Rounding Off Nonsignificant Digits Example: calculator display reads 12.846239 and the original measurement had only three significant digits The first nonsignificant digit is 4 (12.846239), round to 12.8 Example: calculator display reads 12.856239 and the original measurement had only three significant digits The first nonsignificant digit is 5 (12.856239), round to 12.9 Rounding off with a placeholder zero, example: display reads 151 and the original measurement had only two significant digits Round to 150 (not 15!) Rounding 1068 to two significant digits gives 1100 11
Performing Calculations with Measurements There are different rules for rounding in a calculation, depending on if you add/subtract or multiply/divide If you have a multi-step calculation, do not round until the final answer Be sure to consider how units change when multiplying/dividing!! See the following examples 1 cm 1 cm = 1 cm 2 1 km 1 km 1 km = 1 km 3 1 m 3 1 m = 1 m 2 1 g 1 ml = 1 g/ml 12
Performing Calculations with Measurements For this class, round the final answer to the same number of significant digits given in the problem For example, perform the following calculations and round to the correct number of significant digits: Multiply 2.4 cm by 1.2 cm by 3.7 cm 2.4 cm 1.2 cm 3.7 cm = 10.656 cm 3 Each given value had 2 significant digits round to 11 cm 3 Divide 43.6 g by 22.1 ml 43.6 g 22.1 ml = 1.97285 g/ml Each given value had 3 significant digits round to 1.97 g/ml 13
Exponential Numbers and Powers of 10 An exponent is used to indicate that a number has been multiplied by itself, an exponent is expressed as a superscript For example, 2 2, or (2) (2) = 2 2 and (2) (2) (2) = 2 3 A power of 10 is a number that results when 10 is raised to an exponential power base number 10 n exponent greater than 1 less than 1 14
Scientific Notation Science often deals with numbers that are very large or very small, to avoid this problem, scientific notation is used The decimal is placed after the first significant digit and the size of the number is set using a power of 10 There are two steps to apply scientific notation 1. Place the decimal point after the first nonzero digit in the number, followed by the remaining significant digits 2. Indicate how many places the decimal is moved by the power of 10. When the decimal is moved to the left, the power of 10 is positive. When the decimal is moved to the right, the power of 10 is negative. significant digits D.DD 10 n power of 10 15
Scientific Notation Examples The mass of one mercury atom is 0.000 000 000 000 000 000 000 333 g three significant digits (3.33) and decimal moves 22 places right (10-22 ) in scientific notation format: 3.33 10-22 g There are 40,800,000,000,000,000,000,000 atoms in 1 ml mercury three significant digits (4.08) and decimal moves 22 places left (10 22 ) in scientific notation format: 4.08 10 22 atoms *Note: 333 10-24 and 40.8 10 21 are not in proper scientific notation 16
Calculators and Scientific Notation A scientific calculator has an exponent key (often EXP or EE ) for expressing powers of 10 If your calculator reads 7.45 E-17, the proper way to write the answer in scientific notation is 7.45 x 10-17 To enter the number in your calculator, type 7.45, then press the exponent button ( EXP or EE ), and type in the exponent (17 followed by the +/ key) 17
Convert Between Ordinary Number and Scientific Notation 6.02 10 23 = 602,000,000,000,000,000,000,000 0.000 000 000 881 = 8.81 10-10 1.59 10-4 = 0.000159 3,457,000 = 3.457 10 6 18
Basic Units and Symbols Up until the 1800s, the English system was most commonly used for measurements The metric system was later adopted, as it offers simplicity and basic units the meter (m) for length, the gram (g) for mass, the liter (L) for volume, and the second (s) for time Original metric references: 19
Metric Prefixes The metric system is a decimal system, it uses a prefix to express a multiple or a fraction of a basic unit 20
Metric Conversion Factors A unit equation relates two quantities that are equal For example, 1000 meters = 1 kilometer (1000 m = 1 km), also known as an exact equivalent Further examples: 1 kg = 1000 g 1 s = 1,000,000,000 ns 1 L = 1 10 6 µl A unit factor is the ratio of two equivalent quantities, the numerator and denominator are equivalent ratio can be inverted to reciprocal 1 m = 100 cm unit factors are: 1 m 100 cm and 100 cm 1 m 21
Metric-Metric Conversions The unit analysis method is very effective for the problems found in introductory chemistry Step 1: Write down the unit asked for in the answer Step 2: Write down the given value related to the answer Step 3: Apply unit factor(s) to convert the unit in the given value to the unit in the answer 22
Metric-Metric Conversions Problem: find the mass in grams of a 325 mg aspirin tablet unit 325 mg = g factor 1 g = 1000 mg 1 g 1000 mg or 1000 mg 1 g 1 g 325 mg = 0.325 g 1000 mg 23
Metric-Metric Conversions The mass of Earth is 5.98 10 24 kg. What is the mass in megagrams? given value unit factor 1 unit factor 2 unit in answer 5.98 10 24 1 kg 1000 g 1 Mg 1,000,000 g kg or or =? Mg 1000 g 1kg 1,000,000 g 1 Mg 1000 g 5.98 10 24 1 Mg kg = 5.98 10 21 Mg 1kg 1,000,000 g 24
Metric-English Conversions The United States is the last major world nation to formally adopt the metric system and progress is slow to achieve full compliance Therefore, the following conversions are useful to know: 25
Metric-English Conversions A can of soda contains 12.0 fl oz (1 quart = 32 fluid ounces). What is the volume of soda in milliliters? 1 qt 946 ml 12.0 fl oz = 355 ml 32 fl oz 1 qt If a tennis ball weighs 2.0 oz (16 oz = 1 lb), what is the mass of the tennis ball in grams? 1 lb 454 g 2.0 oz = 57 g 16 oz 1 lb 26
Set Up the Following Conversion Equations An elephant weighs 5,100 kg. What is its mass in pounds? 1000 g 1 lb 5,100 kg = 11,000 lb 1 kg 454 g A television screen measures 42 in. What is the size of the screen in meters? 2.54 cm 1 m 42 in. = 1.1 m 1 in. 100 cm Light travels through the universe at a velocity of 3.00 10 10 cm/s. How many gigameters does light travel per second? 1 Gm 3.00 10 10 1 m cm/s 1 10 9 = 0.300 Gm/s 100 cm m 27
The Percent Concept A percent (symbol %) expresses the amount of a single quantity compared to an entire sample A dime is 10% of a dollar, and a quarter is 25% of a dollar one quantity total sample 100% = N% After 1971, 5 cent coins were composed of both nickel and copper. If a coin contains 3.80 g copper and 1.27 g nickel, what is the percent of copper in the coin? 3.80 g (3.80 + 1.27) g = 0.750 100% = 75.0% 28
Percent Calculations The Moon contains 4.70% iron. What is the mass of iron in a lunar sample that weighs 235 g? mass of iron 235 g 100% = 4.70% mass of iron = 11.0 g A moon sample is found to contain 7.50% aluminum. What is the total mass of the lunar sample if the amount of aluminum is 5.25 g? 5.25 g total mass 100% = 7.50% total mass = 70.0 g 29
Volumes of Solids, Liquids, and Gases A liter (L) is equivalent to the volume occupied by a cube, 10 cm per side Calculated volume of a liter: 1 L = 10 cm 10 cm 10 cm = 1000 cm 3 Recall that 1 L = 1000 ml 1000 cm 3 = 1 L = 1000 ml 1000 cm 3 = 1000 ml Therefore: 1 cm 3 = 1 ml Note in medicine, a cm 3 is often abbreviated as cc 30
Volume by Calculation Volume of a rectangular solid can be calculated if length (l), width (w), and thickness (t) are known l w t = volume The volume of a solid that measures 3 cm by 2 cm by 1 cm is: 3 cm 2 cm 1 cm = 6 cm 3 l w t 31
Volume Calculations A cube is 1.2 cm on each side. What is the volume of the cube in cm 3? In ml? 1.2 cm 1.2 cm 1.2 cm = 1.7 cm 3 1.7 cm 3 = 1.7 ml A windowpane is 0.53 cm thick and 95 cm wide. How tall is the windowpane, assuming its volume is 12,600 cm 3? l 95 cm 0.53 cm = 12,600 cm 3 l = 250 cm 32
Thickness Calculation A sheet of aluminum foil measures 25.0 mm by 10.0 mm and the volume is 3.75 mm 3. What is the thickness of the foil in mm? l w t = volume 25.0 mm 10.0 mm t = 3.75 mm 3 (solve for t): 250. mm 2 t = 3.75 mm 3 3.75 mm t = 3 250 mm 2 t = 0.0150 mm 33
The Density Concept Which weighs more a ton of feathers or a ton of bricks? They have the same mass, but very different volume! cnx.org 34
The Density Concept The density (symbol d) expresses the concentration of its mass Density is defined as the amount of mass per unit volume mass volume = density Different units can be used to express density for solids and liquids usually g/ml or g/cm 3, and for gases usually g/l 35
The Density Concept Identify the liquids and solids Choose from: water ethyl ether chloroform rubber ice aluminum ethyl ether water L 2 chloroform L 3 ice rubber aluminum 36
Density Calculations If a platinum nugget has a mass of 214.50 g and a volume of 10.0 cm 3, what is the density of the metal? mass volume = density 214.50 g 10.0 cm 3 = 21.5 g/cm 3 Carbon tetrachloride is a solvent used for degreasing electronic parts. If 25.0 ml of carbon tetrachloride has a mass of 39.75 g, what is the density of the liquid? 39.75 g 25.0 ml = 1.59 g/ml 37
Density Calculations What is the volume in ml of 75.5 g of liquid mercury (d = 13.6 g/ml) 75.5 g V ml = 13.6 g/ml V = 5.55 ml A 1.00-in cube of copper measures 2.54 cm on a side. What is the mass in grams of the copper cube (d = 8.96 g/cm 3 )? V = (2.54 cm)(2.54 cm)(2.54 cm) = 16.4 cm 3 M g 16.4 cm 3 = 8.96 g/cm 3 M = 147 g 38