Measurements and Calculations Chapter 2 Chemistry Chapter 2

Scientific Method A logical approach to solving problems by: Observing and collecting data Formulating hypotheses Testing hypotheses, and Formulating theories that are supported by data Chemistry Chapter 2

Observing Using the five senses to gather information Often involves making measurements and collecting data Chemistry Chapter 2

Qualitative data Descriptive Not numerical Example – the sky is blue Chemistry Chapter 2

Quantitative data Numerical Measurable or countable Example – the temperature of the water went up 1 °C Chemistry Chapter 2

System A specific portion of matter in a given region of space Has been selected for study during an experiment or observation Must be defined by the experimenter Chemistry Chapter 2

Formulating hypotheses Hypothesis – testable statement Generalizations about data Basis for making predictions and designing experiments Usually if-then statements Chemistry Chapter 2

Testing hypotheses Doing experiments You must be ready to reject a hypothesis that is proven wrong Chemistry Chapter 2

Theorizing Model – an explanation of how phenomena occur and how data or events are related May include a physical object or drawing May be visual, verbal, or mathematical Theory – a broad generalization that explains a body of facts or phenomena Must predict to be successful Chemistry Chapter 2

Discuss Section Review Page 31 Chemistry Chapter 2

Quantity Something that has magnitude, size, or amount. Chemistry Chapter 2

SI Measurement Le Système International d’Unités Metric system Seven base units – the rest are derived Chemistry Chapter 2

Standards of measurement Objects or phenomena that are of constant value, easy to preserve and reproduce, and practical in size. Note – ten thousand is written 10 000, not 10,000. Some countries use the comma as a decimal point. Chemistry Chapter 2

Mass Measure of the quantity of matter Kilogram is base unit kg Your textbook has a mass of about 1 kg A paper clip has a mass of about 1 g, or 1/1000 of a kg Chemistry Chapter 2

Mass vs. weight Weight is the measure of the gravitational pull on matter. The weight of an object on the moon is 1/6 its weight on earth, but its mass is the same. Chemistry Chapter 2

Length Meter m About 39 inches – width of a doorway 1 km = 1000 m 1 m = 100 cm Chemistry Chapter 2

Other base units Time – seconds – s Temperature – kelvin – K Amount of substance – mole – mol Electric current – ampere – A Luminous intensity – candela – cd Chemistry Chapter 2

Prefixes Used to indicate multiples of 10 See table 2-2 on page 35 Chemistry Chapter 2

Derived SI units Combinations of base units Can also use prefixes Chemistry Chapter 2

Volume Amount of space occupied by an object. SI unit is cubic meters, or m3 We often use cubic centimeters, or cm3 Important – 1 cm3 = 1 mL 1 m3 = 1 000 000 cm3 We also use the liter, or L Equal to 1 cubic dm, or dm3 There are 1000 mL in 1 L Chemistry Chapter 2

Density The ratio of mass to volume Chemistry Chapter 2

Density SI unit is kg/m3 We often use g/mL or g/cm3 in Chemistry g/L or kg/m3 might be used for gases Chemistry Chapter 2

Conversion factors Used to convert from one unit to another A ratio derived from equality Chemistry Chapter 2

Example How many seconds are in 1 day? Chemistry Chapter 2

Example How many centigrams are there in 6.25 kg? Chemistry Chapter 2

Units When doing conversions, keep track of your units. They should cancel out to get units you want at the end. Chemistry Chapter 2

Examples using table Convert 10 cm to m. Convert 25 mL to L. Convert 50 mg to kg. Convert 33 cm3 to mm3. Chemistry Chapter 2

Discuss Section Review Page 42 Chemistry Chapter 2

Accuracy vs. Precision Accuracy – closeness to correct or accepted value Precision – closeness of a set of measurements of the same quantity made the same way See page 44, figure 2-3 Chemistry Chapter 2

Percent error Finds accuracy of a single value or an average value. See sample problem 2-3 on page 45 Chemistry Chapter 2

Reading instruments Estimate the last digit. Example – a ruler is marked to a tenth of a centimeter. Your measurement should be to the nearest hundredth of a centimeter. Example – a thermometer is marked to the nearest degree. Your measurement should be to the nearest tenth of a degree Chemistry Chapter 2

Significant Figures All the digits known in a measurement, plus one that is somewhat uncertain. All nonzero digits are significant Zeros are governed by four rules Zeros between nonzero digits are significant 203 has 3 sig figs 5.0279 has 5 sig figs Chemistry Chapter 2

Significant Figures Zeros in front of all nonzero digits are not significant 0.0035 has 2 sig figs 0.0008 has 1 sig fig Zeros at the end of a number and after the decimal point are significant. 75.000 has 5 sig figs 0.000800 has 3 sig figs Chemistry Chapter 2

Significant Figures Zeros at the end of a number but before the decimal point may or may not be significant. If a zero is just a placeholder, it is not significant. If it has been measured, it is significant. To show all zeros are significant, use a decimal point. To show some are, use scientific notation (tomorrow) 2000 has 1 sig fig 2000. has 4 sig figs Chemistry Chapter 2

How many sig figs? 2.5 2 sig figs 2.50 3 sig figs 250 2.50 x 102 250.0 4 sig figs 0.0025 2 sig figs 0.00250 3 sig figs 0.002501 1-2 min modeling Chemistry Chapter 2

Rounding If the next digit is less than five, round down. 3.044 → 3.04 If the next digit is more than five, round up. 3.046 → 3.05 If the next digit is a five and there are nonzero digits after it, round up 3.0452 → 3.05 If the next digit is a five and not followed by nonzero digits round to the even number 3.045 → 3.04 3.035 → 3.04 Chemistry Chapter 2

Adding or subtracting with sig figs The answer must have the same number of digits after the decimal point as there are in the measurement with the fewest digits after the decimal point. Chemistry Chapter 2

Example Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Round the answer to 1.253 1 min modeling Chemistry Chapter 2

Multiplication and Division The result should have the same number of significant figures as the least number of significant figures in any factor. 1 min instruction Chemistry Chapter 2

Example Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would round our answer to 1.6 1 min modeling Chemistry Chapter 2

Conversion factors Are not considered when finding the number of significant figures. Are exact Chemistry Chapter 2

Discuss How do you round a number that ends in a five if you are rounding to the place before the five? What is the difference between accuracy and precision? How many significant figures are in the answer when you multiply? When you subtract? Chemistry Chapter 2

Scientific Notation Useful when writing very small or very large numbers 696 000 000 m = 6.96 x 108 m 4 000 000 km = 4 x 106 km 0.012 kg = 1.2 x 10-2 kg 0.000 000 000 567 s = 5.67 x 10-10 s Chemistry Chapter 2

Scientific notation The mantissa (number in front) is greater than or equal to 1 but less than 10. Only significant figures are shown. All digits shown are significant figures. 2000 has 1 sig fig 2000. has 4 sig figs 2.0 x 103 has 2 sig figs 2.00 x 103 has 3 sig figs Chemistry Chapter 2

Multiplying in Scientific Notation Multiply the mantissas. Multiply the units. Add the exponents. Chemistry Chapter 2

Example Chemistry Chapter 2

Dividing in scientific notation Divide the mantissas. Divide the units Subtract the exponents. Chemistry Chapter 2

Example Chemistry Chapter 2

Addition and subtraction If the exponents (and units) are the same, you can simply add or subtract the mantissas and keep the exponents and units the same. If the exponents are different, do it on your calculator. Your book shows you how, but most people don’t like to do it that way. If the units are different, you can’t add or subtract. Chemistry Chapter 2

Direct proportions Two quantities are directly proportional if dividing one by the other gives a constant. Graph is a straight line that passes through the origin General forms of the equation: Chemistry Chapter 2

Inverse proportions Two quantities are inversely proportional if their product is constant. Graph is a hyperbola (see page 57) General forms of the equation: Chemistry Chapter 2