Measurements and Calculations

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Presentation transcript:

Measurements and Calculations Chapter 2 Measurements and Calculations

2-1 The 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 Hypothesis – testable statement, if-then Hypotheses not supported by data must be rejected

2-1 Observing and Collecting Data Qualitative data – descriptive, what is it like? The ice water was clear and colorless. Quantitative data – numerical, how much? The ice water was 4˚C. The volume of the ice water was 125 mL.

2-1 System A specific portion of matter in a given region of space that has been selected for study during an experiment or observation. The scientist determines the system. Anything outside of the system is called the surroundings.

2-1 Hypotheses, Models and Theories Scientists form hypotheses – a hypothesis is a testable statement, if-then Scientists test hypotheses – a hypothesis is tested through experimentation. If a hypothesis is not supported by data it must be rejected. If a hypothesis is supported by experimental data, a model is constructed – a model is an explanation of how data and events are related. If a model successfully explains a phenomenon, it may become part of a theory – a theory is a broad generalization that explains a body of facts.

2-2 Units of Measurement Measurements represent QUANTITIES. A quantity is anything that has magnitude, size or amount. Length, width, temperature, mass, area, volume and time are examples of quantities.

2-2 SI Measurement Quantity SI Base Unit length meter (m) mass kilogram (kg) time second (s) temperature kelvin (K) amount of substance mole (mol) electric current ampere (A) luminous intensity candela (cd) SI is the International System – a version of the metric system used by all scientists

2-2 Mass Mass – amount of matter, SI unit is kilogram Based on International Prototype Kilogram – a cylinder of platinum-iridium alloy kept near Paris Scientists also use grams, milligrams

2-2 Weight Weight – measure of gravitational pull on matter, can vary with location because gravity is not the same everywhere, directly proportional to mass Weight can vary. Mass can NOT vary

2-2 Other Base Quantities Length – distance between 2 points, SI base unit is meter, scientists also use decimeter, centimeter, millimeter Temperature – hotness or coldness, average kinetic energy, SI base unit is degree kelvin, scientists also use degree Celsius Time – interval between events, base unit is second

2-2 SI Prefixes

2-2 Derived Units Derived units are formed by combining SI base units Quantity symbol unit unit abbreviation derivation area A square meter m2 length x width volume V cubic meter m3 L x W x H density D kilograms per cubic meter kg/m3 mass/volume Molar mass M kilograms per mole kg/mol mass/amount concentration c moles per liter mol/L amount/volume Molar volume Vm cubic meters per mole m3/mol volume/amount energy E joule J force x length

2-2 Volume Amount of space occupied by an object SI derived unit is cubic meters Scientists often use liters (L) or milliliters (mL) for liquid volume. 1 L = 1 dm3 1 mL = 1 cm3

2-2 Density The ratio of mass to volume Each pure substance has a characteristic density Density can sometimes be used to identify substances. What is the mass of a 12.4 cm3 sample of gold? (Gold’s density is 19.31 g/cm3.)

2-2 Conversion Factors A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other example: 1 m = 10 dm

2-2 Using Conversion Factors Express 5.712 g in milligrams and kilograms

2-2 Using Conversion Factors Express 16.45 m in centimeters and kilometers.

2-2 Using Conversion Factors Express 1500 cm3 in cubic meters.

2-2 Using Conversion Factors Express 15 km/hr in meters per second.

2-2 Using Conversion Factors Express 1.975 g/cm3 in kilograms per cubic meter.

2-3 Accuracy and Precision Accuracy refers to closeness of measurements to correct or accepted value. Precision refers to closeness of measured values to each other.

2-3 Accuracy and Precision The boiling point of acetone is 56.3˚C. student 1: 50.6˚C, 61.7˚C, 51.0˚C student 2: 50.1˚C, 49.9˚C, 50.2˚C student 3: 56.1˚C, 56.5˚C, 56.9˚C Which student was accurate and precise? Which student was only precise but not accurate? Which student was neither precise nor accurate?

2-3 Percent Error Percent error is a measure of accuracy. P.E. = Valueaccepted – Valueexp x 100 Valueaccepted If acepted value is greater than experimental value, PE is positive. If accepted value is less than experimental value, PE is negative.

2-3 Percent Error A student measures the mass and volume of copper and calculates its density to be 8.50g/cm3. The accepted value is 8.92g/cm3. What is the percent error of this measurement?

2-3 Significant Figures Any measurement contains some uncertainty. Scientists use significant figures to show how certain they are of a measurement. Example: Which measurement represents a greater degree of certainty? 4000 g 4005.32 g

2-3 Significant Figures Represent any position for which real measurement has been made, plus one final digit which is an estimated position The number of significant figures you can record when measuring with an instrument depends on the sensitivity of the instrument

2-3 Significant Figures Record all digits that you can read off the instrument, plus ONE ESTIMATED digit.

2-3 Significant Figures All nonzero digits are significant. Zeros between nonzero digits are significant. Zeros in front of all nonzero digits are NOT significant. Zeros at the end of a number and to the right of a decimal point are significant.

2-3 Significant Digits Determine the number of significant digits in the following measurements: 804.05 g 0.0144030 km 1002 m 400 mL 30000. cm 0.000625000 kg

2-3 Significant Figures and Calculations Addition/subtraction – go by smallest number of decimal places Multiplication/division – go by smallest number of significant figures 4.57 g + 3.2 g 7.77g  7.8 g 3.21 m X 4.512 m 14.48352 m2  14.5 m2

2-3 Significant Figures and Conversions Equalities are definitions, and therefore have NO uncertainty. There are EXACTLY 100 cm in a meter, by definition. When you convert a value, your answer will have the SAME number of significant figures as the original value. 4.608 m x 100cm/1m = 460.8 cm

2-3 Scientific Notation Numbers are written in the form M x 10n, where M is a number greater than or equal to one but less than 10 and n is a whole number. Express the following in scientific notation: 67000 0.00325 9732000000 0.0000017 621.0

2-3 Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value y/x = k k is the proportionality constant Ratio between the variables remains constant Rearrange to get y = kx (straight line) Therefore, a graph of a directly proportional relationship will be linear. (e.g. density)

2-3 Inverse Proportions Two quantities are inversely proportional to each other if their product is a constant xy = k k is the proportionality constant A graph of an inversely proportional relationship produces a curve called a hyperbola

Gas Volume v. Pressure