 # Measurements and Calculations

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Measurements and Calculations
Modern Chemistry Chapter 2

Scientific Method – logical approach to solving problems
- Observe - Collect Data (gather information) - qualitative data – descriptive data - quantitative data - numerical data (a system is a specific portion of matter selected for study) - Form a Hypothesis – a testable statement (usually if-then) possible solution - Experiment – test your hypothesis - Model – explanation of how phenomena occur and how data/events are related - Form a Theory – broad generalization explaining a body of facts or phenomena 2-1 Scientific Method

2-2 Units of Measurement Measurements are quantitative information
Quantities are a magnitude, size, or amount (ex: volume, mass, length, etc.) SI System of measurement – measurement system accepted worldwide with 7 base units Quantity Abbreviation Unit Unit Length l meter m Mass m kilogram kg Time t second s Temperature T kelvin K Amount Substance n mole mol Electric Current I ampere A Luminous Intensity Iv candela cd Common Metric Prefixes Mega (M) 106 no prefix (g, m, L…) 1 micro (μ) 10-6 Kilo (k) 103 deci (d) nano (n) 10-9 hecto (h) 102 centi (c) pico (p) 10-12 deka (da) 10 milli (m) 10-3 2-2 Units of Measurement

Mass – quantity of matter (measured with a balance)
Weight – measure of gravitational pull on matter (measured with a spring scale) Derived units – combinations of SI units (from calculations) - Volume – amount of space occupied by an object - SI unit for volume is cubic meter (m3) - common units are 1 liter (L) = 1 dm3 and 1 milliliter (mL) = 1 cm3 - Density – ratio of a substance’s mass to its volume - density = mass/volume OR D = m/V - it is a characteristic physical property of a substance useful of identification 2-2 Units of Measurement

Example 2-1:. A sample of aluminum metal has a mass of 8. 4 g
Example 2-1: A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum. For practice do p. 40 #1 and 3 2-2 Units of Measurement

2-2 Units of Measurement The density of water is 1g/mL.
If an object has a density GREATER than 1g/mL it will sink in water. If an object has a density LESS that 1g/mL it will float in water. 2-2 Units of Measurement

2-2 Units of Measurement Dimensional Analysis (Factor Label)
- Conversion Factor – ratio derived from the equality between two different units used to convert from one unit to the other (each conversion factor equals 1) Ex 1: 4 quarters = 1 dollar: 4 quarters = 1 dollar = dollar 1 dollar quarter 1 quarter Ex 2: 365 days = 1 year: 365 days = 1 year 1 year days Ex 3: 453g = 1 ounce: 453g OR 1 oz. 1 oz g Ex 4: What will the following become? a. 1000ml = 1 liter b cm = 1 in c. 4 quarts = 1 gallon 2-2 Units of Measurement

- Rules for doing Dimensional Analysis (factor label method)
1. Write down the known (the unit you are starting with). 2. Write down what you want to find (unknown). 3. Write down the conversion factor(s) that will help you get from #1 to #2. 4. Do the math. (Multiply by the conversion factor fraction that has your known unit in the bottom and your unknown unit in the top. Divide the known number by the number in the bottom of the c.f. and multiply by the top.) 2-2 Units of Measurement

2-2 Units of Measurement Dimensional Analysis (Factor Label)Practice
We will do the Dimensional Analysis WS odds together. 2-2 Units of Measurement

2-3 Using Scientific Measurement
Scientific Notation – expresses a number with one digit to the left of the decimal - General Form: M x 10n - Only show significant figures when putting a number in scientific notation EX: = x 105 = 2.0 x 10-3 EX using scientific notation in a calculation: 5.44 x 10 7 g ÷ 8.1 x 10 4 mol = 6.7 x 102 g/mol EX: Calculate the volume of a sample of aluminum that has a mass of kg. The density of aluminum is 2.70 g/cm3. K: m = kg => kg x 1000g = g D = 2.70 g/cm kg unk: V = ? D = m/V OR V = m/D V = 3057g = cm3 = x 103 cm3 2.70 g/cm3 2-3 Using Scientific Measurement

2-3 Using Scientific Measurements
Significant Figures in a measurement consist of all digits known with certainty plus one final digit which is somewhat uncertain or is estimated. Only significant figures are reported. • Determining the number of significant figures: Table 2-5 p. 47 • absent decimal point – start counting at the first nonzero digit occuring on the right side of the measurement ( Atlantic side) • present decimal point – start counting at the first nonzero digit occurring from the left side of the measurement (Pacific side) EX: a m = b V = c kg = d L = 2-3 Using Scientific Measurements

2-3 Using Scientific Measurements
Answers obtained from calculations must be rounded to indicate the correct number of significant figures. An answer can only be as precise as its least precise measurement. Rules for Rounding • Addition and Subtraction: answer must have its last significant figure in the same decimal place as the measurement with the most uncertainty. EX: a g g = g b cm cm = cm • Multiplication and Division: answer can have no more significant figures than are in the measurement with the fewest number of significant figures. EX: 3.05g/8.47mL = g/mL *Conversion factors DO NOT limit the number of significant figures in the final answer! Do the practice problems on p. 50. 2-3 Using Scientific Measurements

2-3 Using Scientific Measurements
For a reported measurement to be useful there must be some indication of its reliability or uncertainty. - Accuracy – closeness of a measurement to the correct or accepted value - Precision – closeness of a set of measurements of the same quantity made in the same way (agreement between measurements) - % Error = experimental value – accepted value x 100 accepted value EX: A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The accepted value of the density is 1.36 g/mL. What is the percent error of the students measurement? known: experimental value = 1.40 g/mL accepted value = 1.36 g/mL unknown: % error % error = experimental value – accepted value x 100 % error = 1.40 g/mL – 1.36 g/mL x100 1.36 g/mL %error = 2.9% Error in measurement may be due to the skill of the measurer, conditions of the measurement, or the measuring instruments. 2-3 Using Scientific Measurements

2-3 Using Scientific Measurements
Two quantities are directly proportional if dividing one by the other gives a constant value. (When one value increases, the other value increases.) - can be represented by y α x OR y/x = k - all directly proportional relationships produce linear graphs that pass through the origin (straight lines) Two quantities are inversely proportional if their product is constant. (When one increases, the other decreases.) - can be represented by y α 1/x OR yx = k - all inversely proportional relationships produce a hyperbola graph (a curved line) 2-3 Using Scientific Measurements