Measurement and Calculation Unit 2

The Fundamental SI Units (le Système International, SI) Physical QuantityNameAbbreviation Mass Length Time Temperature Electric Current Amount of Substance Luminous Intensity kilogram meter second Kelvin Ampere mole candela kg m s K A mol cd

SI Units

SI Prefixes Common to Chemistry Base unit Deci (d) 1/ Centi (c) 1/ Milli (m) 1/ Micro (μ) 1/ Nano (n) Pico (p) Kilo (k) 1, Mega (M) 1,000, Giga (G) 10 9

Dimensional Analysis A simple mathematical approach to converting between units. Involves conversion factors (fractions). Follows simple math functions (x/÷) We can use conversion factors for metric conversions as well as other conversions. Dim. analysis can be used to convert from 1 unit to another. One step or several steps. Each conversion factor represents a math function – treat it as such.

Dimensional analysis Set up: looking for given Example: 25 cm = ? mm 1 cm = 10 mm; cm is given, mm is looking for Conversion factor: 10 mm = 1cm 25 cm x 10 mm = 250 mm 1 cm

Unit conversions Practice: 1. What is the volume of a 250-mL beaker in L? 2. What is the mass of a 9.5 g sugar cube in mg? 3. A car travels 74,000 meters. How many km is this trip?

Accuracy vs. Precision Accuracy refers to how close a measurement is to the true or actual value. Precision refers to how close a series of measurements are to one another.

Accuracy vs. Precision Are the following pictures illustrating accuracy, precision, neither, or both?

Accuracy vs. Precision A class of chemistry students determined the mass of a quarter to be g. To confirm this, several students reported their “massing” 4 times. The following data was collected. Classify these students results as precise, accurate, neither, or both. STUDENTMASS (g) A B C D

Reporting Measurements To indicate the uncertainty of a single measurement scientists use a system called significant figures Our data can only be as precise as the least precise measuring tool/instrument The last digit on any measurement is estimated by the reporter

How HOT are you?? Heat (energy) cannot be measured directly. We can measure heat transfer by change in temperature. We define temperature as the average kinetic energy of a system. movement within a substance Measure temperature with a thermometer.

Temperature Scales Fahrenheit Scale, °F Relative scale Celsius Scale, °C Relative scale Water’s freezing point = 0°C, boiling point = 100°C Kelvin Scale, K Absolute scale Water’s freezing point = 273 K, boiling point = 373 K o C = K K = o C + 273

Temperature Conversion Practice Convert the following from o C to K: o C o C o C o C o C Convert the following from K to o C: K K K K K

Graphing 1.Determine the variables. -Independent  x-axes -Dependent  y-axes 2.Determine the range of values. 3.Utilize all of 1 side of the graph paper. -usually start at ‘0’ but NOT ALWAYS 4. Makes scales easy & keep consistent

Graphing 5. Label both axes (include unit). - draw axes with a straight edge 6.Give your graph an appropriate title. - dependent vs. independent 7. Titles, axes, & labels must be in INK! 8. Plot data with ‘x’ not ‘’ (may be in pencil) 9. Draw “best-fit” line through your data

Graphing 10. You may be asked to use your graph to draw conclusions & make predictions. Two examples would include: Interpolation – within the limits of the data Extrapolation – beyond the limits of the data

“Best-Fit” Line Distance vs. Time for Freefall

Scientific Notation A shorthand method of expressing large and small numbers using exponents. Expresses values to the precision of the instrument. M x 10 n M = any number between 1 & 10 n = any integer (including 0) Example: 2.34 x x 10 -4

Scientific Notation Identify the correct scientific notations: 3 x x x x 10 -2

Scientific Notation Express the following in scientific notation: 1. 2,300, Express the following in long-hand form: x x x x 10 -4

Scientific Notation Perform the following calculations, expressing your answer in scientific notation. 1. (6.0 x 10 4 ) (2.0 x 10 5 ) 2. (4.0 x 10 4 ) (2.0 x ) 3. (8.0 x 10 3 ) / (2.0 x 10 6 ) 4. (2.0 x ) / (4.0 x )

Rules for Counting Significant Figures 1. Nonzero integers are always significant Ex m  3 sig. figs g  4 sig. figs 2. ‘0’ between nonzero digits are significant. Ex L  3 sig. figs km  5 sig. figs.

Significant Figures 3. ‘0’ in front of nonzero digits are not significant. Ex m  4 sig. figs kg  1 sig. fig. *The zeros in these cases are ‘placeholders’; they are used for spacing.

Significant Figures 4. Zeros are the end of a number and to the right of a decimal are significant. Ex  4 sig. figs  10 sig. figs. 5. A decimal point placed after zeros indicates that the zeros are significant. Ex  4 sig. figs 2000  1 sig. fig.

Significant Figures Do NOT count sig. figs. in the following numbers: 1. Counting numbers 2. Constants 3. Conversion factors

Practice: Give the SigFigs x x

Adding/Subtracting Numbers with Significant Figures When adding/subtracting, look for the LEAST DECIMAL measurement to determine the correct number of sig. figs. (the least precise) Round answer to the same decimal place Ex. 54 g g g = mL – 2.1 mL =

Multiplication/Division with Significant Figures Result has the same number of significant figures as the measurement with the smallest number of significant figures Count the number of significant figures in each measurement Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures 4.5 cm x cm = 0.90 cm 2 2 sig figs3 sig figs 2 sig figs

Practice: give the SigFigs – x / x π

Density Density is a property of matter representing the mass per unit volume For equal volumes, denser object has larger mass For equal masses, denser object has small volume

Density Solids = g/cm 3 1 cm 3 (length x width x height) = 1 mL Liquids = g/mL 1 mL of H 2 O = 1 g at 4 o C Gases = g/L Volume of a solid can be determined by water displacement

Using Density in Calculations

Example A piece of lead has a mass of 127 g and a volume of 11.2 cm 3. Calculate the density. Density = 127 g / 11.2 cm 3 = 11.3 g/cm 3.

Practice Methanol has a density of g/mL. What is the mass of 22.3 mL methanol?