Table of SI prefixes

Transcription

1 Chapter 2: Analyzg Data Units and Measurement Système Internationale d Unités (SI) Base units: (fundamental units) an dependent unit of measure from a physical standard Time t (s) from the frequency of radiation given by cesium-133 Length l (m) from the distance light travels 1 / seconds Mass m (kg) from a physical artifact France (Le Grand K) Temperature T (K) from the lowest possible energy condition Amount N (mol) based on the number of 12 C required to mass 12 g Current I (A) flow of one coulomb per second ( x e ) Lumosity L (cd) from 1 /683 watt per steradian of green light (540 x Hz) Note that only mass is based on a physical artifact (somethg man-made) and is also the only unit that has a prefix (kilo) The scope of this class cludes only the first five base units SI prefixes (from Table of SI prefixes Factor Name Symbol yotta Y zetta Z exa E peta P tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 2 hecto h 10 1 deka da Factor Name Symbol 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n pico p femto f atto a zepto z yocto y SI specifies deca but NIST uses deka for 10 1 Temperature conversions ºC = (ºF 32) ( 5 /9 ) K = ºC

2 Derived units: are defed by a combation of base units Volume SI uses m 3 but this is too large for ordary use the lab Chemists commonly use the liter (L) = dm 3 or the milliliter (ml) = 10 3 L Density ( d = m /V ) Where d = mass grams and V = volume ml or cm 3 for most solids and liquids Sample Problem: When a piece of alumum ( d = 2.70 g ml 1 ) is placed a 25 ml graduated cylder contag 10.5 ml of water, the water level rises to 13.5 ml. Fd the mass of the alumum. Make a shoppg list (write everythg you know): d = 2.70 g ml 1 Vi = 10.5 ml Vf = 13.5 ml m =? Write the equation(s) or conversion factor(s) V = Vf Vi and d = m /V Make substitutions and evaluate V = Vf Vi = 13.5 ml 10.5 ml = 3.0 ml Rewrite the second equation for the unknown (note the cyclg for the two equations) d = m /V, therefore: m = d ( V ) Make substitutions and evaluate m = V ( d ) = 3.0 ml ( 2.70 g ml 1 ) = 8.1 g Check your answer The units did cancel out to give g (which is a mass), so that looks good Check to see if this mass gives the correct density d = m /V = (8.1 g) / (3.0 ml) = 2.7 g ml 1, this looks good!

3 Scientific Notation and Dimensional Analysis (Conversion Factors) Scientific Notation Decimals and Scientific Notation g = 2.3 x g 2.15 x atoms = atoms For decimal and scientific notation conversions, do Practice Problems on page 41. Addg and Subtractg 6.51 x = 6.51 x x = x x or 6.54 x x = 6.51 x x = x x or 6.08 x For addition and subtraction, do Practice Problems on page 42. Multiplyg and Dividg 6.8 x x 2.3 x x or 1.6 x x x x 10 2 or 3.0 x 10 2 (Why not 300?) For multiplication and division, do Practice Problems on page 43. Dimensional Analysis (Conversion Factors) Conversion factors are always the number 1 disguise (1 cognito) For example: 12 = 1 ft dicates that two conversion factors are possible or Sample Problem: How many ches are 2.54 ft? Make a shoppg list (write everythg you know): s =? 12 = 1 ft Write the conversion factor (note that ft must occur the denomator) s =? 12 = 1 ft ft

4 Make substitutions s =? 12 = 1 ft = ft Evaluate s =? 12 = 1 ft = ft = = Check: both the units and the numbers checked and rechecked so round to the appropriate number of significant figures (three this case from 2.54 ft) Uncertaty Data s =? 12 = 1 ft Accuracy and precision = ft = = or 30.5 Accuracy: how close measured answers are to the accepted value Scientists show accuracy by reportg percent error: Experimental Value Accepted Value % error = x 100% Accepted Value Precision: how close a series of measured answers are to each other Scientists show precision by The number of significant figures they write: g (the precision is assumed to be ± 1 the last digit [the 8] ) Reportg the range the last digit parenthesis: (3) g (this precision is correct for our triple beam balances) Reportg the smallest gradient on an strument: the smallest rule on the triple beam balances is 0.01 g Reportg the precision range of an strument: the precision of the triple beam balances is ± g Reportg the estimated deviation: % deviation = Estimated Deviation Measured Value x 100% = g x 100% (for this example of our triple beam balances) g

5 Significant Figures Rule 1: Nonzero numbers are always significant Rule 2: Zeros between nonzero numbers are always significant Rule 3: All fal zeros to the right of the decimal are significant Rule 4: Placeholder zeros are not significant (use scientific notation to remove placeholder zeros) Rule 5: Defed constants and tegers have an fite number of significant figures 27.4 g = 3 sig figs 20.4 g = 3 sig figs g = 4 sig figs 2070 g = 3 sig figs g = 3 sig figs 60 s = 1 m 6 molecules Roundg Numbers Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant digit (e.g to 3 sig figs rounds to 1920, not 1930) Rule 2: If the digit to the right of the last significant figure is more than 5, round up the last significant digit (roundg to 2 sig figs is 210) Rule 3: If the digit to the right of the last significant figure is equal to 5, do not change the last significant digit if it is even but do round up the last significant digit if it is odd (roundg to 3 sig figs = 2.08 and roundg to 3 sig figs = 2.10) Significant Figure Rules for Addition and Subtraction The precision of the answer must end the highest place column of the fal significant figure the values to be added or subtracted 650 g 10s place precision (second digit before the decimal) g 100 th place precision (second digit after the decimal) g 10 th place precision (first digit after the decimal) g The worst precision the numbers added is the 10s column 810 g The fal answer rounded properly to the 10s column (2 sig figs) Significant Figure Rules for Multiplication and Division The number of significant digits the answer should be the same as that of the quantity with the fewest significant digits of the quantities beg multiplied or divided 650 cm x cm 650 cm has 2 sig figs and cm has 4 sig figs = cm 2 The answer from a calculator = cm 2 The fal answer rounded properly to 2 sig figs 651 g cm g has 3 sig figs and cm has 5 sig figs = g cm 3 The answer from a calculator = 4.90 g cm 3 The fal answer rounded properly to 3 sig figs

6 Representg Data Graphg Circle or Pie Charts: best used to represent parts of a fixed whole (percent values) and these graphs do not show changes over time Percentage of Gases Dry Air N O2 Ar CO2 Other Bar Graphs or Histograms: best used to represent how quantities vary across categories (comparg US population and resource usage to Cha s population and resource usage) and are best used when the changes are fairly large USA Cha Population and Energy Consumption Energy (as oil, millions of barrels) Population (hundred thousands) Le plots: best used to track small changes over short or long time periods or to compare several items that change over the same time period or to compare variables when order is important Temperature ( C) Hourly Temperature Changes Over a One Day Period Time (hours, military format)

7 Scatter plots or X Y plots: best used to determe the relationships between variables (look for correlations) look for positive vs. negative, direct vs. verse, or exponential relationships Temperature ( C) Temperature vs. Volume Volume (ml) When plottg (especially) le or scatter plots: Always put the dependent (manipulated) variable on the x-axis Always put the dependent (respondg) variable on the y-axis Titles on graphs are usually Y (dependent variable) versus X (dependent variable) Slope equation for a straight le graph: slope = rise = Δy run Δx = y2 y1 x2 x1 Interpolation: determe a value between two measured pots Extrapolation: determe a value beyond the measured pots Interpretg ozone data: (See the Section 2.4 assessment on page 58)