Analyzing Data

Units and Measurements

 Units  Système Internationale D’Unités ▪ Units were not always exact ▪ Scientists report data, and this data should be reproducible by other scientists ▪ A need for standard units was acknowledged ▪ 1960, an international committee of scientists met to update the existing metric system ▪ The revised system is called the Système Internationale D’Unités  AKA SI

 Base Units and SI Prefixes  Base Unit – is a defined unit a system of measurement that is based on an object or event in the physical world ▪ Independent of other units ▪ Time – seconds (s) ▪ Length – meter (m) ▪ Mass – kilogram (kg) ▪ Temperature – kelvin (K) ▪ Amount of a substance – mole (mol) ▪ Electric current – ampere (A) ▪ Luminous intensity – candela (cd)

 Base Units and Prefixes  Time ▪ SI base unit is second (s) ▪ Physical standard used to define the second is the frequency of the radiation given off by a cesium-133 atom ▪ Cesium based clocks are used when highly accurate timekeeping is required ▪ Many chemical reactions take place within a fraction of a second

 Base Units and SI Prefixes  Length ▪ SI base unit is meter (m) ▪ A meter is the distance that light travels in a vacuum in 1/299,792,458 of a second ▪ A meter is close to a yard

 Base Units and SI Prefixes  Mass ▪ SI base unit is kilogram (kg) ▪ A platinum and iridium cylinder kept in France defines the kilogram ▪ The cylinder is kept in a vacuum under a triple bell jar to prevent oxidation ▪ About 2.2 pounds

 Base Units and SI Prefixes  Prefixes (refer to table 2.2) ▪ Giga ▪ Mega ▪ Kilo ▪ Deci ▪ Centi ▪ Milli ▪ Micro ▪ Nano ▪ Pico

 Base Units and SI Prefixes  Temperature ▪ A quantitative measurement of the average kinetic energy of the particles that make up an object ▪ As particles in motion in an object increase, so does temperature ▪ Three scales have been developed

 Base Units and SI Prefixes  Temperature ▪ Fahrenheit  °F  Used in the US  Gabriel Daniel Fahrenheit (German scientist) devised it in 1724  Water freezes at 32°F  Water boils at 212°F

 Base Units and SI Prefixes  Temperature ▪ Celsius  °C  Used throughout much of the rest of the world  Anders Celsius (Swedish astronomer) devised this scale  Based on freezing and boiling points of water  Freezing 0°C  Boiling 100°C  °F = 1.8(°C) + 32

 Base Units and SI Prefixes  Temperature ▪ Kelvin ▪ K; SI unit ▪ William Thomson, known as Lord Kelvin (Scottish physicist and mathematician) devised kelvin ▪ 0K is the lowest possible energy state ▪ Water freezes K ▪ Water boils K ▪ K = °C + 273

 Derived Units  Derived Unit – a unit that is defined by a combination of base units ▪ Volume – the space occupied by an object ▪ Found by multiplying the length, width, and depth ▪m3▪m3 ▪ Liter – is equal to one cubic decimeter; commonly used ▪ Density – a physical property

 Derived Units ▪ Density – a physical property of matter and is defined as the amount of mass per unit volume ▪ Gram per cubic centimeter for solids ▪ Gram per cubic milliliter for gases or liquids ▪ Density = mass/volume

Scientific Notation and Dimensional Analysis

 Scientific Notation  Scientific Notation – can be used to express any number as a number between 1 and 10 (known as the coefficient) multiplied by 10 raised to a power (known as an exponent). ▪ Addition and subtraction ▪ Exponents must be the same ▪ Multiplication and Division ▪ First, multiply or divide coefficients ▪ Second, add or subtract exponents ▪ Third, rewrite into scientific notation if needed

 Dimensional Analysis  Dimensional Analysis – is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another  Conversion Factor – a ratio of equivalent values having different units

Uncertainty in Data

 Accuracy and Precision  Accuracy – refers to how close a measured value is to an accepted value  Precision – refers to how close a series of measurements are to one another

 Error and Percent Error  Error – is defined as the difference between an experimental value and an accepted value ▪ Error = experimental value – accepted value  Percent Error – expresses error as a percentage of the accepted value ▪ Percent Error = ____Ι error Ι______ x 100 accepted value

 Significant Figures  Significant Figures – include all known digits plus one estimated digit ▪ Nonzero numbers are always significant ▪ Zeros between nonzero numbers are always significant ▪ Placeholder zeroes are not significant. To remove placeholder zeroes write the number in scientific notation ▪ Counting number and defined constants have an infinite number of significant figures

 Rounding Numbers  Based on number of significant figures  Calculators won’t do this for you  Addition and Subtraction ▪ Answer must have the same # of digits to the right of the decimal as the original value having the fewest number of digits to the right of the decimal  Multiplication and Division ▪ Answer must have the same # of sig figs as the measurement with the fewest amount of sig figs

Representing Data

 Graphing  Graph – is a visual display of data ▪ Circle Graph (Pie Chart) ▪ Show parts of a whole

 Graphing  Bar Graphs ▪ Often used to show how a quantity varies across categories

 Graphing  Line Graphs ▪ In chemistry most graphs you create, will interpolate between the lines. ▪ Independent Variable – plotted on the X-axis ▪ Dependent Variable – plotted on the Y-axis ▪ Relationship between variables ▪ If best fit is a straight line – linear relationship

 Graphing  Line Graphs ▪ Relationship between variables ▪ If best fit is a straight line – linear relationship  Rises to the right – positive  Sinks to the right – negative ▪ Slope = rise/run ▪ Slope= Δy/Δx

 Interpreting Graphs  Interpolation and extrapolation ▪ Continuous data allows you to read the value from any point that fall between the recorded data points. This is called interpolation. ▪ You can also extend a line beyond the plotted points, and this is called extrapolation. ▪ You must be careful, because it can easily lead to errors and inaccurate predictions.