Scientific Measurement A quantity is anything having a measurable size or amount For Example: 5 But 5 what? A unit assigns value to a measured quantity For Example: 5 ft, 5 gal, 5 sec, 5 m, 5 g. Base Units Units Provide standard comparison for measured values. Prefixes Scale the unit. SI Units Standard unit for reporting a given measurement Handout Measured Quantities in Chemistry and Their Base Units Quantity Base Unit Symbol length meter m mass gram g time second s volume Liter L amt. substance mole mol temperature Kelvin K Temperature Temperature Anders Celsius 1701-1744 A measure of the average kinetic energy of the particles in a sample. In scientific measurements, the Celsius and Kelvin scales are most often used. The Celsius scale is based on the properties of water. 0C is the freezing point of water. 100C is the boiling point of water. Lord Kelvin (William Thomson) 1824-1907 The Kelvin is the SI unit of temperature. It is based on the properties of gases. There are no negative Kelvin temperatures.
Metric Prefixes SI Units Prefixes convert the base units into units that are appropriate for the item being measured. Système International d Unités Uses a different base unit for each quantity Derived Quantities in Chemistry and Their Base Units Quantity SI Unit Symbol Volume cubic meter m 3 Weight Newtons N Density kilogram per liter Kg/L Energy kilojoule KJ Specific Gravity Density is often expressed in units of g/ml or g/cm 3 instead of SI units. The specific gravity is defined as the ratio of the density of the substance to the density of water : dsubstance sp. gr. d water The specific gravity of a substance: Is less than one for substances less dense than water Is greater than one for substances more dense than water Is independent of units Joule(J) the kinetic energy required to move a 2Kg mass a distance of one meter in one sec. From the equation of KE: J kg m s KE = ½ mv 2 2 2 James Joule 1818-1889 calorie Commonly, energies are described in the units of calories. A calorie is the amount of heat needed to raise the temperature of 1 gram H 2 0, 1 degree centigrade 1 cal = 4.184 J nutritional calorie Calorie 1 Cal = 1 Kcal
Measurements: Always involve a comparison Require units Involve numbers that are inexact (numbers in mathematic theory are exact) Include uncertainty due to the inherent physical limitations of the observer and the instruments used (to make the measurement) Uncertainty is also called error Uncertainty in Measurements Different measuring devices have different uses and different degrees of accuracy. Therefore, It is important to make accurate measurements To make an accurate measurement, you must always include an uncertain digit, or a guessed last digit beyond the scale of the measurement tool. For example, Notice how the difference in the accuracy of the measuring tool results in a different degree of accuracy in the measurement according to the uncertain digit? Only 1 digit and it is uncertain 1 certain and 1 uncertain 2 certain and 1 uncertain Let s Make Some Accurate Measurements Measure the Following: Width of your book with a ruler. Temperature of the room. Volume of water in a graduated cylinder. Time to start and stop a stopwatch. Certain Uncertain 4.75 cm. Reading Digits There can never be more than one value of uncertainty Measure the line on your handout and identify the uncertain digit.
Relaying the Degree of Accuracy of a Measurement By including the uncertain digit in a measurement, the accuracy can be defined as a value ± the estimated uncertainty of the estimated digit. Dimensional Analysis (aka. The Factor-Label Method) for problem solving Simple but important method used to solve chemistry and physics problems based on units. Uses the form of the conversion factor that puts the sought-for unit in the numerator: Example: a line measures 21.23 ± 0.01 cm We will discuss errors associated with measurements more in the next lecture desired unit Given unit given unit Conversion factor desired unit Some examples of conversion factors USING UNITS IN CALCULATIONS The factor-label method for solving numerical problems is a four-step systematic approach to problem solving. Step 1: Write down the known or given quantity. Include both the numerical value and units of the quantity. Step 2: Determine the relationship between the units of the known quantity and the unknown quantity. Step 3: Multiply the known quantity by one or more conversion factors such that the units of the conversion factor cancel the units of the known quantity and generate the units of the unknown quantity. Step 4: After you generate the desired units of the unknown quantity, do the necessary arithmetic to produce the final numerical answer. Let s do the following conversions together: 56.23 in to yds 1450000 mg to g 59.2 hs to s 98.365 µm to Km 109 ml to m 3
Temperature conversions can not be done using the factor-label method due to the fact that they are additive conversions, not multiplicative. F = 9/5(C) + 32 C = 5/9(F 32) K = C + 273.15 Remember, each measured quantity must have an uncertain digit. The uncertain digit relays the accuracy of a measurement. That accuracy is maintained when converting between units in the metric system by ensuring you have as many digits after the conversion as you had before. How then does the accuracy of a set of measurements become relayed in other unit conversions or in other derived quantities? A calculated quantity can not be more accurate than the least accurate measurement! So, how is accuracy relayed to calculated values from measured values? The answer: By use of. Observe: 21.32 cm x 1.3 cm O.K. That works for multiplication but what about addition: 1.3 cm + 21.32 cm + 1.3 cm + 21.3 cm =? From these profs, comes the concept and use of significant figures. If the answer may only contain 1 uncertain digit, what is the accuracy of the measurement? The term significant figures refers to digits in a number that were measured. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers. Determining 1. All nonzero digits are significant. 2. Zeroes between two significant figures are themselves significant. 3. Zeroes at the beginning of a number are never significant. 4. Zeroes at the end of a number are significant if a decimal point is written in the number.
1. How many significant figures are in each of the following measurements? 24 ml 2 significant figures 3001 g 4 significant figures 0.0320 m 3 3 significant figures 6.4 x 10 4 molecules 2 significant figures When addition or subtraction is performed, answers are rounded to the least significant decimal place. When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation. 560 kg 2 significant figures Addition or Subtraction The answer cannot have more digits to the right of the decimal point than any of the original numbers. 89.332 + 1.1 one significant figure after decimal point 90.432 round off to 90.4 3.70-2.9133 0.7867 two significant figures after decimal point round off to 0.79 Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x 3.6666 = 16.536366 = 16.5 3 sig figs round to 3 sig figs 6.8 112.04 = 0.0606926 = 0.061 2 sig figs round to 2 sig figs The accuracy in a measurement may be increased by using a more precise instrument Using the first thermometer, the temperature is 24.3 ºC (3 significant digits). Using the more precise (second) thermometer, the temperature is 24.32 ºC (4 significant digits) Rules for Rounding If the number to be retained is followed by a number larger than 5, round up. If the number to be retained is followed by a number less than 5, drop. If the number following the number to be retained is 5 followed by any non-zero number, round up. If the last number to be retained is a 5 and is followed by a zero, then always make it even.
Perform each of the following, rounding the answer to the correct number of sig. fig s.: 1. 298 g 43.7 g 2. 4.218 cm x 6.6 cm 3. 4.23 m 2 18.941 m 4. 0.0653 g + 0.08538 g + 0.07654 g + 0.0432 g 5. 50 L x 5.23 L 6. 85.621 s 5.5 s Math Concepts You Should Know Uncertainties in Measurement Exponential Notation Logarithms Graphing Functions Quadratic Equation Study Appendix A to review these concepts