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Let ’ s Review: The Tools of Quantitative Chemistry

Let ’ s Review: The Tools of Quantitative Chemistry. The Tools of Quantitative Chemistry. "In physical science the first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it.

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Let ’ s Review: The Tools of Quantitative Chemistry

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  1. Let’s Review: The Tools of Quantitative Chemistry

  2. The Tools of Quantitative Chemistry "In physical science the first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be." Lord Kelvin, "Electrical Units of Measurement", 1883-05-03

  3. Note About Math & Chemistry Numbers and mathematics are an inherent and unavoidable part of general chemistry. Students must possess secondary algebra skills and the ability to recognize orders of magnitude quickly with respect to numerical information to assure success in this course. The material presented in this chapter is considered to be prerequisite to this course.

  4. Units of Measure Science predominantly uses the “SI” (System International) system of units, more commonly known as the “Metric System”.

  5. Units of Measure The base units are modified by a series of prefixes which you will need to memorize.

  6. Temperature Units Temperature is measured in the Celsiusan the Kelvintemperature scale.

  7. Temperature Conversion

  8. Length, Volume, and Mass The base unit of length in the metric system is the meter. Depending on the object measured, the meter is scaled accordingly.

  9. Length, Volume, and Mass Unit conversions: How many picometers are there in 25.4 nm? How many yards?

  10. Length, Volume, and Mass The base unit of volume in the metric system is the liter. 1 L = 103 mL 1 mL=1 cm3 1 cm3 = 1 mL

  11. Length, Volume, and Mass The base unit of volume in the metric system is the gram. 1kg = 103g

  12. Energy Units Energy is confined as the capacity to do work. The SI unite for energy is the joule (J). Energy is also measured in calories (cal) 1 cal = 4.184J A kcal (kilocalorie) is often written as Cal. 1 Cal =103 cal

  13. Making Measurements: Precision Theprecisionof a measurement indicates how well several determinations of the same quantity agree.

  14. Making Measurements: Accuracy Accuracyis the agreement of a measurement with the accepted value of the quantity. Accuracy is often reflected by Experimental error.

  15. Making Measurements: Standard Deviation TheStandard Deviation of a series of measurements is equal to the square root of the sum of the squares of the deviations for each measurement from the average divided by one less than the number of measurements (n). Measurements are often reported to  the standard deviation to report the precision of a measurement.

  16. Mathematics of Chemistry Exponential or Scientific Notation: Most often in science, numbers are expressed in a format the conveys the order of magnitude. 3285 ft = 3.285  103 ft 0.00215kg = 2.15  103 kg

  17. Exponential part Exponential or Scientific Notation 1.23  104 Coefficient or Mantissa (this number is 1 and <10 in scientific notation Base Exponent

  18. Mathematics of Chemistry Significant figures: The number of digits represented in a number conveys the precision of the number or measurement. A mass measured to  0.1g is far less precise than a mass measured to  0.0001g. 1.1g vs. 1.0001g (2 sig. figs. vs. 5 sig. figs) In order to be successful in this course, you will need to master the identification and use of significant figures in measurements and calculations!

  19. Counting Significant Figures • All non zero numbers are significant • All zeros between non zero numbers are significant • Leading zeros are NEVER significant. (Leading zeros are the zeros to the left of your first non zero number) • Trailing zeros are significant ONLY if a decimal point is part of the number. (Trailing zeros are the zeros to the right of your last non zero number).

  20. not trapped by a decimal place. zeros written explicitly behind the decimal are significant… Determining Significant Figures Determine the number of Sig. Figs. in the following numbers 1256 4 sf 1056007 7 sf 0.000345 3 sf 0.00046909 5 sf 1780 3 sf 4 sf 770.0 0.08040 4 sf

  21. Rounding Numbers 1. Find the last digit that is to be kept. 2. Check the number immediately to the right: If that number is less than 5 leave the last digit alone. If that number is 5 or greater increase the previous digit by one.

  22. Rounding Numbers Round the following to 2 significant figures: 1056007 1100000 0.000345 0.00035 1780 1800

  23. Sig. Figures in Calculations Multiplication/Division The number of significant figures in the answer is limited by the factor with the smallest numberof significant figures. Addition/Subtraction The number of significant figures in the answer is limited by the least precise number(the number with its last digit at the highest place value). NOTE: counted numbers like 10 dimes never limit calculations.

  24. Sig. Figures in Calculations Determine the correct number of sig. figs. in the following calculation, express the answer in scientific notation. from the calculator: 4 sf 2 sf 4 sf = 1996.501749 10 sf 23.50  0.2001  17 Your calculator knows nothing of sig. figs. !!!

  25. Sig. Figures in Calculations Determine the correct number of sig. figs. in the following calculation, express the answer in scientific notation. 1.996501749  103 in sci. notation: 2.0  103 Rounding to 2 sf:

  26. Sig. Figures in Calculations Determine the correct number of sig. figs. in the following calculation:  12.6 391 + 156.1456

  27. no digits here Sig. Figures in Calculations To determine the correct decimal to round to, align the numbers at the decimal place: One must round the calculation to the least significant decimal.  12.6 391 +156.1456 391 12.6 +156.1456

  28. one must round to here 391 -12.6 +156.1456 round to here (units place) Sig. Figures in Calculations 534.5456 (answer from calculator) Answer: 535

  29. Sig. Figures in Calculations Combined Operations:When there are both addition & subtraction and or multiplication & division operations, the correct number of sf must be determined by examination of each step. Example:Complete the following math mathematical operation and report the value with the correct # of sig. figs. (26.05 + 32.1)  (0.0032 + 7.7) = ???

  30. Sig. Figures in Calculations Example:Complete the following math mathematical operation and report the value with the correct # of sig. figs. (26.05 + 32.1)  (0.0032 + 7.7) = ??? 2nd determine the correct # of sf in the denominator (bottom) 1st determine the correct # of sf in the numerator (top) The result will be limited by the least # of sf (division rule)

  31. 3 sf 58.150 = 7.7032 2 sf Sig. Figures in Calculations 26.05 + 32.1 0.0032 + 7.7 The result may only have 2 sf

  32. 3 sig figs 2 sig figs! Round to here Sig. Figures in Calculations Carry all of the digits through the calculation and round at the end. 58.150 7.7032 = 7.5488 = 7.5 2 sf

  33. Dimensional Analysis: Dimensional analysis converts one unit to another by using conversion factors (CF’s). The resulting quantity is equivalent to the original quantity, it differs only by the units. unit (1) = unit (2)  conversion factor Problem Solving and Chemical Arithmetic

  34. Dimensional Analysis: Dimensional analysis converts one unit to another by using conversion factors (CF’s). Conversion factors come from equalities: 1 m = 100 cm 1 m 100 cm or 100 cm 1 m Problem Solving and Chemical Arithmetic

  35. Examples of Conversion Factors Exact Conversion Factors:Those in the same system of units 1 m = 100 cm Use of exact CF’s will not affect the significant figures in a calculation.

  36. Examples of Conversion Factors Inexact Conversion Factors:CF’s that relate quantities in different systems of units 1.000 kg = 2.205 lb SI units British Std. (4 sig. figs.) Use of inexact CF’s will affect significant figures.

  37. Problem Solving and Chemical Arithmetic • Problem solving in chemistry requires “critical thinking skills”. • Most questions go beyond basic knowledge and comprehension. (Who is buried in Grant’s tomb?) • You must first have a plan to solve a problem before you plug in numbers. • You must evaluate the result to see if it makes sense. (units, order of magnitude) • You must also practice to become proficient because... Chem – is – try

  38. Problem Solving and Chemical Arithmetic • Before starting a problem, devise a “Strategy Map”. • Use this to collect the information given to work your way through the problem. • Solve the problem using Dimensional Analysis. • Check to see that you have the correct units along the way.

  39. Problem Solving and Chemical Arithmetic Most importantly, before you start... PUT YOUR CALCULATOR DOWN! Your calculator wont help you until you are ready to solve the problem based on your strategy map.

  40. Problem Solving and Chemical Arithmetic Example: How many meters are there in 125 miles? First: Outline of the conversion:

  41. Problem Solving and Chemical Arithmetic Example: How many meters are there in 125 miles? First: Outline of the conversion: m miles  ft  in  cm  Each arrow indicates the use of a conversion factor.

  42. Problem Solving and Chemical Arithmetic Example: How many meters are there in 125 miles? Second: Setup the problem using Dimensional Analysis: miles  ft  in  cm  m =

  43. Problem Solving and Chemical Arithmetic Example: How many meters are there in 125 miles? Third: Check your sig. figs. & cancel out units. m miles  ft  in  cm  = / / / / 3 sf exact exact 3 sf exact / / / /

  44. Problem Solving and Chemical Arithmetic Example: How many meters are there in 125 miles? Fourth: Now use your calculator. : m miles  ft  in  cm  / / / / = / / / / 3 sf exact exact 3 sf exact Carry though all digits, round at end

  45. Problem Solving and Chemical Arithmetic Example: How many meters are there in 125 miles? Lastly: Check your answer for sig. figs & magnitude. m miles  ft  in  cm  / / / / = / / / / 3 sf exact exact 3 sf exact or 2.01  105 m (3 sf) 2.01168  105

  46. Problem Solving and Chemical Arithmetic Example: How many square feet are there in 25.4 cm2? Map out your conversion: ft2 cm2 in2 / / = 2.73403  10-2 ft2 / / 3 sf exact exact or 2.73  10-2 ft2 (3 sf)

  47. Problem Solving and Chemical Arithmetic Example: How many cubic feet are there in 25.4 cm3? Map out your conversion: ft3 cm3 in3 / / = 8.96993  10-4 ft3 / / 3 sf exact exact or 8.97  10-4 ft3 (3 sf)

  48. Problem Solving and Chemical Arithmetic Example: What volume in cubic feet would 0.851 grams of air occupy if the density is 1.29 g/L? Map out your conversion: g  L  cm3 in3 ft3 / / / / / / / / 3 sf 3 sf 3 sf 3 sf exact 3 sf

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