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# Ch 3 final ppt

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The Mathematics of Chemistry

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• Measurements are made up of both accuracy and precision Accuracy, how close the measured value is to the accepted value Precision, how finely divided the measurement scale is on the device
• How close a measurement is to the accepted value When ever a measurement is taken, there is always a chance for human error
• How finely divided the measurement scale is on an instrument Repeated measurements should yield nearly identical values A set of measurements can be accurate without being precise, precise without being accurate, neither accurate nor precise, or both accurate and precise
• All scientists use these to measure
• All units are multiples of ten Consist of base unit and prefix
• Give students handout with these rules
• Every number written in scientific notation has two basic parts.  The first part is always a decimal number between 1.00 and 9.99… The second part is 10 times some exponent Notice that in each of these, the first part is a decimal number between 1.00 and 9.99… the exponent on the 10 tells you which direction to move the decimal and how many times it should be moved. POSITIVE EXPONENT means move RIGHT NEGATIVE EXPONENT means move LEFT
• The first part has to be between 1.00 and 9.99... Move your decimal until you have a number that qualifies 7.82 Remember that the exponent tells you the number of spaces that you moved it.  So the answer is either 7.82 X 10 6 or 7.82 X 10 -6 A standard notation number LOWER than 1 means NEGATIVE exponent A standard notation number GREATER than 1 means POSITIVE exponent
• Simple unit conversions
• We need a conversion factor, a relationship between the units These both give us a relationship between in. and ft.
• The great thing about dimensional analysis is that sometimes you can solve problems without equations. Here is such a case:
• ### Ch 3 final ppt

1. 1. Monday September 20, 2010 <ul><li>Chapter 3 </li></ul><ul><li>Math: The Central Language </li></ul><ul><li>of Science </li></ul>
2. 2. Measurement <ul><li>Consists of 1) a number </li></ul><ul><li>2) a unit </li></ul>Ex: 1 mile 10.0 grams 450.00 mL
3. 3. Accuracy and Percent Error <ul><li>Percent error: how accurate a measurement is to the accepted value </li></ul><ul><li>How to calculate percent error: </li></ul><ul><ul><li>Accepted value – Experimental Value X 100% </li></ul></ul><ul><ul><li>Accepted value </li></ul></ul>
4. 4. Sample Problem <ul><li>You measure the mass of a product in a chemical reaction to the 3.80 g. Theoretical calculations predict that you should have obtained 3.92 g. What is the percent error? </li></ul>
5. 5. <ul><li>Precision versus Accuracy </li></ul>Tuesday September 21, 2010
6. 7. SI units <ul><li>Internationally agreed upon units of measurement </li></ul>
7. 8. Metric System Commonly Used Prefixes kilo k 1,000 10 3 hecto h 100 10 2 deka da 10 10 1 no prefix 1 10 0 deci d 0.1 10 -1 centi c 0.01 10 -2 milli m 0.001 10 -3 micro µ 0.000001 10 -6 nano n 0.000000001 10 -9
8. 9. Significant Figures Made Easy By Miss Virginia Williams
9. 10. Significant Figures Rules: <ul><li>All nonzero numbers are significant. </li></ul><ul><li>All zeros between two nonzero digits are significant. </li></ul><ul><li>When a decimal is in the number, the first nonzero number present and all the numbers after it are significant. </li></ul><ul><li>When the number is written in scientific notation, all the numbers to the left of the multiply sign are significant. </li></ul>
10. 11. Determine the number of significant digits in the following quantities: <ul><li>9.370 kg </li></ul><ul><li>63,000 g </li></ul><ul><li>705.06 mL </li></ul><ul><li>0.0001 s </li></ul><ul><li>2300.000 m </li></ul>
11. 12. Significant Digits and Mathematical Operations <ul><li>After add and sub, the answer cannot be more precise than the least precise measurement </li></ul><ul><li>Ex. 50.23m + 14.678m + 23.7m = 88.608 </li></ul>23.7 only goes to the tenth place, therefore the answer must be rounded to the tenth place, 88.6 m
12. 13. Significant Digits and Mathematical Operations <ul><li>2) In multiplication or division, the answer cannot contain more significant digits than the measurement with the least number of significant digits </li></ul><ul><li>Ex: (0.238 m)(0.31 m) = 0.07378 m 2 </li></ul><ul><ul><li>The answer must be rounded off to 0.074 m 2 </li></ul></ul><ul><ul><li>Because 0.31 m only has 2 sig figs </li></ul></ul>
13. 14. Significant Digits and Mathematical Operations <ul><li>3) The rule for rounding: (same as normal rounding rules) </li></ul><ul><li>If the digit to be dropped is less than 5, simply drop the digit. </li></ul><ul><li>If the digit is or greater, increase the preceding digit by one </li></ul><ul><li>Ex: 12.4489 expressed to 3 sig figs = </li></ul><ul><li>12.4489 expressed to 4 sig figs = </li></ul>12.4 12.45 Do Sample problems pg 51
14. 15. Monday Sept 27, 2010 Scientific Notation Allows us to write very big and very small numbers
15. 16. Scientific Notation <ul><li>3.42 x 10 6 or 8.005 x 10 -3 </li></ul>
16. 17. Scientific Notation <ul><li>3.42 x 10 6 means </li></ul>3.42 x (10 x 10 x 10 x 10 x 10 x 10) or 3,420,000
17. 18. Scientific Notation <ul><li>8.005 x 10 -3 means </li></ul>or 0.008005 8.005 x (0.1 x 0.1 x 0.1)
18. 19. Scientific Notation <ul><ul><li>Let's say you wanted to convert the following number to scientific notation: </li></ul></ul><ul><ul><li>0.00000782 </li></ul></ul>
19. 20. Convert to Scientific Notation <ul><li>1) 3,400 </li></ul><ul><li>2) 0.000023 </li></ul><ul><li>3) 101,000 </li></ul><ul><li>4) 0.010 </li></ul>
20. 21. Perform the following operations, give answer with correct number of significant digits. <ul><li>(3.55 x 10 4 g) + (3.55x 10 3 g) = 3.91 x 10 4 g </li></ul><ul><li>(6.22x 10 -2 m) (8.4x 10 -4 m) = 5.2 x 10 -5 m </li></ul><ul><li>(3.55x 10 4 cm) /(3.55x 10 3 cm)=1.00 x 10 1 cm </li></ul><ul><li>(6.22x 10 -2 kg) - (8.4x 10 -4 kg)=6.1x10 -2 kg </li></ul>
21. 22. Dimensional Analysis – converting from one unit to another ex: feet/sec to miles/hour Tuesday September 28, 2010
22. 23. Dimensional Analysis <ul><li>Convert 2 feet to inches </li></ul>
23. 24. Dimensional Analysis <ul><li>The units cancel out leaving only </li></ul><ul><li>Giving us an answer of 24 in. </li></ul>
24. 25. Dimensional Analysis <ul><li>Convert 48 inches to feet. </li></ul>
25. 26. Dimensional Analysis <ul><li>Convert 5 days to hours. </li></ul>
26. 27. Dimensional Analysis <ul><li>How many seconds are there in 4 minutes? </li></ul>
27. 28. Dimensional Analysis <ul><li>Convert 27.2 cm to meters. </li></ul>
28. 29. Dimensional Analysis <ul><li>Convert 147 cm/s to m/s </li></ul>
29. 30. Dimensional Analysis <ul><li>Convert 60 miles/hour to feet/second </li></ul>
30. 31. <ul><li>Analysis of an air sample reveals that it contains 3.5 x 10-6 g/L of carbon monoxide. Express the concentration of carbon monoxide in lb/ft 3 . (Use 1.00 lb = 454 g; 1 in = 2.54 cm) </li></ul>
31. 32. <ul><li>All matter has a property called a specific heat capacity. For silver, this specific heat capacity is 0.24 J/°C · g. How much energy (in Joules) would be required to heat 120.0 g of silver (Ag) so that its temperature changes by 32°C? Use dimensional analysis, not an equation. </li></ul>
32. 33. <ul><li>Based on how you set up the problem above, what would be the equation ? Fill in the rest of this expression to form your own equation (that you figured out by using dimensional analysis above.) You will use the terms “ mass ” “ specific heat ” and “ temperature ” and some mathematical operation signs). This answer is an equation, not a dimensional analysis setup. Energy (J) = </li></ul>