Calculations in Chemistry

1. Calculations in Chemistry Scientific Math

2. Over the next few lessons you will learn some basic math essential to studying chemistry: • Temperature Scales/Conversions • Scientific Notation • Significant Figures in Measurement/Calculations

3. I CAN convert between common and scientific temperature scales.

4. Temperature vs Heat • What is TEMPERATURE and how is it different from HEAT? • Temperature and Heat are NOT the same thing. • How are they different? Remember KINETIC ENERGY? • HEAT is a measure of the TOTAL ENERGY possessed by a substance. • TEMPERATURE is a measure of the AVERAGE ENERGY possessed by the particle of a substance.

5. Example • Two beakers of water are placed on a hot plate and heated until both reach the boiling point of water, 100 °C. • What is the TEMPERATURE of each beaker? • 100 °C • Which beaker of water has MORE ENERGY? • The larger one on the right.

6. Temperature Scales • Since the invention of the first modern thermometer in 1724, scientists have created a number of temperature scales. • A common widely used scale is the FAHRENHEIT scale. • Freezing Point (water) 32 oF. • Boiling Point (water) 212 oF. • 180 degree range between FP and BP. • Temperatures can be LESS THAN ZERO.

7. CELSIUS TEMPERATURE SCALE • The Celsius Scale is the preferred scale for most scientific work. • Part of the SI (Metric) System • Freezing Point is 0 oC. • Boiling Point is 100oC. • 100 degree range between FP and BP. • Temperatures can be LESS THAN ZERO.

8. For most science work the Celsius Scale is fine. However, in some calculation, temperatures less than ZERO present a problem. • Example Volume/Mass calculations cannot use temperatures less than zero because volume or masses CANNOT BE NEGATIVE. • In these instances, a third scale is used.

9. The KELVIN SCALE is based on the expansion and contraction of matter. • For every degree of change (+ or -) Kelvin, matter expands or contracts by 1/273.15of its original volume. • If matter’s temperature could be lowered to -273.15 K, matter would have a ZERO VOLUME, which is THEORETICALLY impossible.

10. This temperature is known as ABSOLUTE ZERO. • At this temperature matter would possess NO KINETIC ENERGY! • Scientist have come within a few millionths of a degree of absolute zero!

11. Temperature Calculations • Often in scientific work, it is necessary to convert temperatures from one system to another. • This is easily done with the appropriate equation.

12. Fahrenheit to Celsius • To convert a temperature given in oF to Celsius, use this equation: • oC = 0.56(oF-32)

13. Celsius to Fahrenheit • To convert a temperature in oC to Fahrenheit, use this equation: • oF = 1.8 (oC) + 32

14. Converting Celsius Kelvin • K = oC + 273.15 • oC = K – 273.15 • (Generally just 273 is fine!)

15. Fahrenheit  Kelvin • To convert Fahrenheit to Kelvin: K = 0.56 (oF-32) + 273.15

16. Practice Problems • Complete the practice problems sheet.

17. I CAN convert number to and from SCIENTIFIC NOTATION.

18. What are Measurements • A measurement is a QUANTITY with both a NUMBER and a UNIT. • In science, you will encounter very, very large numbers as well as very, very small ones. • To simply the handling of such numbers, we often write them in a compressed form called SCIENTIFIC NOTATION.

19. In scientific notation, numbers with many digits are often written as a coefficient and a power of 10. • Example 6.022 x 1023 • Coefficient • Power of 10

20. Converting Numbers to Scientific Notation • Converting numbers to scientific notation is easy. • 1. Locate the DECIMAL [may be an understood decimal] • 2. MOVE the decimal to the LEFT or to the RIGHT until it is to the RIGHT OF THE FIRSTNON-ZERO DIGIT in the number. • Example 24567.88 would be 2.456788 • 3. COUNT THE NUMBER OF PLACES the decimal was moved…this is the POWER OF 10.

21. When the decimal is moved to the LEFT the power of 10 is POSITIVE. • When the decimal is moved to the RIGHT the power of 10 is NEGATIVE. • You may DROP TERMINAL ZEROS to round off or follow the directions in the problem.

22. SAMPLE PROBLEM • Convert this number to scientific notation: • 602200000000000000000000 • Locate the decimal. • Decide if the decimal needs to move left or right. • Count the number of places it has to move. • Rewrite the number with the decimal in its new location [drop terminal zeros]. • Add the power of 10 with the correct sign.

23. 602200000000000000000000 • Since there was no written decimal it is understood to be at the end of the number. • Which direction should it be moved? • We will need to move it toward the LEFT to get it between the first two non-zero digits. • 602200000000000000000000 • The decimal was moved a total of 23 places to the left.

24. 6 02200000000000000000000 • Drop the terminal zeros to get • 6 022 • Since the decimal moved 23 places to the LEFT, the power of 10 is POSITIVE 23.

25. So the number in scientific notation is: 6.022 X 1023

26. MORE PRACTICE • Write this number is Scientific Notation: • 0.0000475000

27. 0.0000475000 • Decimal First two non-zero digits • This time the decimal has to be moved to the RIGHT. This will make the power of 10 NEGATIVE. • 000004.75000 • DROP these zeros!

28. 4.75 • The decimal was moved 5 places to the right, so the power of 10 is -5. • 4.75 X 10-5

29. Write each number in scientific notation. 0.07882 = 0.00000272338 = 118000 = 87200 = 0.00002786 = 0.000000664 = 450 = 74171.7 = 770 = 0.0000085 =

30. 0.07882 = 7.882 × 10-2 0.00000272338 = 2.72338 × 10-6 118000 = 1.18 × 105 87200 = 8.72 × 104 0.00002786 = 2.786 × 10-5 0.000000664 = 6.64 × 10-7 450 = 4.5 × 102 74171.7 = 7.41717 × 104 770 = 7.7 × 102 0.0000085 = 8.5 × 10-6