1. Logarithms

2. The logarithm of a number is the number of times 10 must be multiplied by itself to equal that number.

3. Logarithms 1000 = 10 x 10 x 10 log 1000 = 3

4. Logarithms To find the logarithm of a number, count the zeroes. If the number is in scientific notation, look at the exponent.

5. Logarithms 1 = 1 x 10 0 10 = 1 x 10 1 100 = 1 x 10 2 0.1 = 1 x 10 -1 0.01 = 1 x 10 -2 log 1 = 0 log 10 = 1 log 100 = 2 log 0.1 = -1 log 0.01 = -2

6. Logarithms You can multiply two numbers by adding their logarithms.

7. Logarithms You can multiply two numbers by adding their logarithms. 100 x 1000 = 100,000

8. Logarithms You can multiply two numbers by adding their logarithms. 100 x 1000 = 100,000 2 + 3 = 5

9. Logarithms You can multiply two numbers by adding their logarithms. 1 x 10 8 = 100,000,000

10. Logarithms You can multiply two numbers by adding their logarithms. 1 x 10 8 = 100,000,000 0 + 8 = 8

11. Logarithms You can multiply two numbers by adding their logarithms. 2 x 10 8 = 200,000,000 ? + 8 = ?

12. Logarithms So what’s the logarithm of 2? You have to look it up. 2 x 10 8 = 200,000,000 ? + 8 = ?

13. Logarithms So what’s the logarithm of 2? You have to look it up. 2 x 10 8 = 200,000,000 0.301 + 8 = 8.301

14. Logarithms What if the number is small instead of big?

15. Logarithms What if the number is small instead of big? 0.0003 = 3 x 10 -4

16. Logarithms What if the number is small instead of big? 0.0003 = 3 x 10 -4 log 0.0003 = log 3 + log 10 -4

17. Logarithms What if the number is small instead of big? 0.0003 = 3 x 10 -4 log 0.0003 = log 3 + log 10 -4 = 0.477 – 4

18. Logarithms What if the number is small instead of big? 0.0003 = 3 x 10 -4 log 0.0003 = log 3 + log 10 -4 = 0.477 – 4 = -3.523

19. Logarithms Try a few!

20. Logarithms log 10 3 =

21. Logarithms log 10 3 = 3

22. Logarithms log 10 8 =

23. Logarithms log 10 8 = 8

24. Logarithms log 10 -10 =

25. Logarithms log 10 -10 = -10

26. Logarithms log 2 =

27. Logarithms log 2 = 0.301

28. Logarithms log 5.8 =

29. Logarithms log 5.8 = 0.763

30. Logarithms log 9.2 =

31. Logarithms log 9.2 = 0.963

32. Logarithms log 4 x 10 12 =

33. Logarithms log 4 x 10 12 = 0.602 + 12

34. Logarithms log 4 x 10 12 = 0.602 + 12 = 12.602

35. Logarithms log 8.3 x 10 5 =

36. Logarithms log 8.3 x 10 5 = 0.919 + 5

37. Logarithms log 8.3 x 10 5 = 0.919 + 5 = 5.919

38. Logarithms log 7.1 x 10 -3 =

39. Logarithms log 7.1 x 10 -3 = 0.851 - 3

40. Logarithms log 7.1 x 10 -3 = 0.851 - 3 = -2.149

41. Logarithms log 4.8 x 10 -11 =

42. Logarithms log 4.8 x 10 -11 = 0.681- 11

43. Logarithms log 4.8 x 10 -11 = 0.681- 11 = -10.319

44. pH pH = -log [H + ] pOH = -log [OH - ] pH + pOH = 14

45. [H + ] = 0.0035 What is the pH?

46. [H + ] = 0.0035 0.0035 = 3.5 x 10 -3

47. [H + ] = 0.0035 0.0035 = 3.5 x 10 -3 log 0.0035 = log 3.5 + log 10 -3

48. [H + ] = 0.0035 0.0035 = 3.5 x 10 -3 log 0.0035 = log 3.5 + log 10 -3 = 0.544 – 3

49. [H + ] = 0.0035 0.0035 = 3.5 x 10 -3 log 0.0035 = log 3.5 + log 10 -3 = 0.544 – 3 = –2.456

50. [H + ] = 0.0035 0.0035 = 3.5 x 10 -3 log 0.0035 = log 3.5 + log 10 -3 = 0.544 – 3 = –2.456 pH = 2.456

51. pH = 6.13 What is the [H + ]?

52. pH = 6.13 –pH = –6.13

53. pH = 6.13 –pH = –6.13 = 0.87 – 7

54. pH = 6.13 –pH = –6.13 = 0.87 – 7 [H + ] = 7.4 x 10 -7

55. pH = 8.7 What is the pOH?

56. pH = 8.7 pOH = 14 - pH

57. pH = 8.7 pOH = 14 - pH = 14 – 8.7

58. pH = 8.7 pOH = 14 - pH = 14 – 8.7 = 5.3

59. pH = 8.7 pOH = 14 - pH = 14 – 8.7 = 5.3 The solution is acidic.

60. Always Remember:

61. The molarity of a solution refers to how many moles per liter it has.

62. Always Remember: The molarity of a solution refers to how many moles per liter it has. 1.0 M = 1.0 mol/L

63. Always Remember: A strong acid or base dissociates completely in water.

64. Always Remember: A strong acid or base dissociates completely in water. 1.0 M HCl = 1.0 M H +

65. Always Remember: A strong acid or base dissociates completely in water. 1.0 M HCl = 1.0 M H + 1.0 M NaOH = 1.0 M OH -

66. Always Remember: Polyprotic acids have more than one hydrogen.

67. Always Remember: Polyprotic acids have more than one hydrogen. 1.0 M H 2 SO 4 = 2.0 M H +

68. Always Remember: Polyprotic acids have more than one hydrogen. 1.0 M H 2 SO 4 = 2.0 M H +.

69. Suggested Homework Page 609 # 18 Page 611 # 19 Page 612 # 20