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

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Presentation on theme: "Logarithms. The logarithm of a number is the number of times 10 must be multiplied by itself to equal that number."— Presentation transcript:

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

69 Daily Quiz – pH and logarithms

70 1. What is true of [H + ] and [OH - ]? a. [H + ] = [OH - ] b. [H + ] x [OH - ] = 1 x 10 -7 c. [H + ] ÷ [OH - ] = 1 x 10 -7 d. [H + ] x [OH - ] = 1 x 10 -14 e. [H + ] ÷ [OH - ] = 1 x 10 -14

71 Daily Quiz – pH and logarithms 2. In a neutral solution, pH = a. 0 b. 0.5 c. 1 d. 7 e. 14

72 Daily Quiz – pH and logarithms 3. 1 x 10 -5 = ? a. 5 b. 100,000 c. 0.000,01 d. 0.000,001

73 Daily Quiz – pH and logarithms 4. Which number is bigger? a. 1 x 10 -2 b. 1 x 10 -6

74 1.You have a 1.0M solution of HI (a strong acid). What is the pH? a.0.0 b.1.0 c.10.0 d.13.0 Daily Quiz [H+], [OH-], and pH

75 2.You have a 1.0M solution of HNO 3 (a strong acid). What is the pH? a.0.7 b.1.3 c.2.0 d.5.0 Daily Quiz [H+] & [OH-] to pH

76 3.You have a 1.0M solution of KOH (a strong base). What is the pH? a.0.0 b.1.0 c.7.0 d.14.0 Daily Quiz [H+], [OH-], and pH

77 4.You have a 10 -5 M solution of Mg(OH) 2 (a strong base). What is the pH? a.4.32 b.4.62 c.9.38 d.9.68 Daily Quiz [H+], [OH-], and pH

78 Daily Quiz – pH and logarithms 1. What is true of [H + ] and [OH - ]? a. [H + ] = [OH - ] b. [H + ] x [OH - ] = 1 x 10 -7 c. [H + ] ÷ [OH - ] = 1 x 10 -7 d. [H + ] x [OH - ] = 1 x 10 -14 e. [H + ] ÷ [OH - ] = 1 x 10 -14

79 Daily Quiz – pH and logarithms 1. What is true of [H + ] and [OH - ]? a. [H + ] = [OH - ] b. [H + ] x [OH - ] = 1 x 10 -7 c. [H + ] ÷ [OH - ] = 1 x 10 -7 d. [H + ] x [OH - ] = 1 x 10 -14 e. [H + ] ÷ [OH - ] = 1 x 10 -14

80 Daily Quiz – pH and logarithms 2. In a neutral solution, pH = a. 0 b. 0.5 c. 1 d. 7 e. 14

81 Daily Quiz – pH and logarithms 2. In a neutral solution, pH = a. 0 b. 0.5 c. 1 d. 7 e. 14

82 Daily Quiz – pH and logarithms 3. 1 x 10 -5 = ? a. 5 b. 100,000 c. 0.000,01 d. 0.000,001

83 Daily Quiz – pH and logarithms 3. 1 x 10 -5 = ? a. 5 b. 100,000 c. 0.000,01 d. 0.000,001

84 Daily Quiz – pH and logarithms 4. Which number is bigger? a. 1 x 10 -2 b. 1 x 10 -6

85 Daily Quiz – pH and logarithms 4. Which number is bigger? a. 1 x 10 -2 b. 1 x 10 -6

86 1.You have a 1.0M solution of HI (a strong acid). What is the pH? a.0.0 b.1.0 c.10.0 d.13.0 Daily Quiz [H+], [OH-], and pH

87 1.You have a 1.0M solution of HI (a strong acid). What is the pH? a.0.0 b.1.0 c.10.0 d.13.0 Daily Quiz [H+], [OH-], and pH

88 1.You have a 1.0M solution of HI (a strong acid). What is the pH? a.0.0 b.1.0 c.10.0 d.13.0 Daily Quiz [H+], [OH-], and pH Why?

89 Daily Quiz [H+], [OH-], and pH 1.0M HI [H + ] = 1.0 x 10 0 log[H + ] = 0.00 + 0 pH = 0.00

90 2.You have a 1.0M solution of HNO 3 (a strong acid). What is the pH? a.0.7 b.1.3 c.2.0 d.5.0 Daily Quiz [H+] & [OH-] to pH

91 2.You have a 1.0M solution of HNO 3 (a strong acid). What is the pH? a.0.7 b.1.3 c.2.0 d.5.0 Daily Quiz [H+] & [OH-] to pH

92 2.You have a 1.0M solution of HNO 3 (a strong acid). What is the pH? a.0.7 b.1.3 c.2.0 d.5.0 Daily Quiz [H+] & [OH-] to pH Why?

93 Daily Quiz [H+], [OH-], and pH 0.050M HNO 3 [H + ] = 5.0 x 10 -2 log[H + ] = 0.70 – 2 pH = 1.30

94 3.You have a 1.0M solution of KOH (a strong base). What is the pH? a.0.0 b.1.0 c.7.0 d.14.0 Daily Quiz [H+], [OH-], and pH

95 3.You have a 1.0M solution of KOH (a strong base). What is the pH? a.0.0 b.1.0 c.7.0 d.14.0 Daily Quiz [H+], [OH-], and pH

96 3.You have a 1.0M solution of KOH (a strong base). What is the pH? a.0.0 b.1.0 c.7.0 d.14.0 Daily Quiz [H+], [OH-], and pH Why?

97 Daily Quiz [H+], [OH-], and pH 1.0M KOH [OH - ] = 1.0 x 10 0 log[OH - ] = 0.00 + 0 pOH = 0.00 pH = 14.00

98 4.You have a 10 -5 M solution of Mg(OH) 2 (a strong base). What is the pH? a.4.32 b.4.62 c.9.38 d.9.68 Daily Quiz [H+], [OH-], and pH

99 4.You have a 10 -5 M solution of Mg(OH) 2 (a strong base). What is the pH? a.4.32 b.4.62 c.9.38 d.9.68 Daily Quiz [H+], [OH-], and pH

100 4.You have a 10 -5 M solution of Mg(OH) 2 (a strong base). What is the pH? a.4.32 b.4.62 c.9.38 d.9.68 Daily Quiz [H+], [OH-], and pH Why?

101 2.4 x 10 -5 M Mg(OH) 2 [OH - ] = (2.4 x 10 -5 ) x 2 log[OH - ] = 0.68 – 5 pOH = 4.32 pH = 9.68 Daily Quiz [H+], [OH-], and pH.

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

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