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 transcript:

Logarithms

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

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

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

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

Logarithms You can multiply two numbers by adding their logarithms.

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

Logarithms You can multiply two numbers by adding their logarithms. 100 x 1000 = 100, = 5

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

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

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

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

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

Logarithms What if the number is small instead of big?

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

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

Logarithms What if the number is small instead of big? = 3 x log = log 3 + log = – 4

Logarithms What if the number is small instead of big? = 3 x log = log 3 + log = – 4 =

Logarithms Try a few!

Logarithms log 10 3 =

Logarithms log 10 3 = 3

Logarithms log 10 8 =

Logarithms log 10 8 = 8

Logarithms log =

Logarithms log = -10

Logarithms log 2 =

Logarithms log 2 = 0.301

Logarithms log 5.8 =

Logarithms log 5.8 = 0.763

Logarithms log 9.2 =

Logarithms log 9.2 = 0.963

Logarithms log 4 x =

Logarithms log 4 x =

Logarithms log 4 x = =

Logarithms log 8.3 x 10 5 =

Logarithms log 8.3 x 10 5 =

Logarithms log 8.3 x 10 5 = = 5.919

Logarithms log 7.1 x =

Logarithms log 7.1 x =

Logarithms log 7.1 x = =

Logarithms log 4.8 x =

Logarithms log 4.8 x =

Logarithms log 4.8 x = =

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

[H + ] = What is the pH?

[H + ] = = 3.5 x 10 -3

[H + ] = = 3.5 x log = log log 10 -3

[H + ] = = 3.5 x log = log log = – 3

[H + ] = = 3.5 x log = log log = – 3 = –2.456

[H + ] = = 3.5 x log = log log = – 3 = –2.456 pH = 2.456

pH = 6.13 What is the [H + ]?

pH = 6.13 –pH = –6.13

pH = 6.13 –pH = –6.13 = 0.87 – 7

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

pH = 8.7 What is the pOH?

pH = 8.7 pOH = 14 - pH

pH = 8.7 pOH = 14 - pH = 14 – 8.7

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

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

Always Remember:

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

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

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

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

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

Always Remember: Polyprotic acids have more than one hydrogen.

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

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

Daily Quiz – pH and logarithms

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

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

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

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

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

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

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

4.You have a 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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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?

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

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

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

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?

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

4.You have a 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

4.You have a 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

4.You have a 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?

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

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