Section 6.2 pg. 238 - 244

pH and pOH Calculations

Pure Water

• Pure water actually self ionizes (called “auto-ionization”), so it contains H⁺_(aq) and OH^-_(aq) ions, but their concentrations are so low that a conductivity test is negative.

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• In a sample of pure water, about two out of every billion molecular collisions are successful in forming hydronium and hydroxide ions

2H₂O_(l) 🡪 H₃O⁺_(aq) and OH^-_(aq)

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• In pure water at SATP, the hydronium ion concentration is very low; about 1 x 10^-7 mol/L
• This concentration is often negligible and will show no conductivity unless very sensitive equipment is used (pg. 238 – Figure 1)

Pure Water

• Adding acid to water adds H⁺_(aq) ions causing the H⁺_(aq) concentration to increase, thus it makes the solution conductive

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• Adding base to water adds OH^-_(aq) ions causing the OH^-_(aq) concentration to increase, thus it makes the solution conductive

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• Aqueous solutions exhibit a wide range of hydronium ion concentrations – from more than 10 mol/L for concentrated HCl_(aq) to less than 10^-15 mol/L for concentrated NaOH_(aq)

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• This range is called pH; meaning “power of hydrogen”
• “the negative of the base ten exponent for the hydronium ion concentration”

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[H₃O ⁺_(aq)] = 10 ^-pH

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pH – power of hydrogen

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• This range is called pH; meaning “power of hydrogen”
• “The negative of the base ten exponent for the hydronium ion concentration”

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[H₃O ⁺_(aq)] = 10 ^–pH

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1 x 10¹ mol/L

1 x 10^-7 mol/L

1 x 10^-15 mol/L

pH = -1

pH = 7

pH = 15

Acidic solution

Basic solution

Neutral

pH – power of hydrogen

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[H₃O ⁺_(aq)] = 10 ^-pH

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The pH scale is used to communicate a broad range of hydronium ion concentrations. Most common acids and bases have pH values between 0 and 14

pH changes

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Changes in pH can be deceptive. Adding vinegar to pure water might change the pH from 7 to 4. While this change of 3 pH units may not appear significant, the change in hydronium ion concentration is 10³ or 1000 times larger

Practice

• Try pg. 239 #1-3

pH Calculations

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• Do you think solutions always have a pH that is an integer or simply a power of 10?

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• No, scientists often need pH measurements to one or more decimal places

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• So our definition of [H₃O ⁺_(aq)] =10 ^–pH must be improved so we can convert numbers like 6.7 x 10^-8 mol/L to a pH

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• Our new definition:

pH = -log [H₃O ⁺_(aq)]

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pH = -log [ 6.7 x 10^-8] * the units are dropped because a log has no units

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pH = - (-7.1739252)

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pH = 7.1739252 – but how many sig digs can it have?

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pH Calculations

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• Sig digs for pH:

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“The number of digits following the decimal point in the pH value is equal to the number of sig digs in the hydronium ion concentration.”

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[H₃O ⁺_(aq)] = 6.7 x 10 ^-8 (two sig digs)

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pH = 7.17 (two sig digs)

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pH Calculations

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• So from [H₃O ⁺_(aq)] to pH we use:

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pH = -log [H₃O ⁺_(aq)]

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pH = -log (4.5 x 10^-10)

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pH = 9.35 (two sig digs)

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• But to go from pH to [H₃O ⁺_(aq)] we can still use:

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[H₃O ⁺_(aq)] =10 ^–pH

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[H₃O ⁺_(aq)] = 10 ^-9.35

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[H₃O ⁺_(aq)] = 4.5 x 10 ^-10 mol/L

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Since pH has no units, the definition of pH includes the requirement that concentration be in mol/L; you will need to add the units to your answer.

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Using your calculator:

• Go to pg. 241 and read the two Learning Tips

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• Numbers in scientific notation are best entered using the exponent key (EE) – because the calculator treats the entry as one value.

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• The 10^x key is not recommended because you may obtain the incorrect result in some situations

log

Try it: Turn [H₃O ⁺_(aq)] ₌ 4.7 x 10^-11 mol/L into a pH value

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Calculator:

4

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7

2nd

,

(-)

1

(-)

enter

1

Using your calculator:

• A solution has a pH of 5.3. Calculate its hydronium ion concentration.

[H₃O ⁺_(aq)] =10 ^–pH

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[H₃O ⁺_(aq)] =10 ^–5.3

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[H₃O ⁺_(aq)] = 5.0118 x 10^-6

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Sig digs? (pH = 5.3 – only 1 sig dig) = 0.5 x 10 ^-5 mol/L

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log

Try it with your calculator:

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Calculator:

3

.

2nd

5

(-)

enter

pOH and Hydroxide ion Concentration

• Although pH is used more commonly, in some applications it is more practical to describe hydroxide ion concentration.

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• The definition of pOH follows the same format as pH

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• Example: Calculate the hydroxide ion concentration of water with a pOH of 6.3.

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pOH = -log [OH ^-_(aq)]

[OH ^-_(aq)] =10 ^–pOH

[OH ^-_(aq)] =10 ^–pOH

[OH ^-_(aq)] =10 ^{– 6.3}

⁼ 5 x 10^-7 mol/L

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Summary

• The number of digits following the decimal point in a pH or pOH value is equal to the number of significant digits in the corresponding hydronium or hydroxide concentration.

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• For both pH and pOH, an inverse relationship exist between the ion concentration and the pH or pOH. The greater the hydronium ion concentration, the lower the pH is.

pOH = -log [OH ^-_(aq)]

[OH ^-_(aq)] =10 ^–pOH

[H₃O⁺_(aq)] =10 ^–pH

pH = -log [H₃O⁺_(aq)]

Practice

• Pg. 242 #4-7 (pH)

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• Pg. 243 #9-11 (pOH)