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How is pH defined? The pH of a solution is the negative logarithm of the hydrogen-ion concentration. The pH may be represented mathematically, using the following equation: pH = –log[H+] In pure water or a neutral solution, [H+] = 1 × 10–7M, and the pH is 7. pH = –log(1 × 10–7) = –(log 1 × log 10–7) = –(0.0 + (–7.0)) = 7.0 If the [H+] of a solution is greater than 1 × 10–7M, the pH is less than 7.0. If the [H+] of the solution is less than 1 × 10–7M, the pH is greater than 7.0.

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**Sample problem: Calculating pH**

What is the pH of a solution with a hydrogen-ion concentration of 4.2 × 10–10M? (contd.)

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**Sample problem: Calculating pH**

Calculate the pH of a solution with a hydroxide concentration of 1.2 × 10–3M.

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**How are [H+] and [OH–] related in an aqueous solution?**

The reaction in which water molecules produce ions is called the self-ionization of water. This reaction can be written as a simple dissociation. H2O(l) ⇄ H+(aq) + OH–(aq) The self-ionization of water occurs to a very small extent. In pure water at 25°C, the concentration of hydrogen ions is only 1 × 10–7M. The concentration of OH– is also 1 × 10–7M because the numbers of H+ and OH– ions are equal in pure water. Any aqueous solution in which [H+] and [OH–] are equal is a neutral solution.

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For aqueous solutions, the product of the hydrogen-ion concentration and the hydroxide-ion concentration equals 1.0 10–14. [H+] [OH–] = 1.0 10–14 This equation is true for all dilute aqueous solutions at 25°C. The product of the concentrations of the hydrogen ions and the hydroxide ions in water is called the ion-product constant for water (Kw). Kw = [H+] × [OH–] = 1.0 × 10–14 A solution in which [H+] is greater than [OH–] is an acidic solution. In acidic solutions, the [H+] is greater than 1 × 10–7M. A basic solution is one in which [H+] is less than [OH–]. The [H+] of a basic solution is less than 1 × 10–7M. Basic solutions are also known as alkaline solutions.

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**You can use this equation to convert between pH and pOH**

Kw = pH + pOH Kw always equals 14 So.. pH + pOH = 14 You can use this equation to convert between pH and pOH 7

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**Sample problem: Calculating pH**

Calculate the pH of a solution with a pOH of 12. 8

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**Sample problem: Calculating pH**

Calculate the pOH of a solution with a pH of 9. 9

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**Sample problem: Calculating pH**

Calculate the hydrogen ion concentration of a solution with a pH of 8.5. 10

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**Sample problem: Calculating pH**

Calculate the hydrogen ion concentration of a solution with a pOH of 13.5. 11

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Acids and Bases. Ionization of Water H 2 O + H 2 O H 3 O + + OH - K w = [H 3 O + ][OH - ] = 1.0 10 -14.

Acids and Bases. Ionization of Water H 2 O + H 2 O H 3 O + + OH - K w = [H 3 O + ][OH - ] = 1.0 10 -14.

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