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Get Started Now- Intro Lesson: a4:20
- Intro Lesson: b5:10
- Intro Lesson: c3:38
- Lesson: 1a2:30
- Lesson: 1b4:23

In this lesson, we will learn:

- To recall the expressions for pH and pOH.
- To use the antilog to relate pH and pOH back to aqueous ion concentration.
- How pH and pOH are related to the K
_{w}expression.

- We learned earlier in Introduction to acid-base theory , that pH is defined by the concentration of H
_{3}O^{+}ions in solution:pH = -log[H _{3}O^{+}] - In the same way, pOH can be measured, which is defined by the concentration of OH
^{-}ions in solution:pOH = -log[OH ^{-}]

Be careful with significant figures – with logarithms, only the values in decimal places are considered significant figures. - The reverse of the logarithm is known as the
__antilog__, so the antilog can be used to__convert pH into [H___{3}O^{+}]__and pOH into [OH__^{-}]. The antilog is found by rising 10 to the value for which you are getting the antilog:Antilog (x) = 10 ^{x}__Make sure your calculator gives antilogs in scientific notation, or standard form__. As stated above, the decimal places are the significant figures in a logarithm value. The first digit represents the order of magnitude. For example, log(10) = 2.0 and log(100) = 3.0; 3 is one greater than 2, so 3 as a logarithm is one order of magnitude (10x) greater than 2 as a logarithm.

With this, we can show expressions to find [H_{3}O^{+}] and [OH^{-}] using pH and pOH:[H _{3}O^{+}] = 10^{-pH}[OH ^{-}] = 10^{-pOH} - Because [H
_{3}O^{+}] and [OH^{-}] in aqueous solution at 25^{o}C are related to K_{w}, pH and pOH are related to pK_{w}– which is just the negative log of the K_{w}constant!- pH and pOH give logarithmic expressions of the aqueous ion concentration. Recall that:
K _{w}= [H_{3}O^{+}_{(aq)}] [OH^{-}_{(aq)}] = 1.00 $*$ 10^{-14}at 25^{o}CTaking the negative log of these aqueous ion concentrations, we can determine: pH + pOH = pK _{w}= 14

With these we can relate the four expressions in a ‘grid’ below:

- pH and pOH give logarithmic expressions of the aqueous ion concentration. Recall that:

- Introduction
__Relating pH, H___{3}O^{+}__and K___{w}.a)Defining pH and pOH.b)Antilogs: Using pH and pOH to find [H_{3}O^{+}] and [OH^{-}].c)Connecting pH → [H_{3}O^{+}] → [OH^{-}] → pOH → pH - 1.
**Find the concentration of acidic and basic solutions when given from the pH.**a)A solution of HCl, a strong acid, has a pH of 1.74. What is the H_{3}O^{+}_{(aq)}concentration of this solution? Give your answer to three significant figures.b)A solution of potassium hydroxide, KOH, has a pH of 12.89. Find the concentration of OH^{-}_{(aq)}ions in this solution. Give your answer to three significant figures.

2.

Acid-Base Theory

2.1

Introduction to acid-base theory

2.2

Conjugate acids and bases

2.3

Strong and weak acids and bases

2.4

pH and pOH

2.5

Acid dissociation constant

2.6

Relative strength of acids and bases

2.7

Ionic product of water: K_{w}

2.8

K_{a} and K_{b} calculations

2.9

Acid-base titration

2.10

pH indicators

2.11

Titration curves

2.12

Buffer solutions