Table of contents

1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
8. Gases, Liquids and Solids3h 25m
9. Solutions4h 10m
10. Acids and Bases3h 29m
11. Nuclear Chemistry56m
BONUS: Lab Techniques and Procedures1h 38m
BONUS: Mathematical Operations and Functions47m
12. Introduction to Organic Chemistry1h 34m
13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
17. Amines39m
18. Amino Acids and Proteins1h 51m
19. Enzymes1h 37m
20. Carbohydrates1h 41m
21. The Generation of Biochemical Energy2h 8m
22. Carbohydrate Metabolism2h 22m
23. Lipids2h 26m
24. Lipid Metabolism1h 45m
25. Protein and Amino Acid Metabolism1h 37m
26. Nucleic Acids and Protein Synthesis2h 54m

10. Acids and Bases

Auto-Ionization

GOB Chemistry

10. Acids and Bases

Auto-Ionization

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1:35 minutes

Problem 51

Textbook Question

How is K_w defined, and what is its numerical value at 25 °C?

Verified step by step guidance

K_w is the ionization constant of water, which represents the equilibrium constant for the self-ionization of water. The reaction is:

H_{+} (aq) + OH (aq) \leftrightarrow H O_{2} (l)

The expression for K_w is derived from the equilibrium concentrations of the ions produced during water's self-ionization:

K_{w = [H_{+}] \times [OH]}

At 25 °C, the concentrations of

H_{+}

and

OH

in pure water are both equal to

{1.0}^{\times 10 -7}

Substitute these values into the K_w expression:

K_{w = [H_{+}] \times [OH] = {1.0}^{\times 10 -7} \times {1.0}^{\times 10 -7}}

Simplify the expression to find the numerical value of K_w at 25 °C, which is typically expressed as

{1.0}^{\times 10 -14}

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ion Product of Water (K_w)

K_w, or the ion product of water, is a constant that represents the equilibrium constant for the self-ionization of water. It is defined as the product of the concentrations of hydrogen ions (H⁺) and hydroxide ions (OH⁻) in pure water at a given temperature. This concept is crucial for understanding acid-base chemistry and the behavior of water in various chemical reactions.

Self-Ionization of Water

The self-ionization of water is a process where two water molecules interact to produce one hydroxide ion (OH⁻) and one hydronium ion (H₃O⁺). This reaction is reversible and occurs to a very small extent in pure water, leading to the formation of equal concentrations of H⁺ and OH⁻ ions. Understanding this process is essential for grasping the concept of pH and the neutrality of water.

Numerical Value of K_w at 25 °C

At 25 °C, the numerical value of K_w is 1.0 x 10⁻¹⁴. This value indicates that in pure water, the concentrations of H⁺ and OH⁻ ions are both 1.0 x 10⁻⁷ M, reflecting the neutral nature of water at this temperature. This constant is fundamental in calculations involving pH, pOH, and the acidity or basicity of solutions.

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