How can Kb be used to determine Ka for a conjugate base in chemistry?

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SUMMARY

The discussion centers on the relationship between the base dissociation constant (Kb) and the acid dissociation constant (Ka) for conjugate bases in chemistry. Specifically, the formula Kw = Ka x Kb = 1 x 10^-14 is highlighted, indicating that the product of Ka and Kb for a conjugate acid-base pair equals the ion product of water. For example, given a weak base with Kb = 1.5 x 10^-9, the corresponding Ka can be calculated using the equation Ka = Kw / Kb, resulting in Ka = 6.67 x 10^-6. This relationship is crucial for understanding acid-base equilibria.

PREREQUISITES
  • Understanding of acid-base chemistry concepts
  • Familiarity with dissociation constants (Ka and Kb)
  • Knowledge of the ion product of water (Kw)
  • Basic algebra for solving equations
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  • Learn how to calculate Ka from Kb using the formula Ka = Kw / Kb
  • Study the concept of pKa and its relationship to Ka
  • Explore examples of weak acids and their conjugate bases
  • Investigate the significance of dissociation constants in chemical equilibria
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Chemistry students, educators, and anyone interested in mastering acid-base equilibria and the calculations involving dissociation constants.

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Hey guys, I am new here. I am a college student that is trying to brush up on some chemistry. I am reading an old textbook that I have, and I didnt understand something.

I was wondering how some would use the Kb of a weak base, how they would determine the value of Ka for the conjugate base?

A sample problem in the book is: A weak acid has a Kb= 1.5 x 10^-9. What is the value of Ka for the conjugate base?


I have read the whole chapter over Acid & Bases, but it says this problem is on the cd-rom that is included with my book. Yet, i never received that cd when I bought my book. I have tried searching but have had no luck. Any help would be great. I am just trying to understand the relationship between Ka and Kb. Thanks again.
 
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Kw = Ka x Kb = 1 x 10^-14
 
K is called a dissociation constant

What K states is that there is a certain amount of dissociation at any given time, and almost everything has one of these numbers. Something like lead chloride will have a K value to say how soluble it is. Here you are talking about water, and K relates to water breaking from HOH into H and OH. For water, the dissociation constant is 10^-14.

[H^+] * [OH^-] = 10^{-14}

K_A * K_B = 10^{-14}

pK_A + pK_B = 14
 

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