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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

A weak base has Kb = 1.5 × 10−9. What is the value of Ka for the conjugate acid?

Interpretation Introduction

Interpretation:

The Ka value for conjugate acid of a weak base has to be calculated by using the Kb of weak base.

Concept introduction:

A base (B) undergoes dissociation in an aqueous medium. The base dissocition gives ions BH+(aq.) and OH(aq.). The conjugate acid BH+(aq.) may interact with H2O and forms BOH(aq.) and it can be represented as following equilibrium.

  B(aq.)+ H2O(l)BH+(aq.)+ OH1(aq.)                                                 (1)

The dissociation constant for the acid is Kb,

  Kb=[BH+][OH][B]

Interaction of conjugate acid BH+(aq.) with water is represented as,

  BH+(aq.)+ H2O(l)B(aq.)+ H3O+(aq.)                                                 (2)

The dissociation constant for the conjugate acid is Ka,

  Ka=[B][H3O+][BH+]

From equation (1) and (2) the net equilibrium will be

  2H2O(l)H3O+(aq.)+ OH1(aq.)                                                             (3)

The equation (3) is known as the auto-ionization of water molecule. The dissociation constant for water is written as follows,

  Kw=[H3O+][OH]

Thus from equation (1) and (2), there is an important relation established between ionization constant Kb for base and ionization constant Ka of conjugate acid i.e.

  Kw=Ka×Kb                                                                                               (4)

The ionisation constant of water has a constant value i.e. Kw=1×10-14. On taking negative logarithm of equation (4), a new relation established in terms of pKa,pKb and pKw as follows,

  -log(Kw)=-log(Ka×Kb)

   pKw= pKa+pKb                                                                                           (5)

Explanation

The Ka value for conjugate acid (BH+) of the given weak base (B) is calculated below.

Given:

Value of Kb for weak base is 1.5×109.

Value of Kw for water is 1.0×1014.

Using equation (4),Ka for conjugate acid is calculated as follows,

  Kw=Ka×Kb

Substitute the value of Kb and Kw

1

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Chapter 16 Solutions

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Sect-16.10 P-1.2ACPSect-16.10 P-1.3ACPSect-16.10 P-2.1ACPSect-16.10 P-2.2ACPSect-16.10 P-2.3ACPSect-16.10 P-2.4ACPSect-16.10 P-2.5ACPCh-16 P-1PSCh-16 P-2PSCh-16 P-3PSCh-16 P-4PSCh-16 P-5PSCh-16 P-6PSCh-16 P-7PSCh-16 P-8PSCh-16 P-9PSCh-16 P-10PSCh-16 P-11PSCh-16 P-12PSCh-16 P-13PSCh-16 P-14PSCh-16 P-15PSCh-16 P-16PSCh-16 P-17PSCh-16 P-18PSCh-16 P-19PSCh-16 P-20PSCh-16 P-21PSCh-16 P-22PSCh-16 P-23PSCh-16 P-24PSCh-16 P-25PSCh-16 P-26PSCh-16 P-27PSCh-16 P-28PSCh-16 P-29PSCh-16 P-30PSCh-16 P-31PSCh-16 P-32PSCh-16 P-33PSCh-16 P-34PSCh-16 P-35PSCh-16 P-36PSCh-16 P-37PSCh-16 P-38PSCh-16 P-39PSCh-16 P-40PSCh-16 P-41PSCh-16 P-42PSCh-16 P-43PSCh-16 P-44PSCh-16 P-45PSCh-16 P-46PSCh-16 P-47PSCh-16 P-48PSCh-16 P-49PSCh-16 P-50PSCh-16 P-51PSCh-16 P-52PSCh-16 P-53PSCh-16 P-54PSCh-16 P-55PSCh-16 P-56PSCh-16 P-57PSCh-16 P-58PSCh-16 P-59PSCh-16 P-60PSCh-16 P-61PSCh-16 P-62PSCh-16 P-63PSCh-16 P-64PSCh-16 P-65PSCh-16 P-66PSCh-16 P-67PSCh-16 P-68PSCh-16 P-69PSCh-16 P-70PSCh-16 P-71PSCh-16 P-72PSCh-16 P-73PSCh-16 P-74PSCh-16 P-75PSCh-16 P-76PSCh-16 P-77PSCh-16 P-78PSCh-16 P-79PSCh-16 P-80PSCh-16 P-81PSCh-16 P-82PSCh-16 P-83PSCh-16 P-84PSCh-16 P-85GQCh-16 P-86GQCh-16 P-87GQCh-16 P-88GQCh-16 P-89GQCh-16 P-90GQCh-16 P-91GQCh-16 P-92GQCh-16 P-93GQCh-16 P-94GQCh-16 P-95GQCh-16 P-96GQCh-16 P-97GQCh-16 P-98GQCh-16 P-99GQCh-16 P-100GQCh-16 P-101GQCh-16 P-102GQCh-16 P-103GQCh-16 P-104GQCh-16 P-105GQCh-16 P-106GQCh-16 P-107GQCh-16 P-108GQCh-16 P-109GQCh-16 P-110GQCh-16 P-111ILCh-16 P-112ILCh-16 P-113ILCh-16 P-114ILCh-16 P-115ILCh-16 P-116ILCh-16 P-117ILCh-16 P-118ILCh-16 P-119SCQCh-16 P-120SCQCh-16 P-121SCQCh-16 P-122SCQCh-16 P-123SCQCh-16 P-124SCQCh-16 P-125SCQCh-16 P-126SCQCh-16 P-127SCQCh-16 P-128SCQCh-16 P-129SCQ

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