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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

The chromium(III) ion in water, [Cr(H2O)6]3+. Is a weak acid with pKa = 3.95. What is the value of Kb for its conjugate base, [Cr(H2O)5OH]2+?

Interpretation Introduction

Interpretation:

The dissociation constant (Kb) for weak acid [Cr(H2O)5OH]2+ has to be calculated

Concept introduction:

An acid undergoes dissociation in an aqueous medium. The acid dissocition gives  ions H3O+(aq.) and A(aq.). The conjugate base A(aq.) may interact with H2O and forms HA(aq.) and it can be represented as following equilibrium.

  HA(aq.)+ H2O(l)H3O+(aq.)+ A(aq.)                                               (1)

The dissociation constant for the acid is Ka,

  Ka=[H3O+][A][HA]

Interaction of anion A(aq.) is represented as,

  A(aq.) +  H2O(l)HA(aq.)+ OH(aq.)                                               (2)

The dissociation constant for the conjugate anion is Kb,

  Kb=[HA][OH][A]

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 Ka and ionization constant Kb of conjugate base, i.e.

  Kw=Ka×Kb                                                                                                (4)

The ionisation constant of water has a constant value i.e. Kw=1×1014. 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 value of Kb for conjugate base [Cr(H2O)5OH]2+ is calculated below.

Given:

Value of pKa for the given weak acid [Cr(H2O)6]3+ is 3.95.

Value of Kw for water is 1.0×1014.

By using the relation, pKa=log(Ka). The Ka value for acid is calculated.

Ka=10(pKa)=10(3.95)=1.12×104

Using equation (4),Kb for conjugate base [Cr(H2O)5OH]2+ is calculated as follows,

Kw=Ka×Kb

Substitute the value of Ka 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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