Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198727873
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
Question
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Chapter 5, Problem 5E.1E

(a)

Interpretation Introduction

Interpretation:

The fraction of intact H2PO3 molecules in an aqueous solution of phosphorous acid at pH=5.0 has to be calculated.

Concept Introduction:

Acid equilibrium constant:

The equilibrium constant Ka for the acid dissociation reaction is,

    HAH++A Ka=[H][A][HA]

pH:

The concentration of hydrogen ion in given solution is given as pH.

The negative logarithm of base ten hydrogen ion concentrations is known as pH.

    pH=-log[H+]

(a)

Expert Solution
Check Mark

Explanation of Solution

Given

Phosphorous acid solutionpH=5.0

Phosphorous acid, H2PO3

  Ka1=1.0 ×102pKa=2.00Ka2=2.6×107pKa=6.59

  H2PO3(aq)+H2OHPO3(aq)+H3O+(aq)pKa=2.00 Ka1=[HPO3(aq)][H3O+(aq)]H2PO3(aq)=1.0×102HPO3(aq)+H2OPO32(aq)+H3O+(aq)pKa=6.59 Ka2=[PO32(aq)][H3O+(aq)]HPO3(aq)=2.6×107

From the general rule,

The acid form is dominant for pH < pKa

The conjugate pair have equal concentrations at pH = pKa

The base form is dominant for pH > pKa

At 5.0pH concentration of hydrogen ion is,

    [H3O+]=10-pH=105=0.00001

At the given pH, equilibrium constant of acid is,

    Ka1=[HPO3-(aq)][H3O+(aq)]H2PO3(aq)=1.0×10-21.0×10-2=[0.00001]2H2PO3(aq)H2PO3(aq)=[0.00001]21.0×10-2=1×10-101.0×10-2 =1×10-8M.

Hence, the fraction of intact H2PO3 molecules in an aqueous solution of phosphorous acid at pH=5.0 is 1×10-8M.

(b)

Interpretation Introduction

Interpretation:

The fraction of intact H2PO3 molecules in an aqueous solution of phosphorous acid at pH=9.0 has to be calculated.

Concept Introduction:

Acid equilibrium constant:

The equilibrium constant Ka for the acid dissociation reaction is,

    HAH++A Ka=[H][A][HA]

pH:

The concentration of hydrogen ion in given solution is given as pH.

The negative logarithm of base ten hydrogen ion concentration is known as pH.

    pH=-log[H+]

(b)

Expert Solution
Check Mark

Explanation of Solution

Given

Phosphorous acid solutionpH=9.0

Phosphorous acid, H2PO3

  Ka1=1.0 ×102pKa=2.00Ka2=2.6×107pKa=6.59

  H2PO3(aq)+H2OHPO3(aq)+H3O+(aq)pKa=2.00 Ka1=[HPO3(aq)][H3O+(aq)]H2PO3(aq)=1.0×102HPO3(aq)+H2OPO32(aq)+H3O+(aq)pKa=6.59 Ka2=[PO32(aq)][H3O+(aq)]HPO3(aq)=2.6×107

From the general rule,

The acid form is dominant for pH < pKa

The conjugate pair have equal concentrations at pH = pKa

The base form is dominant for pH > pKa

At 9.0pH concentration of hydrogen ion is,

    [H3O+]=10-pH=109=1×109

At the given pH, equilibrium constant of acid is,

    Ka2=[PO32(aq)][H3O+(aq)]HPO3(aq)=2.6×1071.0×10-2=[1×109]2HPO3(aq)HPO3(aq)=[1×10-9]22.6×107=1×10-182.6×107 =0.38×1012.

At the first dissociation,

    Ka1=[HPO3-(aq)][H3O+(aq)]H2PO3(aq)=1.0×10-21.0×10-2=[0.38×1012]2H2PO3(aq)H2PO3(aq)=[0.38×1012]21.0×10-2=1.44×10-251.0×10-2 =1.44×10-23M.

Hence, the fraction of intact H2PO3 molecules in an aqueous solution of phosphorous acid at pH=9.0 is 1.44×10-23M.

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Chapter 5 Solutions

Elements Of Physical Chemistry

Ch. 5 - Prob. 5D.1STCh. 5 - Prob. 5D.2STCh. 5 - Prob. 5D.3STCh. 5 - Prob. 5D.4STCh. 5 - Prob. 5D.5STCh. 5 - Prob. 5E.1STCh. 5 - Prob. 5E.2STCh. 5 - Prob. 5F.1STCh. 5 - Prob. 5F.2STCh. 5 - Prob. 5F.3STCh. 5 - Prob. 5F.4STCh. 5 - Prob. 5F.5STCh. 5 - Prob. 5G.1STCh. 5 - Prob. 5G.2STCh. 5 - Prob. 5G.3STCh. 5 - Prob. 5H.1STCh. 5 - Prob. 5H.2STCh. 5 - Prob. 5H.3STCh. 5 - Prob. 5I.1STCh. 5 - Prob. 5I.2STCh. 5 - Prob. 5I.3STCh. 5 - Prob. 5I.4STCh. 5 - Prob. 5I.5STCh. 5 - Prob. 5I.6STCh. 5 - Prob. 5J.1STCh. 5 - Prob. 5J.2STCh. 5 - Prob. 5J.3STCh. 5 - Prob. 5J.4STCh. 5 - Prob. 5J.5STCh. 5 - Prob. 5A.1ECh. 5 - Prob. 5A.2ECh. 5 - Prob. 5A.3ECh. 5 - Prob. 5A.4ECh. 5 - Prob. 5A.5ECh. 5 - Prob. 5A.6ECh. 5 - Prob. 5A.7ECh. 5 - Prob. 5A.8ECh. 5 - Prob. 5A.9ECh. 5 - Prob. 5A.10ECh. 5 - Prob. 5A.11ECh. 5 - Prob. 5A.12ECh. 5 - Prob. 5A.13ECh. 5 - Prob. 5B.1ECh. 5 - Prob. 5B.2ECh. 5 - Prob. 5B.3ECh. 5 - Prob. 5B.4ECh. 5 - Prob. 5B.5ECh. 5 - Prob. 5C.1ECh. 5 - Prob. 5C.2ECh. 5 - Prob. 5C.3ECh. 5 - Prob. 5C.4ECh. 5 - Prob. 5D.1ECh. 5 - Prob. 5D.2ECh. 5 - Prob. 5D.3ECh. 5 - Prob. 5D.4ECh. 5 - Prob. 5E.1ECh. 5 - Prob. 5E.2ECh. 5 - Prob. 5F.4ECh. 5 - Prob. 5G.1ECh. 5 - Prob. 5G.2ECh. 5 - Prob. 5G.3ECh. 5 - Prob. 5H.1ECh. 5 - Prob. 5H.2ECh. 5 - Prob. 5H.3ECh. 5 - Prob. 5H.4ECh. 5 - Prob. 5I.1ECh. 5 - Prob. 5I.2ECh. 5 - Prob. 5I.3ECh. 5 - Prob. 5I.4ECh. 5 - Prob. 5J.1ECh. 5 - Prob. 5J.2ECh. 5 - Prob. 5J.3ECh. 5 - Prob. 5J.4ECh. 5 - Prob. 5.1DQCh. 5 - Prob. 5.2DQCh. 5 - Prob. 5.3DQCh. 5 - Prob. 5.4DQCh. 5 - Prob. 5.5DQCh. 5 - Prob. 5.6DQCh. 5 - Prob. 5.7DQCh. 5 - Prob. 5.8DQCh. 5 - Prob. 5.9DQCh. 5 - Prob. 5.10DQCh. 5 - Prob. 5.11DQCh. 5 - Prob. 5.12DQCh. 5 - Prob. 5.13DQCh. 5 - Prob. 5.14DQCh. 5 - Prob. 5.15DQCh. 5 - Prob. 5.16DQCh. 5 - Prob. 5.17DQCh. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10PCh. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - Prob. 5.29PCh. 5 - Prob. 5.30PCh. 5 - Prob. 5.31PCh. 5 - Prob. 5.32PCh. 5 - Prob. 5.33PCh. 5 - Prob. 5.34PCh. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - Prob. 5.41PCh. 5 - Prob. 5.42PCh. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - Prob. 5.45PCh. 5 - Prob. 5.46PCh. 5 - Prob. 5.47PCh. 5 - Prob. 5.48PCh. 5 - Prob. 5.49PCh. 5 - Prob. 5.50PCh. 5 - Prob. 5.51PCh. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - Prob. 5.56PCh. 5 - Prob. 5.58PCh. 5 - Prob. 5.59PCh. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - Prob. 5.63PCh. 5 - Prob. 5.64PCh. 5 - Prob. 5.66PCh. 5 - Prob. 5.67PCh. 5 - Prob. 5.68PCh. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - Prob. 5.71PCh. 5 - Prob. 5.72PCh. 5 - Prob. 5.73PCh. 5 - Prob. 5.74PCh. 5 - Prob. 5.76PCh. 5 - Prob. 5.77PCh. 5 - Prob. 5.78PCh. 5 - Prob. 5.79PCh. 5 - Prob. 5.1PRCh. 5 - Prob. 5.2PRCh. 5 - Prob. 5.3PRCh. 5 - Prob. 5.4PR
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