Explanation Explanation To determine : The volume of water added in HA to change the pH from 4.000 to 5 .000 . The concentration of [ H 3 O + ] at pH = 4.000 is 1 . 0 × 10 − 4 M _ . Given Initial volume of HA is 50 .0 mL . The initial pH value of HA at 50 .0 mL is 4 .000 . The final pH value of HA after addition of water is 5 .000 . Formula The pH value is calculated using the formula, pH = − log 10 [ H 3 O + ] (1) Where, [ H 3 O + ] is concentration of hydronium ions. Substitute the initial pH value of HA in the above equation. pH = − log 10 [ H 3 O + ] 4 .000 = − log 10 [ H 3 O + ] [ H 3 O + ] = 1 . 0 × 10 − 4 M _ The concentration of HA at pH = 4.000 is 0 . 0 1 0 1 M _ . The concentration of [ H 3 O + ] is 1 .0 × 10 − 4 M . The value of K a is 1 .0 × 10 − 6 . It is assumed that the initial concentration of HA is x . Make the ICE table for the dissociation reaction of HA . HA( a q ) + H 2 O ( l ) ⇌ H 3 O + ( a q ) + A − ( a q ) Initial: x 0 0 Change: − 10 − 4 10 − 4 10 − 4 Equilibrium: x − 10 − 4 10 − 4 10 − 4 The equilibrium constant for the given reaction is, K a = [ H 3 O + ] [ A − ] [ HA ] Substitute the equilibrium concentration values in the above expression. K a = [ H 3 O + ] [ A − ] [ HA ] 1 .0 × 10 − 6 = ( 10 − 4 ) 2 ( x − 10 − 4 ) x = 0.0101 Thus, initial concentration of HA at pH = 4.000 is 0 . 0 1 0 1 M _ . The concentration of [ H 3 O + ] at pH = 5.000 is 1 . 0 × 10 − 5 M . Given Initial volume of HA is 50 .0 mL . The initial pH value of HA at 50 .0 mL is 4 .000 . The final pH value of HA after addition of water is 5 .000 . Substitute the pH value of HA in equation (1). pH = − log 10 [ H 3 O + ] 5

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Chapter 13, Problem 173CP

Interpretation Introduction

Interpretation: The volume of a weak acid HA , its acid dissociation constant and pH value is given. The volume of water added in HA to change the pH from 4.000 to 5.000 is to be calculated.

Concept introduction: The measure of concentration of hydrogen ions is known as pH .

The process of reduction of concentration of a solute in a solution is known as dilution.

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Chapter 13, Problem 172CP

Chapter 13, Problem 174CP

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Chapter 13 Solutions

EBK CHEMISTRY: AN ATOMS FIRST APPROACH

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Solution Summary: The author calculates the volume of a weak acid HA, its acid dissociation constant, and its value using the formula.

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