   Chapter 15, Problem 117CP

Chapter
Section
Textbook Problem

# A few drops of each of the indicators shown in the accompanying table were placed in separate portions of a 1.0-M solution of a weak acid, HX. The results are shown in the last column of the table. What is the approximate pH of the solution containing HX? Calculate the approximate value of Ka for HX. Indicator Color of Hln Color of ln− pKa of Hln Color of 1.0 M HX Bromphenol blue Yellow Blue 4.0 Blue Bromcresol purple Yellow Purple 6.0 Yellow Bromcresol green Yellow Blue 4.8 Green Alizarin Yellow Red 6.5 Yellow

Interpretation Introduction

Interpretation: A table showing colors and pKa of indicators is given. The pH of weak acid HX and the approximate value of Ka is to be calculated.

Concept introduction: The acid-base indicators are the weak acids and they show the end point by the change in color. The pH of indicators lie within a range of pKa±1 . The indicators change their colors within this range.

To determine: The pH of weak acid HX and the approximate value of Ka .

Explanation

Explanation

The table for pH for the given indicators is shown below.

 INDICATOR pH Bromophenol blue 3.0−5.0 Bromocresol purple 5.0−7.0 Bromocresol green 3.8−5.8 Alizarin 5.5−7.5

Figure 1

As it is seen from the table the value of pH of weak acid HX lies almost close to 5.0 Therefore, the pH of weak acid HX is taken to be 5.0

The approximate value of Ka for HX is 1.0×10-10_ .

Explanation

Given

The concentration of HX is 1.0M .

The pH of the solution is shown below.

pH=log[H+]

Where,

• [H+] is the concentration of Hydrogen ions.

Substitute the value of pH in the above equation to find the value of [H+] .

pH=log[H+]5.0=log[H+][H+]=105.0=1×105

Make the ICE table for the dissociation reaction of HX .

HX(aq)H+(aq)X(aq)Initial(M):1.000Change(M):xxxEquilibrium(M):1

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