(a)
Interpretation:
From mass balance 13.15, the equation 13-16 has to be derived.
Concept Introduction:
Ion-pairing in acid-base systems:
The possible ion-pair equilibria in the mixture of sodium hydrogen tartrate (Na+HT−), pyridinium chloride (PyH+Cl-) and KOH are:
Na+ + T2-⇌ NaT-KNaT=[NaT-][Na+][T2-]=8......13−12Na+ + HT-⇌ NaHTKNaT=[NaHT][Na+][HT-]=1.6......13-13
(a)
Explanation of Solution
Derivation of equation 13-16 from mass balance 13-15:
Equation 13-15 (mass balance for sodium) is:
[Na+] + [NaT-] + [NaHT] = FNa = FH2T = 0.0200 M....... 13-15
Equation 13-16 is:
[Na+] = FH2T1+KNaT-[T2-] + KNaHT[HT-]
Consider the two equations,
Na+ + T2-⇌ NaT-KNaT=[NaT-][Na+][T2-]=8......13−12Na+ + HT-⇌ NaHTKNaT=[NaHT][Na+][HT-]=1.6......13-13
Substitute [NaT−]=KNaT-[Na+][T2-] and [NaHT] = KNaHT[Na+][HT-]
[Na+]+KNaT-[Na+][T2-]+KNaHT[Na+][HT-]=FH2T [Na+]{1+KNaT-[T2-]+KNaHT[HT-]}=FH2T[Na+]=FH2T1+KNaT-[T2-] + KNaHT[HT-]
Hence, the equation 13-16 is derived from mass balance 13.15.
(b)
Interpretation:
An expression for [T2-] in terms of [H+], [Na+] and various equilibrium constants has to be derived by substituting equilibrium expressions into mass balance equation 13-17
Concept Introduction:
Mass balance equation for [H2T]:
The mass balance equation for [H2T] is:
FH2T = [H2T] + [HT-] + [T2-] + [NaT-] + [NaHT]......(13-17)
(b)
Answer to Problem 13.17P
The expression for [T2-] is:
[T2-]=FH2T[H+]2K1K2+[H+]K2+1+KNaT-[Na+]+KNaHT[Na+][H+]K2
Explanation of Solution
[H2T] + [HT-] + [T2-] + [NaT-] + [NaHT] = FH2T
Make the following substitutions to find expressions in terms of [T2-], [H+] and [Na+]:
[H2T]=[H+]2K1K2[T2-];[HT-]=[H+]K2[T2-];[NaT-]=KNaT-[Na+][T2-][NaHT]=KNaHT[Na+][HT-] =KNaHT[Na+][H+]K2[T2-]
Put these expressions into the mass balance equation:
[H2T] + [HT-] + [T2-] + [NaT-] + [NaHT] = FH2T[H+]2K1K2[T2-]+[H+]K2[T2-]+[T2-]+KNaT-[Na+][T2-]+KNaHT[Na+][H+]K2[T2-]=FH2T
Solve for [T2-]:
[T2-]=FH2T[H+]2K1K2+[H+]K2+1+KNaT-[Na+]+KNaHT[Na+][H+]K2
Hence, the expression for [T2-] is obtained.
The expression for [T2-] is derived as follows:
[T2-]=FH2T[H+]2K1K2+[H+]K2+1+KNaT-[Na+]+KNaHT[Na+][H+]K2
(c)
Interpretation:
Using the same approach in part (b), the expression for [HT-] and [H2T] has to be derived.
Concept Introduction:
Mass balance equation for [H2T]:
The mass balance equation for [H2T] is:
FH2T = [H2T] + [HT-] + [T2-] + [NaT-] + [NaHT]......(13-17)
(c)
Answer to Problem 13.17P
The expression for [HT-] and [H2T] is:
[HT-]=FH2T[H+]K1+1+K2[H+]+KNaT-[Na+]K2[H+]+KNaHT[Na+][H2T]=FH2T1+K1[H+]+K1K2[H+]2+KNaT-[Na+]K1K2[H+]2+KNaHT[Na+]K1[H+]
Explanation of Solution
To find [HT-], make the following substitutions in the mass balance for H2T :
[H2T]=[H+]K1[HT-]; [T2-]=K2[H+][HT-]; [NaHT]=KNaHT[Na+][HT-][NaT-]=KNaT-[Na+]K2[H+][HT-] Then keep these expressions into the mass balance:
[H+]K1[HT-]+[HT-]+K2[H+][HT-]+KNaT[Na+]K2[H+][HT-]+KNaT[Na+][HT-]=FH2T
And now solve for [HT-]
[HT-]=FH2T[H+]K1+1+K2[H+]+KNaT-[Na+]K2[H+]+KNaHT[Na+]
To find [H2T] make the following substitution in the mass balance for H2T
[HT-]=K1[H+][H2T];[T2-]=K1K2[H+]2[H2T][NaT-]=KNaT-[Na+][T2-]=KNaT-[Na+]K1K2[H+]2[H2T][NaHT]=KNaHT-[Na+][HT-]=KNaHT-[Na+]K1[H+]2[H2T]
Then keep these expressions into the mass balance:
[H2T]+K1[H+][H2T]+ K1K2[H+]2[H2T]+KNaT-[Na+] K1K2[H+]2[H2T]+KNaHT-[Na+] K1[H+][H2T]=FH2T
And solve for [H2T]
[H2T]=FH2T1+K1[H+]+ K1K2[H+]2+KNaT-[Na+] K1K2[H+]2+KNaHT-[Na+] K1[H+]
The expression for [HT-] and [H2T] is derived as follows:
[HT-]=FH2T[H+]K1+1+K2[H+]+KNaT-[Na+]K2[H+]+KNaHT[Na+][H2T]=FH2T1+K1[H+]+K1K2[H+]2+KNaT-[Na+]K1K2[H+]2+KNaHT[Na+]K1[H+]
(d)
Interpretation:
Using excel spreadsheet, the pH of the given solution has to be computed.
(d)
Answer to Problem 13.17P
The pH of the given solution is 4.264
Explanation of Solution
The spreadsheet used to compute pH of the given solution is shown in the below figure 1.
Figure 1
From the above spreadsheet, the pH of the solution is found as 4.264
The pH of the given solution is found out as 4.264
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Chapter 13 Solutions
Quantitative Chemical Analysis 9e And Sapling Advanced Single Course For Analytical Chemistry (access Card)
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