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JEE advanced Problems on Titrations

25 Ultra-Challenging JEE Advanced Problems on Titrations & Volumetric Analysis | Chemca

Masterclass: 25 Solved JEE Advanced Numericals on Titrations & Volumetric Analysis

Conquer the Equivalent Concept! This exhaustive guide features highly complex multi-step problems on Double Titrations, Back Titrations, Iodometry, and Complexometry. Click "View Solution" to reveal the step-by-step breakdown.

Problem 1: Double Titration (NaOH and Na₂CO₃)
A solution contains a mixture of $NaOH$ and $Na_2CO_3$. When titrated with $0.1 \text{ M } HCl$ using Phenolphthalein as an indicator, it requires $30 \text{ mL}$ for the endpoint. A few drops of Methyl Orange are then added to the same solution, and further titration requires an additional $10 \text{ mL}$ of the same $HCl$ to reach the second endpoint. Calculate the mass of $NaOH$ and $Na_2CO_3$ present in the solution.
View Solution

Step 1: Understand Indicator Chemistry
Phenolphthalein (Ph) operates at a higher pH ($\approx 8-10$). It signals the complete neutralization of strong base ($NaOH$) and exactly half of the carbonate ($Na_2CO_3 \rightarrow NaHCO_3$).
Methyl Orange (MeOH) operates at a lower pH ($\approx 3-4$). It signals the complete neutralization of the remaining bicarbonate ($NaHCO_3 \rightarrow CO_2 + H_2O$).

Step 2: Setup Equations
Let equivalents of $NaOH$ be $a$ and total equivalents of $Na_2CO_3$ (for complete neutralization) be $b$.
For Ph endpoint ($V_1 = 30 \text{ mL}$): $a + \frac{b}{2} \propto 30$
For additional MeOH endpoint ($V_2 = 10 \text{ mL}$): This volume is strictly for neutralizing the remaining $NaHCO_3$.
$\frac{b}{2} \propto 10 \implies b \propto 20 \text{ mL}$ of $0.1 \text{ M } HCl$.

Step 3: Solve for 'a'
$a + 10 = 30 \implies a \propto 20 \text{ mL}$ of $0.1 \text{ M } HCl$.

Step 4: Calculate Masses
Equivalents of $NaOH$ ($a$) = $N \times V = 0.1 \text{ N} \times 0.020 \text{ L} = 0.002 \text{ eq}$.
Mass of $NaOH$ = $0.002 \text{ eq} \times 40 \text{ g/eq} = 0.08 \text{ g}$.

Equivalents of $Na_2CO_3$ ($b$) = $N \times V = 0.1 \text{ N} \times 0.020 \text{ L} = 0.002 \text{ eq}$.
Equivalent weight of $Na_2CO_3$ = $106 / 2 = 53 \text{ g/eq}$.
Mass of $Na_2CO_3$ = $0.002 \text{ eq} \times 53 \text{ g/eq} = 0.106 \text{ g}$.

Answer: Mass of $NaOH$ = $0.08 \text{ g}$; Mass of $Na_2CO_3$ = $0.106 \text{ g}$.
Problem 2: Double Titration (Na₂CO₃ and NaHCO₃)
A solution contains a mixture of $Na_2CO_3$ and $NaHCO_3$. $20 \text{ mL}$ of this solution requires $8.0 \text{ mL}$ of $0.1 \text{ N } HCl$ for neutralization using phenolphthalein. Another $20 \text{ mL}$ of the same solution requires $25.0 \text{ mL}$ of $0.1 \text{ N } HCl$ for complete neutralization using methyl orange. Calculate the molarities of $Na_2CO_3$ and $NaHCO_3$.
View Solution

Step 1: Phenolphthalein Endpoint
Phenolphthalein indicates neutralization of half of $Na_2CO_3$ ($Na_2CO_3 \rightarrow NaHCO_3$). It does not react with original $NaHCO_3$.
Let molarity of $Na_2CO_3$ be $M_1$. Its n-factor for this half-reaction is $1$.
$M_1 \times 1 \times 20 \text{ mL} = 0.1 \text{ N} \times 8.0 \text{ mL}$
$20 M_1 = 0.8 \implies M_1 = 0.04 \text{ M}$.

Step 2: Methyl Orange Endpoint
Methyl orange indicates complete neutralization of both salts ($Na_2CO_3 \rightarrow CO_2$ and $NaHCO_3 \rightarrow CO_2$).
Let molarity of $NaHCO_3$ be $M_2$. n-factor for $Na_2CO_3$ is $2$, and for $NaHCO_3$ is $1$.
Total equivalents of acid = $(M_1 \times 2 \times 20) + (M_2 \times 1 \times 20)$.
$0.1 \times 25.0 = (0.04 \times 2 \times 20) + 20 M_2$
$2.5 = 1.6 + 20 M_2$
$0.9 = 20 M_2 \implies M_2 = 0.045 \text{ M}$.

Answer: Molarity of $Na_2CO_3 = 0.04 \text{ M}$; Molarity of $NaHCO_3 = 0.045 \text{ M}$.
Problem 3: Back Titration (Antacid Analysis)
A $1.50 \text{ g}$ sample of an antacid containing $Mg(OH)_2$ is treated with $50.0 \text{ mL}$ of $0.50 \text{ M } HCl$. The unreacted excess acid requires $20.0 \text{ mL}$ of $0.10 \text{ M } NaOH$ for complete neutralization. Calculate the mass percentage of $Mg(OH)_2$ in the antacid. (Molar mass of $Mg(OH)_2 = 58.3 \text{ g/mol}$).
View Solution

Step 1: Calculate Total Acid Equivalents
Total milliequivalents (meq) of $HCl$ added = $50.0 \text{ mL} \times 0.50 \text{ N} = 25.0 \text{ meq}$.

Step 2: Calculate Excess Acid (Back Titration)
The excess acid was neutralized by $NaOH$.
meq of excess $HCl$ = meq of $NaOH$ = $20.0 \text{ mL} \times 0.10 \text{ N} = 2.0 \text{ meq}$.

Step 3: Calculate Acid Reacted with Antacid
Reacted $HCl = \text{Total} - \text{Excess} = 25.0 - 2.0 = 23.0 \text{ meq}$.
Therefore, meq of $Mg(OH)_2$ in the sample = $23.0 \text{ meq} = 0.023 \text{ eq}$.

Step 4: Calculate Mass and Percentage
n-factor of $Mg(OH)_2 = 2$. Equivalent weight = $58.3 / 2 = 29.15 \text{ g/eq}$.
Mass of $Mg(OH)_2 = 0.023 \text{ eq} \times 29.15 \text{ g/eq} = 0.67045 \text{ g}$.
$\text{Mass } \% = \left(\frac{0.67045}{1.50}\right) \times 100 = 44.7\%$.

Answer: The antacid contains $44.7\% \text{ } Mg(OH)_2$.
Problem 4: Oleum Labeling by Titration
A $2.0 \text{ g}$ sample of oleum is diluted with water and requires $45.0 \text{ mL}$ of $1.0 \text{ M } NaOH$ for complete neutralization. Calculate the percentage labeling of the oleum sample.
View Solution

Step 1: Calculate Total Moles of $H_2SO_4$
Oleum is a mixture of $H_2SO_4$ and free $SO_3$. Dilution converts all $SO_3$ into $H_2SO_4$.
Equivalents of $NaOH$ used = $45.0 \text{ mL} \times 1.0 \text{ N} = 45.0 \text{ meq} = 0.045 \text{ eq}$.
Total equivalents of $H_2SO_4$ formed = $0.045 \text{ eq}$.
Since $H_2SO_4$ is dibasic ($n=2$), total moles of $H_2SO_4 = 0.045 / 2 = 0.0225 \text{ moles}$.

Step 2: Calculate Mass of Total $H_2SO_4$
Mass = $0.0225 \text{ mol} \times 98 \text{ g/mol} = 2.205 \text{ g}$.
This means $2.0 \text{ g}$ of oleum upon adding water yielded $2.205 \text{ g}$ of $H_2SO_4$.

Step 3: Define Oleum Labeling
Oleum labeling is the mass of pure $H_2SO_4$ obtained from exactly $100 \text{ g}$ of the oleum sample.
If $2.0 \text{ g}$ oleum yields $2.205 \text{ g}$ $H_2SO_4$,
Then $100 \text{ g}$ oleum yields $= \left(\frac{2.205}{2.0}\right) \times 100 = 110.25 \text{ g}$.

Answer: The oleum is labeled as $110.25\%$.
Problem 5: Kjeldahl's Method Back Titration
$0.25 \text{ g}$ of an organic compound was digested according to Kjeldahl's method. The ammonia evolved was absorbed in $50 \text{ mL}$ of $0.2 \text{ M } H_2SO_4$. The excess unreacted acid required $30 \text{ mL}$ of $0.5 \text{ M } NaOH$ for complete neutralization. Calculate the percentage of Nitrogen in the compound.
View Solution

Step 1: Calculate Total Acid Equivalents
$H_2SO_4$ n-factor = $2$. Normality = $0.4 \text{ N}$.
Total meq of $H_2SO_4 = 50 \text{ mL} \times 0.4 \text{ N} = 20 \text{ meq}$.

Step 2: Calculate Excess Acid (Neutralized by NaOH)
$NaOH$ n-factor = $1$. Normality = $0.5 \text{ N}$.
meq of excess $H_2SO_4$ = meq of $NaOH = 30 \text{ mL} \times 0.5 \text{ N} = 15 \text{ meq}$.

Step 3: Calculate Acid Reacted with Ammonia
Reacted acid = Total - Excess = $20 - 15 = 5 \text{ meq}$.
Therefore, meq of $NH_3$ produced = $5 \text{ meq}$.
Since $NH_3$ has an n-factor of $1$, millimoles of $N$ atoms = $5 \text{ mmol}$.

Step 4: Mass and Percentage of Nitrogen
Mass of N = $5 \times 10^{-3} \text{ mol} \times 14 \text{ g/mol} = 0.07 \text{ g}$.
$\% \text{ N} = \left(\frac{0.07}{0.25}\right) \times 100 = 28\%$.

Answer: The compound contains $28\%$ Nitrogen.
Problem 6: Iodometry (Indirect Titration of Copper)
Excess $KI$ is added to $25.0 \text{ mL}$ of an unknown $CuSO_4$ solution. The liberated Iodine ($I_2$) requires $20.0 \text{ mL}$ of $0.10 \text{ M}$ Sodium Thiosulfate ($Na_2S_2O_3$) for complete reduction. Calculate the mass of $CuSO_4 \cdot 5H_2O$ present per liter of the original solution. (Molar mass = $249.5 \text{ g/mol}$).
View Solution

Step 1: Understand Iodometric Reactions
Reaction 1: $2Cu^{2+} + 4I^- \rightarrow Cu_2I_2 \downarrow + I_2$
Reaction 2: $I_2 + 2S_2O_3^{2-} \rightarrow 2I^- + S_4O_6^{2-}$

Step 2: Apply the Law of Equivalence
Equivalents of $Cu^{2+}$ = Equivalents of $I_2$ liberated = Equivalents of $Na_2S_2O_3$ used.
n-factor for $Cu^{2+} \rightarrow Cu^+$ is $1$.
n-factor for $S_2O_3^{2-} \rightarrow 0.5 S_4O_6^{2-}$ is $1$.
meq of $Na_2S_2O_3 = 20.0 \text{ mL} \times 0.10 \text{ N} = 2.0 \text{ meq}$.
Therefore, meq of $CuSO_4 = 2.0 \text{ meq}$ in $25.0 \text{ mL}$.

Step 3: Calculate Molarity and Strength
Since n-factor = 1, Molarity = Normality.
$M = \frac{2.0 \text{ meq}}{25.0 \text{ mL}} = 0.08 \text{ M}$.
Strength per Liter = $M \times \text{Molar Mass} = 0.08 \text{ mol/L} \times 249.5 \text{ g/mol} = 19.96 \text{ g/L}$.

Answer: Mass per liter is $19.96 \text{ g}$.
Problem 7: Iodimetry (Direct Titration of Vitamin C)
Ascorbic acid (Vitamin C, $C_6H_8O_6$) is a reducing agent that reacts with Iodine to form Dehydroascorbic acid ($C_6H_6O_6$). A $1.00 \text{ g}$ vitamin tablet was dissolved in water and titrated with $0.05 \text{ M } I_2$ solution. The endpoint required $25.0 \text{ mL}$ of the iodine solution. Calculate the mass percentage of Ascorbic acid in the tablet. (Molar mass = $176 \text{ g/mol}$).
View Solution

Step 1: Identify the Redox Change
Reaction: $C_6H_8O_6 + I_2 \rightarrow C_6H_6O_6 + 2HI$.
Ascorbic acid loses 2 Hydrogen atoms (2 electrons). Thus, n-factor of Ascorbic Acid = $2$.
Iodine ($I_2$) goes from $0$ to $-1$ (2 atoms). n-factor of $I_2 = 2$.

Step 2: Calculate Equivalents of Iodine
Normality of $I_2 = M \times n = 0.05 \times 2 = 0.10 \text{ N}$.
meq of $I_2 = 25.0 \text{ mL} \times 0.10 \text{ N} = 2.5 \text{ meq} = 0.0025 \text{ eq}$.

Step 3: Calculate Mass of Ascorbic Acid
Equivalents of Ascorbic acid = $0.0025 \text{ eq}$.
Equivalent weight = $176 / 2 = 88 \text{ g/eq}$.
Mass = $0.0025 \text{ eq} \times 88 \text{ g/eq} = 0.22 \text{ g}$.

Step 4: Percentage Purity
$\% = (0.22 / 1.00) \times 100 = 22.0\%$.

Answer: The tablet contains $22.0\%$ Ascorbic acid.
Problem 8: Permanganometry (Ferrous Oxalate)
What volume of $0.1 \text{ M } KMnO_4$ is required to completely oxidize $0.05 \text{ moles}$ of Ferrous Oxalate ($FeC_2O_4$) in an acidic medium?
View Solution

Step 1: Determine n-factor of $FeC_2O_4$
In $FeC_2O_4$, both $Fe^{2+}$ and $C_2O_4^{2-}$ are oxidized simultaneously.
$Fe^{2+} \rightarrow Fe^{3+} + 1e^-$
$C_2O_4^{2-} \rightarrow 2CO_2 + 2e^-$
Total electron loss per molecule = $1 + 2 = 3$. So, n-factor = $3$.

Step 2: Determine n-factor of $KMnO_4$
In acidic medium, $MnO_4^- \rightarrow Mn^{2+}$ (change of $5e^-$). n-factor = $5$.

Step 3: Law of Equivalence
Equivalents of $FeC_2O_4$ = Equivalents of $KMnO_4$
$(\text{Moles} \times n)_1 = (\text{Molarity} \times n \times \text{Volume in L})_2$
$0.05 \times 3 = 0.1 \times 5 \times V$
$0.15 = 0.5 \times V \implies V = \frac{0.15}{0.5} = 0.3 \text{ L} = 300 \text{ mL}$.

Answer: $300 \text{ mL}$ of $KMnO_4$ is required.
Problem 9: Dichrometry and Mohr's Salt
$3.92 \text{ g}$ of Ferrous Ammonium Sulfate (Mohr's Salt, $FeSO_4 \cdot (NH_4)_2SO_4 \cdot 6H_2O$) is dissolved in water and titrated with Potassium Dichromate ($K_2Cr_2O_7$) in an acidic medium. The titration required $20 \text{ mL}$ of the dichromate solution. Calculate the molarity of the $K_2Cr_2O_7$ solution. (Molar mass of Mohr's salt = $392 \text{ g/mol}$).
View Solution

Step 1: Analyze Mohr's Salt
Only the $Fe^{2+}$ ion oxidizes to $Fe^{3+}$. The ammonium and sulfate ions are spectator ions in this redox reaction.
n-factor of Mohr's salt = $1$.
Moles of Mohr's salt = $3.92 / 392 = 0.01 \text{ moles}$.
Equivalents of Mohr's salt = $0.01 \times 1 = 0.01 \text{ eq}$.

Step 2: Analyze Dichromate
$Cr_2O_7^{2-} \rightarrow 2Cr^{3+}$. Oxidation state changes from $+6$ to $+3$ for two atoms.
n-factor of $K_2Cr_2O_7$ = $6$.

Step 3: Law of Equivalence
Equivalents of $K_2Cr_2O_7$ = Equivalents of Mohr's salt = $0.01 \text{ eq}$.
$N \times V(\text{L}) = 0.01$
$N \times 0.020 = 0.01 \implies N = 0.5 \text{ N}$.
Molarity = Normality / n-factor = $0.5 / 6 = 0.0833 \text{ M}$.

Answer: Molarity of $K_2Cr_2O_7$ is $0.0833 \text{ M}$.
Problem 10: Disproportionation Equivalent Weight
Determine the equivalent weight of Iodine ($I_2$) when it reacts with hot, concentrated $NaOH$ solution. (Molar mass of $I_2 = M$).
View Solution

Step 1: Write the chemical equation
With hot, concentrated base, halogens disproportionate into halide and halate ions.
$3I_2 + 6OH^- \rightarrow 5I^- + IO_3^- + 3H_2O$

Step 2: Calculate individual n-factors for $I_2$
Reduction: $I_2^0 \rightarrow 2I^{-1}$. Change = $|0 - (-1)| \times 2 = 2$. ($n_{red} = 2$).
Oxidation: $I_2^0 \rightarrow 2I^{+5}$. Change = $|0 - 5| \times 2 = 10$. ($n_{ox} = 10$).

Step 3: Calculate the total n-factor
Using the disproportionation formula:
$n_{total} = \frac{n_{ox} \times n_{red}}{n_{ox} + n_{red}} = \frac{10 \times 2}{10 + 2} = \frac{20}{12} = \frac{5}{3}$.

Step 4: Calculate Equivalent Weight
$E = \frac{M}{n_{total}} = \frac{M}{5/3} = \frac{3M}{5}$.

Answer: Equivalent weight of Iodine is $3M/5$.
Problem 11: Complexometric Titration (Water Hardness)
$100 \text{ mL}$ of a hard water sample is titrated against $0.01 \text{ M}$ EDTA solution using Eriochrome Black-T indicator at pH 10. The endpoint required $15.0 \text{ mL}$ of EDTA. Calculate the total hardness of the water sample in parts per million (ppm) of $CaCO_3$.
View Solution

Step 1: Understand EDTA Stoichiometry
EDTA forms a 1:1 complex with $Ca^{2+}$ and $Mg^{2+}$ ions regardless of their charge or the EDTA ionization state. Thus, moles of EDTA = moles of $M^{2+}$.
Moles of EDTA used = $0.01 \text{ M} \times 0.015 \text{ L} = 1.5 \times 10^{-4} \text{ moles}$.
Total moles of $Ca^{2+}/Mg^{2+}$ in $100 \text{ mL}$ = $1.5 \times 10^{-4} \text{ moles}$.

Step 2: Convert to $CaCO_3$ Equivalents
To express hardness, we treat all the metal ions as if they were $CaCO_3$.
Molar mass of $CaCO_3 = 100 \text{ g/mol}$.
Mass of $CaCO_3$ equivalent = $1.5 \times 10^{-4} \text{ moles} \times 100 \text{ g/mol} = 1.5 \times 10^{-2} \text{ g} = 15 \text{ mg}$.

Step 3: Calculate ppm (mg/L)
We have $15 \text{ mg}$ of hardness in $100 \text{ mL}$ ($0.100 \text{ L}$) of water.
Hardness = $\frac{15 \text{ mg}}{0.100 \text{ L}} = 150 \text{ mg/L} = 150 \text{ ppm}$.

Answer: Total hardness is $150 \text{ ppm}$.
Problem 12: Precipitation Titration (Mohr's Method)
A $0.585 \text{ g}$ sample of impure $NaCl$ is dissolved in water and titrated with $0.1 \text{ M } AgNO_3$ using Potassium Chromate ($K_2CrO_4$) as an indicator. The appearance of a reddish-brown precipitate occurs after adding $80.0 \text{ mL}$ of the $AgNO_3$ solution. Calculate the percentage purity of the $NaCl$ sample.
View Solution

Step 1: The Chemical Reaction
$Ag^+ + Cl^- \rightarrow AgCl \downarrow$ (white).
At the endpoint, excess $Ag^+$ reacts with the indicator: $2Ag^+ + CrO_4^{2-} \rightarrow Ag_2CrO_4 \downarrow$ (reddish-brown).

Step 2: Calculate Moles of $Cl^-$
Moles of $AgNO_3$ used = $0.1 \text{ M} \times 0.080 \text{ L} = 0.008 \text{ moles}$.
Due to 1:1 stoichiometry, moles of pure $NaCl$ = $0.008 \text{ moles}$.

Step 3: Calculate Mass of Pure $NaCl$
Molar mass of $NaCl$ = $58.5 \text{ g/mol}$.
Mass = $0.008 \text{ mol} \times 58.5 \text{ g/mol} = 0.468 \text{ g}$.

Step 4: Percentage Purity
$\% \text{ Purity} = \left(\frac{0.468}{0.585}\right) \times 100 = 80\%$.

Answer: The $NaCl$ sample is $80\%$ pure.
Problem 13: Volhard's Method (Back Titration for Halides)
To analyze a chloride sample, $50.0 \text{ mL}$ of $0.1 \text{ M } AgNO_3$ is added to the solution, precipitating all the chloride as $AgCl$. The excess, unreacted $Ag^+$ is then back-titrated with $0.05 \text{ M } KSCN$ using Ferric Alum indicator. The endpoint (red coloration) required $20.0 \text{ mL}$ of $KSCN$. How many milligrams of $Cl^-$ were in the original sample?
View Solution

Step 1: Total $Ag^+$ Added
Initial millimoles of $Ag^+ = 50.0 \times 0.1 = 5.0 \text{ mmol}$.

Step 2: Excess $Ag^+$ (Back Titrated)
Reaction: $Ag^+ + SCN^- \rightarrow AgSCN \downarrow$
Millimoles of $SCN^-$ used = $20.0 \times 0.05 = 1.0 \text{ mmol}$.
Excess $Ag^+ = 1.0 \text{ mmol}$.

Step 3: $Ag^+$ Reacted with Chloride
Reacted $Ag^+ = \text{Total} - \text{Excess} = 5.0 - 1.0 = 4.0 \text{ mmol}$.
Therefore, original $Cl^- = 4.0 \text{ mmol}$.

Step 4: Calculate Mass of Chloride
Molar mass of $Cl = 35.5 \text{ g/mol} = 35.5 \text{ mg/mmol}$.
Mass = $4.0 \text{ mmol} \times 35.5 \text{ mg/mmol} = 142 \text{ mg}$.

Answer: There were $142 \text{ mg}$ of $Cl^-$ in the sample.
Problem 14: Fajan's Method (Adsorption Indicator Concept)
In Fajan's method, $AgNO_3$ is titrated against $NaCl$ using Fluorescein indicator. What specific physical phenomenon causes the color change from yellowish-green to pinkish-red precisely at the equivalence point?
View Solution

Step 1: Before Equivalence Point
Excess $Cl^-$ ions are in solution. The precipitated $AgCl$ particles adsorb $Cl^-$ ions onto their surface, creating a primary negatively charged layer ($AgCl \cdot Cl^-$). The negatively charged Fluorescein anion ($Ind^-$) is repelled by this surface.

Step 2: At/After Equivalence Point
The first tiny excess drop of $AgNO_3$ adds excess $Ag^+$ to the solution. The $AgCl$ particles now adsorb $Ag^+$ ions, creating a primary positively charged layer ($AgCl \cdot Ag^+$).

Step 3: The Color Change
This positively charged surface strongly attracts and adsorbs the negatively charged Fluorescein indicator anions ($Ind^-$) into the secondary layer. The physical deformation of the indicator's electron cloud upon adsorption onto the crystal lattice drastically alters its light absorption properties, turning the precipitate a brilliant pinkish-red.

Answer: The color change is due to the adsorption of the negatively charged indicator onto the newly positively charged ($Ag^+$ coated) precipitate surface exactly at the endpoint.
Problem 15: Volume Strength and Permanganometry
$20 \text{ mL}$ of a commercial $H_2O_2$ solution requires $40 \text{ mL}$ of $0.05 \text{ M } KMnO_4$ for complete oxidation in acidic medium. Calculate the Volume Strength of the $H_2O_2$ solution.
View Solution

Step 1: Calculate Normality of $KMnO_4$
In acidic medium, n-factor of $KMnO_4 = 5$.
Normality = $0.05 \text{ M} \times 5 = 0.25 \text{ N}$.

Step 2: Calculate Normality of $H_2O_2$
$N_1 V_1 = N_2 V_2$
$N \times 20 = 0.25 \times 40 \implies 20 N = 10 \implies N = 0.5 \text{ N}$.
n-factor of $H_2O_2 = 2$. So Molarity = $0.5 / 2 = 0.25 \text{ M}$.

Step 3: Convert Molarity to Volume Strength
Reaction: $2H_2O_2 \rightarrow 2H_2O + O_2$.
$2 \text{ moles}$ $H_2O_2$ yield $22.4 \text{ L}$ $O_2$ at STP. So $1 \text{ mole}$ yields $11.2 \text{ L}$.
Volume Strength = Molarity $\times 11.2$
Volume Strength = $0.25 \times 11.2 = 2.8 \text{ V}$.

Answer: Volume Strength is $2.8 \text{ V}$.
Problem 16: Sequential Double Redox Titration
A solution contains a mixture of $Fe^{2+}$ and $Fe^{3+}$. A $50 \text{ mL}$ aliquot of this solution requires $20 \text{ mL}$ of $0.02 \text{ M } KMnO_4$ in acidic medium. Another $50 \text{ mL}$ aliquot is treated with Zinc dust and acid to completely reduce all Iron to $Fe^{2+}$, and then titrated. This second titration requires $50 \text{ mL}$ of the same $KMnO_4$ solution. Calculate the molarities of $Fe^{2+}$ and $Fe^{3+}$ in the original mixture.
View Solution

Step 1: Analyze First Titration (Only $Fe^{2+}$ reacts)
$Fe^{3+}$ cannot be oxidized further. The $KMnO_4$ reacts only with original $Fe^{2+}$.
$KMnO_4$ Normality = $0.02 \times 5 = 0.1 \text{ N}$.
Equivalents of $Fe^{2+}$ = $0.1 \text{ N} \times 0.020 \text{ L} = 0.002 \text{ eq}$.
Since n-factor of $Fe^{2+} = 1$, moles of $Fe^{2+} = 0.002 \text{ moles}$ in $50 \text{ mL}$.
Molarity of $Fe^{2+} = 0.002 / 0.050 = 0.04 \text{ M}$.

Step 2: Analyze Second Titration (Total Iron)
Zinc reduces $Fe^{3+}$ to $Fe^{2+}$. Now, ALL iron is in the $Fe^{2+}$ state.
Equivalents of Total Iron = $0.1 \text{ N} \times 0.050 \text{ L} = 0.005 \text{ eq}$.
Total moles of Iron in $50 \text{ mL} = 0.005 \text{ moles}$.

Step 3: Calculate $Fe^{3+}$
Moles of original $Fe^{3+} = \text{Total Moles} - \text{Original } Fe^{2+}$
Moles of $Fe^{3+} = 0.005 - 0.002 = 0.003 \text{ moles}$ in $50 \text{ mL}$.
Molarity of $Fe^{3+} = 0.003 / 0.050 = 0.06 \text{ M}$.

Answer: $[Fe^{2+}] = 0.04 \text{ M}$; $[Fe^{3+}] = 0.06 \text{ M}$.
Problem 17: n-factor of a Complex Sulfide
Arsenic trisulfide ($As_2S_3$) is oxidized by concentrated Nitric acid ($HNO_3$) to form Arsenic acid ($H_3AsO_4$) and Sulfuric acid ($H_2SO_4$). Calculate the n-factor and equivalent weight of $As_2S_3$ in this reaction. (Molar mass = M).
View Solution

Step 1: Identify Oxidation State Changes
In $As_2S_3$, Arsenic is $+3$ and Sulfur is $-2$.
In $H_3AsO_4$, Arsenic is $+5$.
In $H_2SO_4$, Sulfur is $+6$.

Step 2: Calculate electron loss per atom
$As^{3+} \rightarrow As^{5+}$ (Loss of $2 e^-$ per As atom).
$S^{2-} \rightarrow S^{6+}$ (Loss of $8 e^-$ per S atom).

Step 3: Sum for the Entire Molecule
One molecule of $As_2S_3$ contains 2 As atoms and 3 S atoms.
Total loss from As = $2 \times 2 = 4 e^-$.
Total loss from S = $3 \times 8 = 24 e^-$.
Total electrons lost per molecule = $4 + 24 = 28$.
n-factor = $28$.

Step 4: Equivalent Weight
$E = \frac{M}{28}$.

Answer: n-factor = $28$; Equivalent weight = $M/28$.
Problem 18: Permanganate in Neutral Medium
$100 \text{ mL}$ of an unknown Thiosulfate solution ($Na_2S_2O_3$) requires $40 \text{ mL}$ of $0.1 \text{ M } KMnO_4$ for complete oxidation in a neutral/faintly alkaline medium. Calculate the molarity of the Thiosulfate solution.
View Solution

Step 1: The Chemistry of the Neutral Medium
In neutral or faintly alkaline media, $KMnO_4$ is reduced to solid $MnO_2$ ($+7 \rightarrow +4$). Thus, n-factor of $KMnO_4 = 3$.
Thiosulfate ($S_2O_3^{2-}$) is oxidized completely to Sulfate ($SO_4^{2-}$), not tetrathionate! (Tetrathionate forms with weak oxidants like $I_2$).
In $S_2O_3^{2-}$, average S is $+2$. In $SO_4^{2-}$, S is $+6$.
Change per S atom = $4$. Total for 2 atoms = $8$. n-factor of Thiosulfate = $8$.

Step 2: Apply Equivalence
$N_1 V_1 = N_2 V_2$
$(M_{\text{thio}} \times 8) \times 100 = (0.1 \times 3) \times 40$
$800 M_{\text{thio}} = 12$
$M_{\text{thio}} = \frac{12}{800} = 0.015 \text{ M}$.

Answer: The molarity of the Thiosulfate solution is $0.015 \text{ M}$.
Problem 19: Available Chlorine (Bleaching Powder)
A $7.1 \text{ g}$ sample of Bleaching powder ($CaOCl_2$) was suspended in water and made up to $1.0 \text{ L}$. $100 \text{ mL}$ of this suspension, when treated with excess $KI$ and dilute acetic acid, liberated Iodine which required $40 \text{ mL}$ of $0.05 \text{ M}$ Hypo ($Na_2S_2O_3$) for titration. Calculate the percentage of "Available Chlorine" in the sample.
View Solution

Step 1: Calculate Hypo Equivalents
n-factor of Hypo is 1. Normality = $0.05 \text{ N}$.
meq of Hypo = $40 \text{ mL} \times 0.05 \text{ N} = 2.0 \text{ meq}$.
Therefore, meq of $Cl_2$ liberated in $100 \text{ mL}$ = $2.0 \text{ meq}$.

Step 2: Scale up to Total Volume
Total meq of $Cl_2$ in $1.0 \text{ L}$ ($1000 \text{ mL}$) = $2.0 \times 10 = 20 \text{ meq} = 0.020 \text{ eq}$.

Step 3: Calculate Mass of Available Chlorine
Equivalent weight of $Cl_2$ gas = Molar mass / 2 = $71 / 2 = 35.5 \text{ g/eq}$.
Mass of $Cl_2 = 0.020 \text{ eq} \times 35.5 \text{ g/eq} = 0.71 \text{ g}$.

Step 4: Percentage Available Chlorine
$\% = \left(\frac{0.71}{7.1}\right) \times 100 = 10\%$.

Answer: Percentage of Available Chlorine is $10\%$.
Problem 20: pH at Equivalence (Weak Acid Titration)
$50 \text{ mL}$ of $0.2 \text{ M}$ Acetic acid ($K_a = 1.8 \times 10^{-5}$) is titrated with $0.2 \text{ M } NaOH$. Calculate the exact pH precisely at the equivalence point.
View Solution

Step 1: Identify Equivalence Point Volume
$M_1 V_1 = M_2 V_2 \implies 0.2 \times 50 = 0.2 \times V_2 \implies V_2 = 50 \text{ mL}$.
Total volume at equivalence = $50 + 50 = 100 \text{ mL}$.

Step 2: Calculate Salt Concentration
Moles of $CH_3COONa$ formed = $0.2 \text{ M} \times 0.050 \text{ L} = 0.01 \text{ moles}$.
Concentration $C = 0.01 \text{ mol} / 0.100 \text{ L} = 0.1 \text{ M}$.

Step 3: Apply Salt Hydrolysis Formula
$CH_3COONa$ is a WA-SB salt. The solution is basic.
$pH = 7 + \frac{1}{2}(pK_a + \log_{10} C)$
$pK_a = -\log_{10}(1.8 \times 10^{-5}) = 4.74$
$\log_{10}(0.1) = -1$
$pH = 7 + \frac{1}{2}(4.74 - 1) = 7 + \frac{1}{2}(3.74) = 7 + 1.87 = 8.87$.

Answer: The pH at equivalence is $8.87$.
Problem 21: Half-Equivalence Point Dynamics
During the titration of a weak monobasic acid with a strong base, the pH of the solution is $5.2$ when $30\%$ of the acid has been neutralized. What will be the pH when $50\%$ of the acid is neutralized?
View Solution

Step 1: Analyze the 30% Neutralization Point
At $30\%$ neutralization, the ratio of Salt formed to unreacted Acid is $30:70$ (or $3:7$).
Apply Henderson-Hasselbalch: $pH = pK_a + \log_{10} \frac{[\text{Salt}]}{[\text{Acid}]}$
$5.2 = pK_a + \log_{10}(3/7)$
$\log_{10}(3) \approx 0.477$, $\log_{10}(7) \approx 0.845$.
$\log_{10}(3/7) = 0.477 - 0.845 = -0.368$.
$5.2 = pK_a - 0.368 \implies pK_a = 5.2 + 0.368 = 5.568$.

Step 2: Analyze the 50% Neutralization Point
At exactly $50\%$ neutralization (the half-equivalence point), $[\text{Salt}] = [\text{Acid}]$.
Therefore, $\log_{10} \frac{[\text{Salt}]}{[\text{Acid}]} = \log_{10}(1) = 0$.
At this specific point, $pH = pK_a$.

Answer: The pH at 50% neutralization is $5.568$.
Problem 22: Polyprotic Acid Titration (Phosphoric Acid)
$H_3PO_4$ is titrated with $NaOH$. Methyl orange indicates the first equivalence point, and Phenolphthalein indicates the second equivalence point. If $V_1$ is the volume of $NaOH$ required to reach the methyl orange endpoint from the start, and $V_2$ is the additional volume required to reach the phenolphthalein endpoint, how do $V_1$ and $V_2$ relate theoretically?
View Solution

Step 1: The First Endpoint ($V_1$)
Methyl orange (pH $\approx 4$) signals the neutralization of the first acidic proton.
$H_3PO_4 + NaOH \rightarrow NaH_2PO_4 + H_2O$.
Here, 1 mole of base neutralizes 1 mole of acid. The volume used is $V_1$.

Step 2: The Second Endpoint ($V_2$)
Phenolphthalein (pH $\approx 9$) signals the neutralization of the second acidic proton.
$NaH_2PO_4 + NaOH \rightarrow Na_2HPO_4 + H_2O$.
The starting material for this step is $NaH_2PO_4$. Since all $H_3PO_4$ became $NaH_2PO_4$, the moles are identical. It requires exactly 1 mole of base to remove the second proton.

Step 3: Conclusion
Because the stoichiometry is 1:1 for both individual proton removals, the volume required for the first step must exactly equal the additional volume required for the second step.

Note: The third proton is so weakly acidic that it cannot be titrated directly in aqueous solution without highly specialized methods.

Answer: Theoretically, $V_1 = V_2$.
Problem 23: Winkler's Method for Dissolved Oxygen
In the Winkler method to determine dissolved oxygen (DO), $500 \text{ mL}$ of water is treated with $MnSO_4$ and basic $KI$. The precipitated $Mn(OH)_2$ oxidizes to $MnO(OH)_2$. Upon acidification, the oxidized Manganese liberates $I_2$, which requires $20 \text{ mL}$ of $0.01 \text{ M } Na_2S_2O_3$ for titration. Calculate the DO in ppm.
View Solution

Step 1: The Equivalent Chain
The beauty of the Winkler method is the equivalent chain: $O_2$ oxidizes $Mn^{2+}$ to $Mn^{4+}$. Acidification makes $Mn^{4+}$ oxidize $I^-$ to $I_2$. The $I_2$ is titrated with Hypo.
Equivalents of $O_2$ = Equivalents of Hypo used.

Step 2: Calculate Equivalents of Hypo
n-factor of Hypo is $1$.
meq of Hypo = $20 \text{ mL} \times 0.01 \text{ N} = 0.2 \text{ meq}$.

Step 3: Calculate Mass of Oxygen
n-factor of $O_2$ ($0 \rightarrow -2$ for two atoms) = $4$.
Equivalent weight of $O_2 = 32 / 4 = 8 \text{ g/eq} = 8 \text{ mg/meq}$.
Mass of $O_2$ = $0.2 \text{ meq} \times 8 \text{ mg/meq} = 1.6 \text{ mg}$.

Step 4: Calculate ppm
We have $1.6 \text{ mg}$ of $O_2$ in $500 \text{ mL}$ ($0.5 \text{ L}$) of water.
ppm = mg / L = $1.6 / 0.5 = 3.2 \text{ mg/L}$.

Answer: Dissolved Oxygen is $3.2 \text{ ppm}$.
Problem 24: Purity of a Silver Coin (Volhard's Method)
A silver coin weighing $5.0 \text{ g}$ is dissolved in Nitric acid to form $AgNO_3$. The solution is titrated directly with $0.1 \text{ M}$ Potassium Thiocyanate ($KSCN$) using Ferric alum indicator. The endpoint requires $400 \text{ mL}$ of the $KSCN$ solution. Calculate the percentage of pure silver in the coin. ($Ag = 108$).
View Solution

Step 1: The Titration Reaction
$Ag^+ + SCN^- \rightarrow AgSCN \downarrow$ (White precipitate).
At the endpoint, excess $SCN^-$ reacts with $Fe^{3+}$ to form the blood-red $[Fe(SCN)]^{2+}$ complex.

Step 2: Calculate Moles of Silver
Because the stoichiometry is 1:1, moles of $Ag^+$ = moles of $KSCN$.
Moles of $KSCN$ = $0.1 \text{ M} \times 0.400 \text{ L} = 0.04 \text{ moles}$.
Therefore, moles of pure Silver ($Ag$) in the coin = $0.04 \text{ moles}$.

Step 3: Calculate Mass and Percentage
Mass of pure $Ag = 0.04 \text{ mol} \times 108 \text{ g/mol} = 4.32 \text{ g}$.
$\% \text{ Purity} = \left(\frac{4.32}{5.0}\right) \times 100 = 86.4\%$.

Answer: The coin contains $86.4\%$ pure Silver.
Problem 25: Master Challenge - Mixed Acid-Base and Redox
A $1.0 \text{ L}$ solution contains a mixture of Oxalic acid ($H_2C_2O_4$) and Sodium oxalate ($Na_2C_2O_4$). $10 \text{ mL}$ of this solution requires $20 \text{ mL}$ of $0.1 \text{ M } NaOH$ for complete neutralization. Another $10 \text{ mL}$ of the same original solution requires $16 \text{ mL}$ of $0.1 \text{ M } KMnO_4$ in acidic medium for complete oxidation. Calculate the ratio of the moles of Oxalic acid to Sodium oxalate in the original mixture.
View Solution

Step 1: Acid-Base Titration ($NaOH$)
Only the Oxalic acid reacts with $NaOH$. Sodium oxalate is already a neutral salt regarding basic titration.
$H_2C_2O_4$ is dibasic (n-factor = 2).
Let Molarity of $H_2C_2O_4 = x$.
$(x \times 2) \times 10 = 0.1 \times 1 \times 20 \implies 20x = 2 \implies x = 0.1 \text{ M}$.

Step 2: Redox Titration ($KMnO_4$)
Both Oxalic acid and Sodium oxalate contain the oxalate ion ($C_2O_4^{2-}$), which oxidizes to $CO_2$. The n-factor for both molecules in redox is $2$.
Let Molarity of $Na_2C_2O_4 = y$.
Total equivalents of oxalate = Equivalents of $KMnO_4$.
$KMnO_4$ n-factor in acid = $5$.
$[(x \times 2) + (y \times 2)] \times 10 = 0.1 \times 5 \times 16$
$20x + 20y = 8$.

Step 3: Solve for y
We know $x = 0.1$.
$20(0.1) + 20y = 8 \implies 2 + 20y = 8 \implies 20y = 6 \implies y = 0.3 \text{ M}$.

Step 4: Calculate the Ratio
Ratio of Moles (or Molarities) of $H_2C_2O_4 : Na_2C_2O_4 = x : y = 0.1 : 0.3 = 1 : 3$.

Answer: The molar ratio of Oxalic acid to Sodium oxalate is $1 : 3$.

Mastering the Erlenmeyer Flask

Congratulations on conquering these 25 highly advanced numericals on Titrations and Volumetric Analysis. This chapter represents the absolute synthesis of stoichiometry, redox chemistry, and ionic equilibrium. By mastering the distinction between an acid-base n-factor and a redox n-factor for the exact same molecule (like Oxalic acid), and learning how to chain equivalence through complex back-titrations and Iodometry, you have built the ultimate physical chemistry toolkit. Keep track of your milliequivalents, and visit Chemca.in for more elite masterclasses!

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