12Volumetric analysis

📚
STANDARD SOLUTION
▢ Definition: Solution of accurately known strength.
▢ Primary Standard Substance / Solution:
❖ Definition: Standard solution prepared directly by weighing known mass of primary standard substance.
❖ Examples:
  • •
    Oxalic acid crystal
  • •
    \(Na_2CO_3\) anhydrous
  • •
    \(K_2Cr_2O_7\)
  • •
    \(AgNO_3\)
  • •
    Sodium oxalate
  • •
    Mohr's salt
❖ Properties:
  • •
    Non-toxic
  • •
    Non-hygroscopic
  • •
    Non-deliquescent
  • •
    Available in pure form
  • •
    Invariant composition in solid + solution state
  • •
    High molecular weight + high equivalent weight → minimum weighing error
▢ Secondary Standard Substance / Solution:
❖ Definition: Standard solution cannot be prepared by direct weighing; prepared by titration with primary standard solution.
❖ Characters:
  • •
    Unstable
  • •
    Impure
  • •
    Volatile / deliquescent / hygroscopic
❖ Examples:
  1. \(NaOH\)
  2. \(HCl\)
  3. \(H_2SO_4\)
  4. \(HNO_3\)
  5. \(KMnO_4\)
  6. \(FeSO_4\)
📚
TITRATION
▢ Definition: Strength determination of unknown solution using standard solution.
▢ Terms:
❖ Titrate: Unknown solution
❖ Titrant: Standard solution
❖ Burette solution: Titrant
❖ Flask solution: Titrand / titrate
❖ Titration error: End point − equivalence point
▢ Acidimetry: Acid strength determination by standard alkali + indicator.
▢ Alkalimetry: Alkali strength determination against standard acid solution.
▢ End Point / Equivalence Point: Termination point of reaction in titration indicated by indicators.
📚
REDOX TITRATIONS

Table 1: Important volumetric titrations

Titration
Main reagent
Use / principle
Important note
Permanganate titration
\(KMnO_4\)
Estimation of reducing agents: ferrous salt, oxalic acid
\(KMnO_4\) = self-indicator due to \(Mn^{2+}\) formation → pale pink
Dichromate titration
\(K_2Cr_2O_7\)
Estimation of iron ores
Done in presence of \(HCl\)
Iodometric titration
\(I_2\) liberated from KI
Liberated iodine titrated against hypo solution
\(Ag^+, Cu^{2+}, Fe^{3+}\) give iodometric titration; \(Pb^{2+}\) does not
\(KMnO_4\) acidification
  • •
    \(KMnO_4\) acidified only with dilute \(H_2SO_4\)
  • •
    With \(HCl\): \(HCl\) oxidised
  • •
    With \(HNO_3\): acts as oxidising agent
  • •
    Acid solution of \(KMnO_4\): no precipitate
  • •
    Neutral / alkaline solution of \(KMnO_4\): precipitate
📚
CONCENTRATION TERMS

Table 1: Ways of expressing concentration

Term
Meaning
Formula / note
Weight percent
Weight of solute per 100 g solution
\((w/w)\% = \dfrac{\text{weight of solute (g)}}{\text{weight of solution (g)}} \times 100\)
Weight / volume percent
Weight of solute per 100 mL solution
\((w/v)\% = \dfrac{\text{weight of solute (g)}}{\text{volume of solution (mL)}} \times 100\)
Volume percent
Volume of solute per 100 mL solution
\((v/v)\% = \dfrac{\text{volume of solute (mL)}}{\text{volume of solution (mL)}} \times 100\)
Normality \((N)\)
Gram equivalents of solute per litre solution
\(N = \dfrac{\text{strength in g/L}}{\text{equivalent weight}}\)
Molarity \((M)\)
Moles of solute per 1000 mL solution
Decreases with increase in temperature
Formality
Formula weight in g dissolved per litre solution
Molarity = formality
Molality \((m)\)
Moles / gram molecules of solute per 1000 g solvent
Not affected by temperature [MOE 2063]
Mole fraction \((X)\)
Moles of component / total moles of solution
Not affected by temperature
ppm
Trace solute mass per total solution mass
\(ppm = \dfrac{\text{mass of solute in trace quantity}}{\text{total mass of solution}} \times 10^6\)
📚
NORMALITY
▢ Definition: Number of gram equivalents of solute present in 1 litre solution.
▢ Normal Solution: Solution having normality = 1.
▢ Formulae:
  • •
    \(N = \dfrac{\text{strength in g/L}}{\text{equivalent weight}}\)
  • •
    \(N = \dfrac{\text{wt. of solute}}{\text{gram eq. wt.} \times \text{volume in mL}} \times 1000\)
  • •
    \(N = \dfrac{(w/W)\% \times \text{density or sp. gravity} \times 10}{\text{equivalent weight}}\)
▢ Mixing Same Solute:
  • •
    \(N = \dfrac{N_1V_1 + N_2V_2}{V_1 + V_2}\)
  • •
    \(N = \dfrac{N_1V_1 + N_2V_2 + \cdots + N_nV_n}{V_1 + V_2 + \cdots + V_n}\)
▢ Dilution:
  • •
    \(N_1V_1 = N_2V_2\)
  • •
    Water added: \(V_2 - V_1 = \left(\dfrac{N_1 - N_2}{N_2}\right)V_1\)
▢ Acid-Base Mixing:

Table 1: \(V_a\) mL acid of \(N_a\) + \(V_b\) mL base of \(N_b\)

Condition
Result
\(V_aN_a = V_bN_b\)
Neutral
\(V_aN_a > V_bN_b\)
Acidic
\(V_aN_a < V_bN_b\)
Basic
▢ Common Terms:
❖ N/2: Seminormal
❖ N: Normal
❖ N/10: Decinormal
❖ 10 N: Decanormal
❖ N/5: Pentinormal
❖ 5 N: Pentanormal
❖ 1 equivalent: 1000 milliequivalent
📚
MOLARITY
▢ Definition: Number of moles of solute present in 1000 mL solution.
▢ Important Points:
  • •
    Molarity decreases with increase in temperature
  • •
    On dilution \(x\) times → molarity decreases by \(x\) times
▢ Formulae:
  • •
    \(M = \dfrac{\text{wt. of solute}}{\text{mol. wt.} \times \text{volume in mL}} \times 1000\)
  • •
    \(M = \dfrac{10 \times \text{sp. gr. of solution} \times (w/W)\%\text{ of solute}}{\text{mol. wt. of solute}}\)
  • •
    \(M_1V_1 = M_2V_2\)
▢ Mixing Same Solute: \(M = \dfrac{V_1M_1 + V_2M_2}{V_1 + V_2}\)
▢ Dilution: Water added: \(V_2 - V_1 = \left(\dfrac{M_1 - M_2}{M_2}\right)V_1\)
▢ Pure Water: Molarity at \(4^\circ C = 55.55\,M\)
▢ Relation With Normality:
❖ Formula: \(N = M \times x\)
❖ \(x\):
    ◈ **type: bullet
  1. \(x = \dfrac{\text{mol. wt.}}{\text{eq. wt.}}\)
  2. Acidity for base
  3. Basicity for acid
  4. Number of electrons lost per mole for reductant
  5. Number of electrons gained per mole for oxidant
  6. Charge on cation × number of cations for salt
❖ Example: 1 M \(H_3PO_4\) = 3 N [IOM 1997]
📚
MOLALITY, MOLE FRACTION & PPM
📖
**c
📝
Molality
    ■ **type: bullet
  1. Moles of solute per 1000 g solvent
  2. Temperature independent [MOE 2063]
📝
Mole Fraction
    ■ **type: bullet
  1. \(X*{solute} = \dfrac{n*{solute}}{n*{solute}+n*{solvent}}\)
  2. \(X*{solvent} = \dfrac{n*{solvent}}{n*{solute}+n*{solvent}}\)
  3. \(n =\) number of moles
  4. Temperature independent
📝
ppm
  • •
    \(ppm = \dfrac{\text{mass of solute in trace quantities}}{\text{total mass of solution}} \times 10^6\)
  • •
    Toothpaste having \(0.2\,gL^{-1}\) fluoride = 200 ppm [BPKIHS]
📚
EQUIVALENT WEIGHT
▢ Oxalic Acid as Reducing Agent:
  • •
    \(H_2C_2O_4 \rightarrow 2CO_2 + H_2O\)
  • •
    \(C_2O_4^{2-} \rightarrow CO_2\)
  • •
    Oxidation number of C: \(+3 \rightarrow +4\)
  • •
    Change per C atom = \(4-3 = 1\)
  • •
    Two C atoms: \(2 \times 1 = 2\)
  • •
    \(\text{Eq. wt. of oxalic acid} = \dfrac{\text{formula wt. of }H_2C_2O_4}{2} = \dfrac{90}{2} = 45\)
▢ Salt: \(\text{Eq. wt. of salt} = \dfrac{\text{mol. wt.}}{\text{total positive or negative valency}}\)
📚
INDICATORS
▢ Definition: Substances showing easily detectable change during titration and indicating end/equivalence point.
▢ Change:
  • •
    Colour change
  • •
    Precipitation
  • •
    One colour in excess titrate
  • •
    Another colour in excess standard solution/reagent
▢ Types:
❖ Internal Indicators:
  1. Acid-base indicator
  2. Self-indicator
  3. Adsorption indicator
❖ External Indicator: Potassium ferricyanide in titration of \(K_2Cr_2O_7\) and ferrous salt

Table 1: Indicators for acid-base titration

Acid
Base
Indicator
pH of colour change
Strong: \(HCl, HNO_3, H_2SO_4\)
Strong: \(NaOH, KOH, Ca(OH)_2\)
Any indicator; best = phenolphthalein; others = methyl orange, litmus
4–10
Strong
Weak: \(NH_4OH, Cu(OH)_2, Fe(OH)_3\)
Methyl orange
4
Weak: formic acid, oxalic acid, acetic acid
Strong
Phenolphthalein
8.5
Weak
Weak
None; no titration
Gradual change

Table 2: Selection of indicators

Indicator
pH range
Acid solution
Neutral solution
Alkali solution
Methyl orange; weak base
3.1–4.4 [IOM]
Red / pink
Orange
Yellow
Methyl red
4.2–6.3
Red
—
Yellow
Litmus
5.5–7.4
Red
Purple / violet
Blue
Phenol red
6.8–8.4
Yellow
—
Red
Phenolphthalein; weak acid
8.2–10.0
Colourless
Colourless
Pink
📚
INDICATOR RULES
▢ Important Points:
  • •
    Methyl orange, not litmus, used for carbonate/bicarbonate titration with acid because evolved \(CO_2\) changes litmus red before completion
  • •
    Phenolphthalein should not be used when \(NH_3\) evolves during titration
  • •
    Methyl orange usable in all cases except weak acid
  • •
    Methyl orange range = 3.1–4.5 [IOM 1998, 1996]
  • •
    Strong acid vs weak base indicator = methyl orange [MOE 2062]
  • •
    Redox titration \(KMnO_4\) with oxalic acid: \(Mn^{2+}\) = autocatalyst; \(KMnO_4\) = self-indicator
  • •
    Phenolphthalein + alkali → pink [IOM 2000]
▢ Good Indicator Characters:
  • •
    Colour change clear + sharp
  • •
    Sensitive
  • •
    pH range should indicate completion of reaction
▢ Universal Indicator: Mixture of many indicators showing colour changes over different pH ranges.
📚
INDICATOR THEORIES
▢ Ostwald's Ionic Theory:
  • •
    Acid-base indicator = weak organic acid or weak base
  • •
    Weak acid indicator example: phenolphthalein
  • •
    Weak base indicator example: methyl orange
  • •
    Undissociated form and ions have different colours
  • •
    Colour change due to ionisation
  • •
    Weak acid indicator: anion colour deeper than unionised form
  • •
    Weak base indicator: cation colour deeper than unionised form
  • •
    Indicator dissociation changes on addition of strong acid / strong base
▢ Quinoid Theory:
  • •
    Benzenoid form and quinonoid form show different colours in different medium
  • •
    Benzenoid ⇌ quinonoid
  • •
    Dynamic equilibrium
  • •
    Tautomeric forms
📚
READ & DIGEST
▢ Indicator Points:
  • •
    Iodine vs sodium thiosulphate titration indicator = starch
  • •
    Strong acid + weak base titration indicator = methyl orange
  • •
    Pink colour of phenolphthalein in alkaline medium due to negative form
  • •
    Phenolphthalein not good indicator for ferrous sulphate vs \(KMnO_4\)
  • •
    Phenolphthalein in \(Na_2CO_3\) vs \(HCl\): no visible change
  • •
    Methyl orange gives red colour in \(HCl\)
  • •
    Best indicator for \(0.1N\,Na_2CO_3\) vs \(0.1N\,HCl\) = methyl red
  • •
    Starch detects traces of iodine in aqueous solution
  • •
    Mohr's salt dissolved in dilute \(H_2SO_4\), not distilled water, to prevent cationic hydrolysis
  • •
    Acidified \(KMnO_4\) decolourised by Mohr's salt
  • •
    pH indicators = weak acids or weak bases
▢ Volumetric Points:
  • •
    Strong acids commonly used as standard solutions in acid-base titration because they titrate both strong and weak bases
  • •
    Equivalents of \(Na_2S_2O_3\) required for volumetric estimation of 1 equivalent \(Cl_2\) = 2
  • •
    \(0.53\,g\,Na_2CO_3\) + \(10\,mL\) N acid → neutral solution [IOM 1997]
📚
NUMERICALS
▢ _*table:
    Q1.
    Adsorption is multilayer in case of
    Q2.
    Which of the following term is negative in adsorption?
    Q3.
    Which of the following is adsorbate?
    Q4.
    The decomposition of \(H_2O_2\) can be slowed by the addition of a small amount of acetamide. The latter acts as
    Q1.
    The no. of millimoles of HCl required to neutralize 10 ml of 0.2 M Na2CO3 is
    📅MOE Model
    Q2.
    100 ml of 0.5 M H2SO4 solution and 0.1 litre of 1 M HCl were mixed. The normality of the resulting solution will be
    📅MOE Model
    Q3.
    200 ml of 0.2 M HCl is neutralized with 0.1 M NaOH. Then during their half neutralization, what will be the molarity of HCl?
    📅MOE 2008
    Q4.
    0.62 g of Na2CO3.H2O is added to 100 ml of 0.1 N H2SO4 solution. The resulting solution will be
    📅MOE 2004•IOM 1998
    Q5.
    Find the molarity of 10% NaOH.
    📅MOE 2003
    Q6.
    10 ml of 2.5 N NaOH is mixed with 20 ml of 1.5 N HCl. The mixture is diluted to 100 ml. What is the nature of mixture?
    📅MOE 2000
    Q7.
    In the reaction H2SO4 + 2KOH → K2SO4 + 2H2O, if 4 N H2SO4 is taken, then normality of K2SO4 is
    📅MOE 2053•IOM 2003•1998
    Q8.
    When 50 ml of HCl reacts with 10 gm of CaCO3, normality of the solution is
    Q9.
    0.4 gm of NaOH is added to 10 ml of 1 N HCl, the resulting solution is
    📅IOM 2002
    Q10.
    10 ml of 2 M H2SO4 is mixed with 10 ml of H2O. 10 ml of mixture can neutralize ____ of 2 N NaOH.
    📅IOM 2002
    Q11.
    The amount of H2SO4 present in 500 ml of 2 N H2SO4 solution is
    Q12.
    Phenolphthalein acts as best indicator in the titration of
    📅IOM 2001
    Q13.
    30 cc of N/2 HCl, 30 cc of N/10 HNO3, and 60 cc of N/5 H2SO4 are mixed. The normality of the mixture is
    📅IOM 1999
    Q14.
    If a solution of pH = 0, 100 ml of pure water is added, then the mixture will be
    📅IOM 1998
    Q15.
    You have 2.5 N and 0.625 N solutions. In which proportion would you mix these solutions to get 1 N of 1 litre solution?
    📅IOM 1997
    Q16.
    The amount of water to be added to change 100 ml of 0.5 N HCl to 0.2 N is
    📅MOE 1996
    Q17.
    The weight of anhydrous Na2CO3 required to neutralize 100 ml of 0.1 M HCl is
    📅MOE 2065
    Q18.
    The no. of millimoles of HCl in 100 ml of 0.2 M HCl is
    📅MOE 2065
    Q19.
    The amount of oxalic acid crystals (H2C2O4.2H2O) for 100 ml of 0.1 N solution is
    📅B.E. 2065•MOE 09
    Q20.
    The normality of 7.3% HCl solution is
    📅IOM 09
    Q21.
    The pH curve indicates the titration between
    📅BPKIHS
    Q22.
    Equivalent weight of KMnO4 in acidic medium is
    📅BPKIHS 2001
    Q23.
    How many ml of 1 M H2SO4 is required to neutralize 2 ml of 1 M NaOH?
    📅BPKIHS 1999
    Q24.
    Which of the following decreases with increase in temperature?
    Q25.
    An acid of 0.6 N neutralizes 150 ml of 0.3 N base. The volume of acid required is
    📅BPKIHS