Equivalent Concepts and Volumetric Analysis Formulas

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1. Equivalent Concept:

• All chemical combinations are followed by the law of equivalence.
• As per the law of equivalence, for the two reacting substances A and B, the number of equivalents of A reacted = the number of equivalents of B reacted.

2. Definition of Equivalent Weight:
The equivalent weight of an element is that weight of the element that will combine with or replace directly or indirectly 1.0 gm (1 gm-atom) of H, 35.5 gm (1 gm atom) of Cl or 8.0 gm. (‘A gm-atom) of O or 108 gm (1 gm-atom) of Ag.

3. Equivalent Weight:
Equivalent weight of element = \(\frac{\text { Atomic wt of the element }}{x \text { factor }}\)
Equivalent weight ot compound = \(\frac{\text { Formula wt of the compound }}{x \text { factor }}\)
Equivalent weight of disproportionation =
The X factor for oxidation = 2, The X factor for reduction = 10
The equivalent wt of Cl₂ = \(\frac{71}{2}+\frac{71}{10}\) = 35.5 + 7.1 = 42.6

4. Determination of Equivalent Weights for various Substances:
Equivalent weight when expressed in grams is known as gram-equivalent weight.
1 equivalent of chlorine = 35.5 gm
1 equivalent of oxygen = 8 gm
∴ 71 gm chlorine = 2 equivalent of chlorine
∴ 32 gm oxygen = 4 equivalent of oxygen.
The no. of equiv. of any substance
= \(\frac{\text { wt. of the subs tance in grams }}{\text { Equiv. wt. of the subs tan ce in grams }}=\frac{w}{\mathrm{E}}\)
[where w and E represent the weight and equiv. wt. of the substance]
Equiv. wt. of any oxidant and reductant is
Equiv. wt. of oxidant = \(\frac{\text { Mol. wt. of oxidant }}{x \text { factor }}\)
Equiv. wt. of reductant = \(\frac{\text { Mol. wt. of reductant }}{x \text { factor }}\)
The given formula is not for disproportionation reaction
Equiv. wt. of acid or base in a acid-base reaction (not the redox reaction) is
Equiv. wt of acid = \(\frac{\text { Mol. wt. of acid }}{\text { Basicity of the acid }}\)
The equiv. wt of acid = \(\frac{\text { Mol. wt. of acid }}{x \text { factor }}\)
The equiv. wt of base = \(\frac{\text { Mol. wt. of base }}{\text { acidity of base }}\)
The equiv. wt of base = \(\frac{\text { Mol. wt.of base }}{x \text { factor }}\)
The equivalent weight of salt E, which is not behave as oxidizing or reducing agent is given by,
E = \(\frac{\text { formula wt. of the salt }}{\text { total valence of designated ion }}\)
For example, the equivalent wt E of Ca₃(PO₄)₂
= \(\frac{\text { formula wt. of } \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}}{3 \times 2}=\frac{310}{6}=51.6\)
Ans.
Equivalent wt of an ion = \(\frac{\text { formula wt. (or At. wt.) of ion }}{\text { its valency }}\)

5. Law of equivalent and its application in the determination of equivalent weights of elements:
(a) Law of Equivalence:
In general we can write for the two reacting substances X and Y as,
\(\frac{\text { wt. of } X}{\text { wt. of } Y}=\frac{\text { Equiv wt. of } X}{\text { Equiv wt. of } Y}\)

(b) Determination of equiv. wt. of metals by hydrogen displacement method:
For example, w, gm. of any metal displaces w2 gm of H from an dilute acid. The,
\(\frac{w_{1}}{w_{2}}=\frac{\text { Equiv. wt. of metal }}{1}\)
[the equiv. wt. of H = 1]
∴ Equiv. wt. of metal = \(\frac{w_{1}}{w_{2}}\)

(c) Determination of equivalent wt. of element from the oxide formation method:
Let w₁ gm of element ‘x’ combines with w₂ gm of O.
∴ equiv. wt of X = × 8.

(d) Determination of equivalent wt. of the elements from their chloride formation:
Let, w₁ gm of the element ‘x’ combines with w₂ gm of Cl.
∴ 35.5 gm Cl combines with \(\frac{w_{1}}{w_{2}}\) × 35.5 gm of X
∴ The equiv. wt. of X = \(\frac{w_{1}}{w_{2}}\) × 35.5

(e) Determination of equivalent weight of metal by double decomposition method:
Let us consider a reaction as
P_mQ_n + R_OS_p → products
Let, amount of P_m Q_n reacted = w₁ gm
Let, amount of R_oS_p reacted = w₂ gm
∴ \(\frac{w_{1}}{w_{2}}=\frac{\text { Equivalent wt of } P_{m} Q_{n}}{\text { Equivalent wt of } R_{o} S_{p}}\)
∴ \(\frac{w_{1}}{w_{2}}=\frac{\text { Equivalent wt of } P+\text { Equivalent wt of } Q}{\text { Equivalent wt of } R+\text { Equivalent wt of } S}\)

6. The Law of Dulong and Petit:
Atomic wt × specific heat ≃ 6.4
approximate atomic weight (A_approx) as A_approx = \(\frac{6.4}{\text { sp.heat }}\)
If the equivalent wts of the elements under consideration E is known to us, we can calculate Y factor of the elements in whole numbers, as
x = \(\frac{A_{\text {approx }}}{\text { Equiv. wt }}\)

7. Mitcherlich’s Law of Isomorphism and Calculation of Atomic Weights:
As per this law, if elements A, and B are forming isomorphous crystal then
\(=\frac{\text { wt. of element } A \text { that combines with a certain wt. of other elements }}{\text { wt. of element } B \text { that } \text { combines with a same wt. of other elements }}\)
= \(\frac{\text { At. wh. of } A}{\text { At. wt. of } B}\)

8. Normality:
∴ N = \(\frac{w \times 1000}{E \times v}\)
1 semi normal means N/2 solution
1 decinormal mean N/10 solution
1 centinormal mean N/100 solution.
1 milli normal means N/1000 solution

9. Volume strength of H₂O₂:
volume strength = 11.2 × molarity strength
volume strength of H₂O₂ = 5.6 × Normality strength

10. Hardness of Water:
(a) Reasons of hardness of water:
The hardness of natural water is generally caused by the presence of the bicarbonates and sulphates of calcium and magnesium but infact all soluble salts that form a scum with soap cause hardness.

Salts containing Mg²⁺, Ca²⁺, Al³⁺ etc. (except the salts of alkali metals ‘ viz, Na, K, Li etc) are responsible for imparting hardness into the
water. Dilute hydrochloric acid also behaves as hard water.

(b) Classification of hardness:

• Temporary hardness
• Permanent hardness.

1. Temporary hardness:
This is due to the presence of bicarbonates of calcium and magnesium.
CaCO₃ + H₂O + CO₂ → Ca (HCO₃)₂
Temporary hardness in water is easily removed by boiling.

Temporary hardness can also be removed by clark’s process which involves the addition of slaked lime, Ca (OH)₂
Ca(HCO₃)₂ + Ca(OH)₂ = 2 CaCO₃↓+ 2H₂O

2. Permanent hardness:
Permanent hardness is introduced when water passes over rocks containing the sulphates or chlorides of Ca, Mg, Al and Fe etc. Permanent hardness cannot be removed by boiling or by the addition of slaked lime.

(c) Methods for the removal of permanent hardess in water:

• Washing soda
• Permutit Process
• Calgon Process and
• Ion exchange resin process

(a) Degree of Hardness:
The degree of hardness of water is defined as the number of parts of calcium carbonate or equivalent to various calcium and magnesium salts present in a million parts of water. This is also symbolically represented ppm (in terms of CaCO₃)
0° —10° hardness is considered to be soft water
10° — 20° hardness is considered to be mild hard water
20° — 30° & above is considered to be hard water

11. Volumetric Analysis:
(i) Briefly, volumetric chemical analysis consists in experimentally finding the volume of a standard solution which will react completely with given quantity or a measured volume of a solution of unknown concentration.

(ii) Usually point at which the reaction is completed is called the end-point and is indicated by suitable colour changes brought about by means of very small quantity of third substances called indicators. The entire process is known as titration.

(a) Primary standard solution:
A primary standard is a substance of high purity, with the purity known within very close limits. It can be measured and weighed on a balance, and it will react stoichiometrically.

(b) Types of primary standard:
There are many types of primary standard for any purpose. All must be capable of:

• Being dried at 100 °C to 110 °C
• Being cooled in weighing bottles inside dessicators.
• Being weighed with no more than ordinary care.
• Reacting stoichiometrically. That is, they must follow exactly the course of a chemical equation.

(c) Primary standard Acids:

• Potassium hydrogen phthalate, KHC₈H₄O₄.
• Benzoic acid: C₆H₅COOH
• Sulphamic acid: HNH₂SO₃
• Oxalic acid H₂C₂O₄. 2H₂0

(d) Primary standard Base:
Na₂CO₃, CaCO₃, Na₂B₄O₇. 10H₂O (borax).
(i) Primary standard oxidizing agents:
Only one primary standard oxidizing agent, K₂Cr₂O₇ is commonly used in the laboratory.

(ii) Primary standard Reducing agents:
☞ Sodium oxalate, Na₂C₂O₄
☞ Arsenic trioxide, As₂O₃
☞ Electrolytic iron, Fe, is available in a high degree of purity.
☞ Mohr’s salt, FeSO₄.(NH₄)₂ SO₄.6H₂O.

(e) Choosing an Indicator:
Choice of indicator for a particular reaction depends on the following factors –

• pH at the equivalence point,
• pH range of the indicator,
• Direction of titration – whether approaching the equivalence point from acid side or from the alkaline side.

(f) Here we are mentioning some common acid-base indicators:

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