Mole Concept And Equivalent Concept

ChemistrySome Basic Concepts of ChemistryFor JEE aspirants

Mole Concept

For Elements

1 g-atom = N atoms = 6.023 × 1023 atoms

= g-atomic mass

e.g., 1 g-atom of oxygen = N atoms of oxygen

= 6.023 × 1023 atoms of oxygen

= 16 g

g-atomic mass: It is the mass of Avogadro's number (N) atoms in g.

Mass of one oxygen atom = 16 amu

= 16 × 1.66 × 10–24 g

$∴$ Mass of N oxygen atom

= 16 × 1.66 × 10–24 × 6.023 × 1023 g = 16g

g-atom of element $= \frac{M a ss o f e l e m e n t}{A t o mi c ma ss o f e l e m e n t}$ …(1)

No. of atoms of element = g-atom of element × Av. No. …(2)

For Compounds

1 g-molecule or 1 mole = N molecules

= 6.023 × 1023 molecules

= g molar mass

1 mole of O2 = N molecules of O2

= 6.023 × 1023 molecules of O2 = 32g

g-molar mass: It is the mass o Avogadro's number (N) molecules in g.

Mass of one O2 molecules = 32 amu = 32 × 1.66 × 10–24 g

$∴$ Mass of N molecules of O2

= 32 × 1.66 × 10–24 × 6.023 × 1023 = 32g

$M o l e = \frac{ma ss}{m o l a r ma ss}$ …(3)

Molecules = mole × Av. No. …(4)

Avogadro's hypothesis: Equal volumes of gases or vapours obeying gas laws under similar conditions of P and T contain equal no. of molecules.

The statement reveals the following facts:

(a) If P1 = P2, T1 = T2 (for two gases) The at V1 = V2; n1 = n2

(b) One mole of all gases contain N molecules.

Dulong and Petits law

Atomic mass × specific heat (cal/g) = 6.4 (for metals only)

Equivalent Mass

Equivalent mass of a substance depends upon the nature of chemical reaction in which substance takes part. The evaluation of equivalent mass of a substance may therefore be cautiously made.

(A) Equivalent mass of an element in a redox change:

Equivalent mass of a compound $= \frac{M o l a r ma ss}{N o . o f ^{'} e ^{'} l os t or g ain e d d u r in g r e d o x}$ …(5)

Change by one molecule of that compound

Equivalent mass of an element $= \frac{A t o mi c ma ss}{N o . o f ^{'} e ^{'} l os t or g ain e d d u r in g r e d o x}$ …(6)

Change by one atom of that element

(B) Equivalent mass of an element or compound in a non redox change:

(i) Equivalent mass of an element:

$E = \frac{A t o mi c ma ss o f e l e m e n t}{V a l e n cy o f e l e m e n t}$ …(7)

(ii) Equivalent mass of ionic compound:

$E = \frac{F or m u l a ma ss o f i o ni c cco m p o u n d}{T o t a l c h ar g e o n c a t i o n s or ani o n s}$ …(8)

Also, Equivalent mass of an ionic compound = Equivalent mass of I part + Equivalent mass of II part …(9)

Eq. (9) is not valid for hydrated compounds.

e.g., (i) $E_{N a C l} = \frac{F . ma ss o f N a C l}{1} = \frac{58.5}{1} = 58.5$ By (8)

(ii) $E_{A l C l_{3}} = \frac{F . ma ss o f A l C l _{3}}{3} = \frac{133.5}{3} = 44.5$ By (8)

$E_{A l C l_{3}} = E . ma s s_{A l} + E . ma s s_{C l} = \frac{27}{3} + 35.5 = 44.5$ By (9)

(iii) $K_{2} S O_{4} \cdot A l_{2} (S O_{4})_{3} \cdot 24 H_{2} O : E_{A l u m} = \frac{M}{8}$ By (9)

(iii) Equivalent mass of an acid or base:

$E q . ma s s_{A c i d} = \frac{M o l a r ma ss o f a c i d}{B a s i c i t y}$ …(10)

(Basicity is no. of H atoms replaced from one molecule of acid)

$E q . ma s s_{B a se} = \frac{M o l a r ma ss o f ba se}{A c i d i t y}$ …(11)

(Acidity is the no. of OH groups replaced from one molecule of base)

e.g., $B a s i c i t y = 2 H_{3} P O_{2} + A c i d i t y = 1 2 N a O H \to N a_{2} H P O_{3} + 2 H_{2} O$

$∴ E_{H_{3} P O_{3}} = \frac{M}{2} E_{N a O H} = \frac{M}{1}$

Note: However if reaction is given as:

(a) H3PO3 + NaOH $\to$ NaH2PO3 + H2O

$E_{H_{3} P O_{3}} = \frac{M}{1}$

(b) Al(OH)3 + HCl $\to$ Al(OH)2Cl + H2O

$E_{A l (O H)_{3}} = \frac{M}{1}$

(iv) Equivalent mass of an ion or radical:

Eq. mass of ion or radical $= \frac{Formula mass of ion or radical}{Charge on ion}$ …(12)

(v) Equivalent mass of an acid salt:

$E = \frac{Molar mass of acid salt}{Replaceable H atom inacid salt}$ …(13)

e.g., $E_{N a H_{2} P O_{4}} = \frac{M}{2}$

However if reaction is given as:

NaH2PO4 + NaOH $\to$ Na2HPO4 + H2O

Then $E_{N a H_{2} P O_{4}} = \frac{M}{1}$

An acid salt is one which has replaceable H atom, e.g., NaHCO3, NaHSO4, Na2HPO4. However, Na2HPO3 is not an acid salt since it does not have replaceable H atom because H3PO3 is dibasic acid. In oxy acids only those H are replaceable which are attached on O atom, e.g.,

\mathop {{\rm{H--O--}}\mathop {\mathop {\rm{P}}\limits^{\mathop \uparrow \limits^{\rm{O}} } {\rm{--O}}}\limits_{\mathop {{\rm{|}}\,\,\,\,\,\,\,\,\,\,\,\,}\limits_{{\rm{O-H}}} } {\rm{--H}}}\limits_{{\rm{Tri}}\,\,{\rm{basic}}}

$Di basic H - - O - - H ∣ P ↑ O - - O - - H$

(vi) Equivalent mass of basic salt:

$E = \frac{Molar mass of basic salt}{Replaceable OH gp in basic salt}$ …(14)

e.g. $E_{Al (OH)_{2} Cl} = \frac{M}{2}$

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