Equivalent mass

Introduction:

Every element has fixed to combine mass for all other elements which are called equivalent mass or simply chemical equivalent.The equivalent masses of element are expressed by taking hydrogen, oxygen, and chlorine as reference element

equivalent mass of an element is defined as the number of parts by mass of an element which combines with or displaces directly or indirectly. 1.008 parts by mass of hydrogen or 8 parts by mass of oxygen or 35.5 parts by mass of chlorine.

2Mg + O₂ → 2MgO

\( 2\: × 24gm \:\:\:\:\:\: 32\: gm\)

32 parts by mass of oxygen combine with 2 x 24 parts by mass of Mg

8 parts by mass of oxygen combines with \( \frac { 2 × 24 × 8}{32}\) =12 P/M of Mg

∴ eq mass of Mg = 12

# Mg + H₂SO₄ → MgSO₄ + H₂

\(24gm \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:2×1.008 gm \)

2 x 1.008 gm Of H₂ is displaced by 24 P/Mof Mg

ie. 1.008 P/M of H₂ is displaced by \( \frac {24}{2}\) P/M = 12 P/M of Mg

Hence, equivalent mass of Mg = 12

# Mg +Cl₂ → MgCl₂

\(24gm \:\:\:\:\:\:\:\:\:\:2×35.5 gm \)

2 x 35.5 gm Of Cl₂ combines with 24 P/Mof Mg

ie.35.5 gm Of Cl₂ combines with \( \frac {24}{2}\) P/M = 12 P/M of Mg

Hence, equivalent mass of Mg = 12

It should be noted that one equivalent of any element always combines with one equivalent of other element. Therefore following relation always holds true for any reaction.

\( \frac {Equivalent\:Mass\:of\:A}{Equivalent\:Mass\:of\:B}\) = \( \frac {Mass\:of\:A}{Mass\:of\:B}\)

# Show that equivalent mass of carbon is 3.

C + O₂ → CO₂

\(12\:gm\:\:\:32\:gm\)

32 P/M of oxygen combines with 12 P/M of carbon

8 P/M of oxygen combines with \( \frac {12 × 8}{32}\) = 3 P/ M of carbon

Hence, equivalent mass of Carbon = 3

# What do you mean by "equivalent mass of 'Mg' is 12 ?

ANS :

The equivalent mass of Mg is 12 means:

i) 12 P/m of magnesium displaces 1.008 P/m of hydrogen from dilute acid.

ii) 12 P/m of magnesium combines with 8 P/m of oxygen and 35.5 P/m of chlorine.

Gram equivalent mass

Equivalent mass of an element is expressed as the combining mass relative to the masses of another element i.r. it is simply a number. So, it has no unit expressed in gram, then it is called gram equivalent mass.

For example : (i) Equivalent mass of Mg = 12

(ii) Equivalent mass of H₂SO₄ = 49 i.e. 49 gm of H₂SO₄ = 1gm equivalent of H₂SO₄

Number of gram equivalnet = \( \frac {Mass\:in\:gram}{Gram\:equivalent\:mass}\)

# Calculate the number of gram equivalent present in 480 gram of Mg

Given mass (M) = 480 gm

Equivalent mass (E) = 12 gm

Hence, Number of gram equivalent = \( \frac{M}{E}\) = \( \frac {480}{12}\) = 40

Variable equivalent mass

When an element combines with oxygen or chlorine to give only one compound, the equivalent mass is fixed. If the element has variable valency, it combines with oxygen or chlorine to give more than one compound and element shows variable equivalent mass. For example Copper combines with oxygen to give tow oxides namely red oxide ( Cu₂O) and black oxide (CuO).

* In red oxide (Cu₂O)

16 P/M of oxygen combines with 2 x 63.5 P/M of Cu

8 P/M combines with \( \frac { 2 × 63.5 × 8} {16}\) = 63.5 P/M of Cu

Hence, equivalent mass of Cu in red oxide = 63.5

*In black oxide

16 P/M of oxygen combines with 63.5 P/M of Cu

8 P/M of oxygen combines with \( \frac { 63.5 × 8} {16}\) = 31.75 P/M of Cu

Hence, equivalent mass of Cu in black oxide = 31.75

Relation between atomic mass, equivalent mass, and valency

Let 'A', 'E' and 'n' be the atomic mass, equivalent mass and valency of an element respectively. The valency of an element is the number of Hydrogen atoms which combines with one atom of that element

→ n atoms of hydrogen combines with one atom of element

→ n x 1.008 P/M of hydrogen combines with 'A' P/M of element

→1.008 P/M of hydrogen combines with \( \frac {A}{n}\) P/M of element

which by definition is equivalent mass of element

∴ Equivalent mass (E) = \( \frac {Atomic\:Mass\:(A)}{Valency\:(n)}\)

Equivalent masses of substances

a) Equivalent mass of an element = \( \frac {Atomic\:Mass}{Valency}\)

Example: Equivalent mass of Mg = \( \frac {24}{2}\) = 12

Equivalent mass of carbon = \( \frac {12}{4}\) = 3

Equivalent mass of Aluminium = \( \frac {27}{3}\) = 9

b) Equivalent mass of acid = \( \frac {Molecular\:Mass}{Basicity}\)

Basicity of acid is the number of H⁺ ion displaced per molecule of acid.

- Equivalent mass of H₂SO₄ = \( \frac {98}{2}\) = 49

- Equivalent mass of HCl = \( \frac {36.5}{1}\) = 36.5

- Equivalent mass of CH₃COOH = \( \frac {60}{1}\) = 60

- Equivalent mass of oxailic acid (anhydrous) i.e. (COOH)₂ = \( \frac {90}{2}\) = 45

- Equivalent mass of oxailic acid (hydrated) i.e. (COOH)₂.2H₂O = \( \frac {126}{2}\) = 63

- Equivalent mass of H₃PO₄ = \( \frac {98}{3}\) = 32.67

# Calculate equivalent mass of H₂SO₄ in following two reactions

a ) NaOH + H₂SO₄ →NaHSO₄ + H₂O

Here, basicity of H₂SO₄ = 1

Hence, equivalent mass of H₂SO₄ = \( \frac {98}{1}\) = 98

b) NaOH + H₂SO₄ →Na₂SO₄ + H₂O

Here, basicity of H₂SO₄ = 2

Hence, equivalent mass of H₂SO₄ = \( \frac {98}{2}\) = 49

c) Equivalent mass of base

\( \frac {Molecular\:Mass}{Acidity}\)

Acidity of acid is the number ofOH^- ion displaced per molecule of base.

- Equivalent mass of NaOH = \( \frac {40}{1}\) = 40

- Equivalent mass of KOH = \( \frac {56}{1}\) = 56

- Equivalent mass of Ca(OH)₂ = \( \frac {74}{2}\) = 37

- Equivalent mass of NH₄OH = \( \frac {35}{1}\) = 35

* For basic oxide , Equivalent mass = \( \frac {Molecular\:Mass}{2 × Number\: of \: oxygen\: atoms\: per\:molecule}\) ]

- Equivalent mass of CaO = \( \frac {56}{2}\) = 28

- Equivalent mass of Al₂O₃ = \(\frac {102}{6}\) = 17

d) Equivalent mass of salts

Equivalent mass of salts = \( \frac {Molecular\:Mass}{Total\:number\:of\:positive\:or\:negative\:charge\:per\:molecule}\)

- Equivalent mass of Na₂CO₃ = \( \frac {106}{2}\) = 53

- Equivalent mass of NaCl = \( \frac {58.5}{1}\) = 58.5

- Equivalent mass of KCl = \( \frac{74.5}{1}\) = 74.5

- Equivalent mass of CaCO₃ = \( \frac{100}{2}\) = 50

- Equivalent mass of Na₂CO₃.10H₂O = \( \frac {286}{2}\) = 143

e) Equivalent mass of radicals

Equivalent mass of radicals = \( \frac {Mass\:of\:radical}{Charge}\)

- Equivalent mass of SO₄^{- -} = \( \frac {96}{2}\) = 48

Equivalent mass of CO₃^{- -} = \( \frac {60}{2}\) = 30

The equivalent mass of comopund can also be calculated by the sumation of mass of cation and anion.

-Equivalent mass of H₂SO₄ = Equivalent mass of H⁺ + Equivalent mass of SO₄^{- -} = 1 + 48 = 49

Equivalent mass of Na₂CO₃ = Equivalent mass of Na⁺ + Equivalent mass of CO₃^{- -} = 13 + 30 = 43

f) Equivalent mass of oxidising or reducing agent

Equivalent mass of oxidising or reducing agent = \( \frac {Molecular\:Mass}{Change\:in\:Oxidation\:Number\:(Or\:Number\:of\:electrons\:involved\:per\:molecule}\)

Example: KMnO₄ (Oxidising agent)

KMnO₄ shows different equivalent mass in different medium

i) Acidic medium

Molecular mass of KMnO₄ = 158

Change in oxidation number = 5

Hence, equivalent mass = \( \frac {158}{5}\) = 31.6

ii) Alkaline medium

Molecular mass of KMnO₄ = 158

Change in oxidation number = 1

Hence, equivalent mass = \( \frac {158}{1}\) = 158

c) Neutral medium

Molecular mass of KMnO₄ = 158

Change in oxidation number = 3

Hence, equivalent mass = \( \frac {158}{3}\) = 52.66

# Equivalent mass of K₂Cr₂O₇ (Oxidising agent)

Molecular mass = 284

Change in oxidation number = 2 x 3 = 6

Equivalent mass = \( \frac {284}{6}\) = 49

# Equivalent mass of oxalic acid (Reducing agent)

Total change in oxidation number = 1 x 2 = 2

Molecular mass (anhydrous) = 90 i.e. Eq. mass = \( \frac {90}{2}\) = 45

Molecular mass (hydrated) = 126 i.e. Eq. mass = \(\frac{126}{2}\) = 63

n

Determination of Equivalent Mass

A. By Hydrogen Displacement Method

Metals above hydrogen in electrochemical series can displace hydrogen from dilute mineral acid (non-oxidising acids) since they are more electropositive than hydrogen. Thus,equivalent mass of such metals like (Zn, Fe, Al, Pb, Sn, Hg) can be determined by hydrogen displacement method. In this method accurately weighed the quantity of metal is treated with the excess of non-oxidising acids like dil. HCl or dil. H₂SO₄.

Mg + H₂SO₄ → MgSO₄ + H₂ ↑

Zn + 2HCl → ZnCl₂ + H₂↑

The volume of hydrogen gas displaced during the reaction is collected over water in eudiometer tube. The volume of H₂ gas evolved after completion of the reaction is noted at lab temperature and pressure. Then this volume is converted into NTP by using combined gas equation. The volume of H₂ gas displaced at NTP is then multiplied by 0.000089 gm to get the mass of hydrogen gas displaced (since the mass of 1 ml of H₂ at NTP= 0.000089 gm). Then the equivalent mass of metal is given by:

Equivalent mass = \( \frac {Mass\:of\:metal\:taken}{Mass\:of\:hydrogen\:displaced} × 1.008 \)

Calculation:

At lab condition,

Mass of metal taken = x gm (known)

Volume of H₂ gas displaced (V₁) = ? ml ( Obtained from eudiometer reading in lab)

Lab temperature = t₁⁰C = (t₁ + 273) K
Aqueous tension = f mmHg

Atmospheric pressure = P mmHg (Pressure of moist gas)

Pressure exerted by dry gas (P₁) = ( P - f) mmHg

The volume of hydrogen gas displaced in lab condition should be converted into colume at NTP.

At NTP,

The volume of H₂ gas displaced (V₂) = ?

Temperature at NTP = 273K

Pressure at NTP = 760 mmHg

Using combined gas equation ,

\( \frac {(P - f) V_1}{T_1}\) = \( \frac {P_2 V_2}{T_2}\)

or, V₂ = \( \frac {(P - f) V_1T_2}{T_1 P_2}\)

or, V₂ = \( \frac {(P - f) }{T_1} × \frac{273}{760}\)

Now,

Mass of H₂ gas displaced at NTP = V₂ x 0.000089 gm

So, V₂ x 0.000089 gm of H₂ is displaced by x gm of metal

1.008 gm of H₂ is displaced by \( \frac { x × 1.008}{V_2 × 0.000089}\) gm of metal

Hence, equivalent mass = \( \frac { x × 1.008}{V_2 × 0.000089}\)

Limitation

i) This method is not applicable to determine the equivalent mass of less active metals which lies below hydrogen in electrochemical series like Cu, Ag, Au since they cannot displace hydrogen from non-oxidising acids.

B. By Oxide formation method

This method is applicable when metal can form oxide directly or indirectly. If a metal cannot displace hydrogen from nonoxidising acids but can form oxide then oxide formation method to determine its equivalent mass. In this method, a fixed mass of metal is converted to oxide directly or indirectly .

(i) Some metals like Mn, Al, Mg can be converted into their oxides directly when heated with the excess of oxygen.

(ii) Some metals like Zn, Cu, Pb do not react easily with oxygen. Such metals are converted into their oxides indirectly. For this, a fixed mass of metal is completely dissolved in conc. HNO₃ to get metal nitrate, metal nitrate thus obtained is then heated strongly to get metal oxide.

Cu + 4HNO₃ → Cu(NO₃)₂ + 2NO₂ + 2H₂O

2Cu(NO₃)₂ 2CuO + 4NO₂ + O₂

Then, the mass of oxygen which combines with metal is calculated and the equivalent mass of metal is given by the formula:

Equivalent mass = \( \frac {Mass\: of \: metal \:taken} {Mass\:of\:oxygen} × 8\)

Calculation

A fixed mass of metal is taken in a crucible and is converted into its oxide directly or indirectly. Then, the crucible is cooled and weighed until the constant mass is observed. The constant mass is then noted and the mass of oxygen which combines with metal is calculated.

Let, mass of empty crucible = M₁ gm

Mass of (crucible + metal ) = M₂ gm

∴ Mass of metal = (M₂ - M₁) gm

Mass of (crucible + metal oxide) = M₃ gm

Mass of metal oxide = ( M₃ - M₁) gm

Mass of oygen = ( M₃ - M₁) - (M₂ - M₁) = (M₃ - M₂) gm

Now, (M₃ - M₂) parts by mass of oxygen combines with (M₂ - M₁) P/M of metal

8 P/M of oxygen combines with \( \frac {M_2 - M_1}{M_3 - M_2} × 8\) P/M of metal

Hence, equivalent mass = \( \frac {M_2 - M_1}{M_3 - M_2} × 8\)