The reaction given below is a balanced reaction where $a, b, c, d, e, f$ and $g$ are the stoichiometric coefficients.
$a H g S + b H C l + c H N O_{3} \to d H_{2} H g C l_{4} + e N O + f S + g H_{2} O$
Find $a + b + c + d + e + f + g$

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Solution

Writing the chemical reaction given along with the oxidation number of the atoms involved:
$+ 2 - 2 H g S + + 1 - 1 H C l + + 1 + 5 - 2 H N O_{3} \to_{2} + 2 - 1 H g C l_{4} + + 2 - 2 N O + 0 S + + 1 - 2 H_{2} O$
The oxidation number of $S$ and $N$ have changed.
$H g - 2 S \to 0 S \cdot \cdot \cdot (i) + 5 H N O_{3} \to + 2 N O \cdot \cdot \cdot (i i)$
Imcrease in oxidation number of $S$ = $2$ units per $H g S$ molecule
Decrease in Oxidation number of $N$ = $3$ units per $H N O_{3}$ molecule
Multiplying eq. (i) by 3 and eq. (ii) by 2 as to make increase and decrease equal
$3 H g S + 2 H N O_{3} \to 3 S + 2 N O$
Balancing Hg and chlorine,
$3 H g S + 2 H N O_{3} + 12 H C l \to 3 H_{2} H g C l_{4} + 3 S + 2 N O$
To balance hydrogen and oxygen, $4 H_{2} O$ molecules are added on RHS. Hence, the balanced equation is
$3 H g S + 2 H N O_{3} + 12 H C l \to 3 H_{2} H g C l_{4} + 3 S + 2 N O + 4 H_{2} O$
So, $a + b + c + d + e + f + g = 3 + 2 + 12 + 3 + 3 + 2 + 4 = 29$

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a H g S + b H C l + c H N O_{3} \to d H_{2} + H g C l_{4} + e N O + f S + g H_{2} O

The values of b, c. e, and g are respectively.

Q. If a:b = c:d, and e:f = g:h, then (ae+bf):(ae-bf)=?

The variable coefficients d, e, f and g are considered for balancing the chemical equation. Relationships between these variable are constructed by balancing the atoms of each element on either side of the reaction. Which of the following are correct?

(Note: Coefficients should be natural numbers.)

(i) 2d= f, d = 3g and e= f + 2g

(ii) 2d = f, 3d = g and 2e = 2f + g

(iii) d = f2, 2d = g and e = 2f + 2g

(iv)d = 1, e = 3.5, f = 4 and g = 6

(v) d = 2, e = 7, f = 4 and g = 6

(vi) d = 2, e = 7, f = 3 and g = 4

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