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Question

The reaction given below is a balanced reaction where a, b, c, d, e, f and g are the stoichiometric coefficients.
aHgS+bHCl+cHNO3dH2HgCl4+eNO+fS+gH2O
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:
+22HgS++11HCl++1+52HNO3+1H2+21HgCl4++22NO+0S++12H2O
The oxidation number of S and N have changed.
Hg2S0S (i)+5HNO3+2NO (ii)
Increase in oxidation number of S = 2 units per HgS molecule
Decrease in Oxidation number of N = 3 units per HNO3 molecule
Multiplying eq. (i) by 3 and eq. (ii) by 2 as to make increase and decrease equal
3HgS+2HNO33S+2NO
Balancing Hg and chlorine,
3HgS+2HNO3+12HCl3H2HgCl4+3S+2NO
To balance hydrogen and oxygen, 4H2O molecules are added on RHS. Hence, the balanced equation is
3HgS+2HNO3+12HCl3H2HgCl4+3S+2NO+4H2O
So, a+b+c+d+e+f+g=3+2+12+3+3+2+4=29

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