Question

What is the formula of sodium dithiosulphatoargentate (I)?
A. $N{a_3}\left[ {Ag{{\left( {{S_2}{O_2}} \right)}_2}} \right]$
B. $Na\left[ {Ag{{\left( {{S_2}{O_4}} \right)}_2}} \right]$
C. $Na\left[ {Ag{{\left( {{S_2}{O_3}} \right)}_2}} \right]$
D. $N{a_3}\left[ {Ag{{\left( {{S_2}{O_3}} \right)}_2}} \right]$

Answer 1

Hint: Argentate (I) is a silver (Ag) ion with +1 charge. Sodium ion is a cation with +1 charge. Dithiosulphate indicates presence of two thiosulphate ions. The charge of each thiosulphate ion is -2. Use this information to derive the formula of dithiosulphatoargentate.

Complete step by step answer:
We are given to derive the formula of sodium dithiosulphatoargentate (I).
Thiosulphate ion is an oxyanion of sulphur. Its formula is ${S_2}{O_3}^{2 - }$. Each thiosulphate in will have a negative charge of -2.
So in sodium dithiosulphatoargentate (I), Dithiosulphate represents the presence of two thiosulphate ions so the resulting charge will be $2 \times - 2 = - 4$
Dithiosulphatoargentate (I) represents that silver with oxidation number +1 bond with two thiosulphate ions, therefore the resulting oxidation number (charge) will be $ - 4 + 1 = - 3$
So to balance this negative charge of -3, we need three sodium ions with each sodium ion having +1 positive charge, as the name sodium dithiosulphatoargentate have sodium in it.
So there will be 3 sodium ions, two thiosulphate ions and one silver ion in the formula of sodium dithiosulphatoargentate.
The formula which matches all the above criteria is $N{a_3}\left[ {Ag{{\left( {{S_2}{O_3}} \right)}_2}} \right]$.
Therefore, the correct option is Option D, $N{a_3}\left[ {Ag{{\left( {{S_2}{O_3}} \right)}_2}} \right]$.

Note:
We have taken the valency of Silver ion as +1 as per the question, but the silver can exhibit both +1, +2 valencies (monovalent and divalent). So read the question carefully before attempting. Do not confuse between sulphate ion and thiosulphate ion, sulphate ion has one sulphur atom and 4 oxygen atoms whereas thiosulphate ion has two sulphur atoms and three oxygen atoms.