Consider an ionic solid $$MX$$ with $$NaCl$$ structure. Construct a new structure $$(Z)$$ whose unit cell is constructed from the unit cell of $$MX$$ following the sequential instructions given below. Neglect the charge balance.
$$(i)\,\,\,\,\,$$ Remove all the anions $$(X)$$ except the central one

$$(ii)\,\,\,\,$$ Replace all the face centered cations $$(M)$$ by anions $$(X)$$

$$(iii)\,\,$$ Remove all the corner cations $$(M)$$

$$(iv)\,\,\,\,$$ Replace the central anion $$(X)$$ with cation $$(M)$$

The value of $$\,\,\left( {{{number\,\,of\,\,anions} \over {number\,\,of\,\,cations}}} \right)\,\,$$ in $$Z$$ is ___________.

The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by $$NiCl{}_2.6{H_2}O$$ to form a stable coordination compound. Assume that both the reactions are $$100\% $$ complete. If $$1584$$ $$g$$ of ammonium sulphate and $$952\,g$$ of $$NiC{l_2}.6{H_2}O$$ are used in the preparation, the combined weight (in grams) of gypsum and the nickel-ammonia coordination compound thus produced is _____________.

(Atomic weights in $$g$$ $$mo{l^{ - 1}}:$$ $$H = 1,N = 14,O = 16,$$ $$S = 32,Cl = 35.5,$$ $$Ca = 40,$$ $$Ni = 59$$

Among the species given below, the total number of diamagnetic species is _____________.

$$H$$ atom, $$N{O_2}$$ monomer, $${O_2}^ - $$ (superoxide), dimeric sulphur in vapor phase, $$M{n_3}{O_4},\,\,$$ $${\left( {N{H_4}} \right)_2}\left[ {FeC{l_4}} \right],$$ $${\left( {N{H_4}} \right)_2}\left[ {NiC{l_4}} \right],\,$$ $$\,{K_2}Mn{O_4},\,$$$${K_2}Cr{O_4}$$

For the electrochemical cell,

$$\left. {Mg\left( s \right)} \right|M{g^{2 + }}\left( {aq,1\,M} \right)\left\| {C{u^{2 + }}} \right.\left( {aq,1M} \right)\left| {Cu\left( s \right)} \right.$$

the standard $$emf$$ of the cell is $$2.70$$ $$V$$ at $$300$$ $$K.$$ When the concentration of $$M{g^{2 + }}$$ is changed to $$x$$ $$M,$$ the cell potential changes to $$2.67$$ $$V$$ at $$300$$ $$K.$$ The value of $$x$$ is ___________.

(given, $${F \over R} = 11500\,K{V^{ - 1}},$$ where $$F$$ is the Faraday constant and $$R$$ is the gas constant, In $$(10=2.30)$$