\(E_{\text{cell}}\) of the following cell is \(345.5\,\text{mV}\). The cell representation is
\[
\text{Pt} \,|\, \mathrm{HSnO_2^-}(aq),\, \mathrm{[Sn(OH)_6]^{2-}}(aq),\, \mathrm{OH^-}(aq)\,||\, \mathrm{Bi_2O_3}(s)\,|\, \mathrm{Bi}(s)
\]
Concentrations:
\(\mathrm{HSnO_2^-}=0.5\,\text{M},\ \mathrm{[Sn(OH)_6]^{2-}}=0.05\,\text{M}\)
Given:
\[
E^\circ_{\mathrm{[Sn(OH)_6]^{2-}/HSnO_2^-}} = -0.90\,\text{V}, \quad
E^\circ_{\mathrm{Bi_2O_3(s)/Bi(s)}} = -0.44\,\text{V}
\]
\(\mathrm{OH^-}\) ion concentration is maintained by a buffer solution of \(x\) mL, \(20\,\text{M}\ \mathrm{NaHCO_3}(aq)\) and \(10\) mL, \(10\,\text{M}\ \mathrm{H_2CO_3}(aq)\).
Find the value of \(\dfrac{x}{1000}\).