Đặt \({n_{{\rm{F}}{{\rm{e}}_3}{{\rm{O}}_4}}} = {\rm{a}}\,\,{\rm{mol}}\)

- Khi hòa tan chất rắn vào dung dịch HCl loãng:

\(\begin{array}{l}{\rm{F}}{{\rm{e}}_3}{{\rm{O}}_4} + 8{\rm{HCl}} \to {\rm{FeC}}{{\rm{l}}_2} + 2{\rm{FeC}}{{\rm{l}}_3} + 4{{\rm{H}}_2}{\rm{O}}\\\,\,{\rm{a}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(mol)\end{array}\)

\(\begin{array}{l}{\rm{Cu}} + 2{\rm{F}}{{\rm{e}}^{3 + }} \to {\rm{C}}{{\rm{u}}^{2 + }} + 2{\rm{F}}{{\rm{e}}^{2 + }}\\a \leftarrow 2a\,\,\,\,\,\,\,\,\, \to \,\,\,a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(mol)\end{array}\)

Dung dịch X chỉ chứa 2 muối \(\left\{ \begin{array}{l}FeC{l_2}:3a\,mol\\CuC{l_2}:a\,mol\end{array} \right.\)

\( \Rightarrow 127.3{\rm{a}} + 135{\rm{a}} = 61,92\; \Rightarrow {\rm{a}} = 0,12\,\,mol\)

\( \Rightarrow \left\{ \begin{array}{l}{n_{F{e_3}{O_4}}} = 0,12\,\,mol\\{n_{Cu}} = 0,12\,\,mol\end{array} \right. \Rightarrow {m_{F{e_3}{O_4}}} + {m_{Cu}} = 35,52\,gam.\)

- Khi cho \(F{e_3}{O_4},Cu\)vào HNO₃

\({n_{HN{O_3}}} = \frac{{280 \cdot 0,36}}{{63}} = 1,6\,mol\)

Dung dịch Y gồm có: \(\left\{ \begin{array}{l}Fe{(N{O_3})_3}:0,36\,mol\\Cu{(N{O_3})_2}:0,12\,mol\\HN{O_3}\,c\`o n:\,x\,mol\end{array} \right.\)

Giả sử, quá trình cho NaOH (1,5 mol) vào Y thì NaOH dư. Khi đó:

Trong dung dịch nước lọc có

\(\begin{array}{l} \Rightarrow 69b + 40 \cdot (1,5 - b) = 100,6\\ \Rightarrow b = 1,4\,mol\end{array}\)

Hỗn hợp khí thoát ra gồm có \({\rm{NO}}\) (y mol) và \({\rm{N}}{{\rm{O}}_2}\)(z mol)

Bảo toàn nguyên tố \({\rm{N}}:y + z = \sum {{n_{N\,(HN{O_3})}}} - {n_{NaN{O_3}}} = 1,6 - 1,4 = 0,2\,mol\)

Bảo toàn \({\rm{e}}:3y + z = 2{n_{Cu}} + {n_{F{e_3}{O_4}}} = 0,12 \cdot 2 + 0,12 = 0,36\)

\( \Rightarrow y = 0,08,z = 0,12\)(mol)

\[\begin{array}{l} \Rightarrow {m_{NO}} + {m_{N{O_2}}} = 0,08 \cdot 30 + 0,12 \cdot 46 = 7,92\,gam\\ \Rightarrow {m_{dd\,\,sau}} = ({m_{F{e_3}{O_4}}} + {m_{Cu}}) + {m_{dd\,HN{O_3}}} - ({m_{NO}} + {m_{N{O_2}}}) = 35,52 + 280 - 7,92 = 307,58\,gam.\end{array}\]

\( \Rightarrow C{\% _{{\rm{Fe}}{{\left( {{\rm{N}}{{\rm{O}}_3}} \right)}_3}}} = \frac{{0,36 \cdot 242}}{{307,58}} \cdot 100\% = 28,32\% .\)

Đáp án: 28,32%