Ta có: \(n_{Al\left(OH\right)_3}=\dfrac{7,8}{78}=0,1\left(mol\right)\)

PTHH: \(2NaOH+H_2SO_4\rightarrow Na_2SO_4+2H_2O\)

                      0,2______0,1                                 (mol)

            \(6NaOH+Al_2\left(SO_4\right)_3\rightarrow3Na_2SO_4+2Al\left(OH\right)_3\downarrow\)

                      0,3________0,05___________________0,1   (mol)

Ta có: \(n_{NaOH}=0,5\left(mol\right)\) \(\Rightarrow V_{ddNaOH}=\dfrac{0,5}{2}=0,25\left(l\right)\)

Gọi \(\left\{{}\begin{matrix}n_{Mg}=x\left(mol\right)\\n_{Al}=y\left(mol\right)\end{matrix}\right.\)

\(n_{BaSO_4}=\dfrac{11,65}{233}=0,05\left(mol\right)\)

\(Mg+CuSO_4\rightarrow MgSO_4+Cu\)

x------>x--------->x------------>x

\(2Al+3CuSO_4\rightarrow Al_2\left(SO_4\right)_3+3Cu\)

y------>1,5y-------->0,5y-------->1,5y

Có hệ \(\left\{{}\begin{matrix}24x+27y=0,78\\x+1,5y=\dfrac{2,56}{64}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0,01\\y=0,02\end{matrix}\right.\)

Giả sử \(CuSO_4\) phản ứng hết, dung dịch C có: \(\left\{{}\begin{matrix}n_{MgSO_4}=x=0,01\left(mol\right)\\n_{Al_2\left(SO_4\right)_3}=0,5y=0,5.0,02=0,01\left(mol\right)\end{matrix}\right.\)

\(MgSO_4+BaCl_2\rightarrow MgCl_2+BaSO_4\) (1)

0,01-------------------------------->0,01

\(Al_2\left(SO_4\right)_3+3BaCl_2\rightarrow3BaSO_4+2AlCl_3\) (2)

0,01------------------------>0,03

Từ PTHH (1), (2) có: \(\Sigma n_{BaSO_4}=0,01+0,03=0,04\left(mol\right)< 0,05\left(mol\right)_{theo.đề}\)

=> Giả sử sai, \(CuSO_4\) dư 

\(CuSO_4+BaCl_2\rightarrow BaSO_4+CuCl_2\)

0,01<-----------------0,01

\(CM_{CuSO_4}=a=\dfrac{x+1,5y+0,01}{0,2}=\dfrac{0,01+1,5.0,02+0,01}{0,2}=0,25\left(M\right)\)

Trong A:

\(n_{Al}=0,02\left(mol\right)\\ n_{Mg}=0,01\left(mol\right)\)

\(a)Bte:3n_{Fe}+3n_{Al}=n_{Ag}\\ \Leftrightarrow n_{Ag_3}=0,1.3+0,1.3\\ \Leftrightarrow n_{Ag}=0,6mol\\ m_{rắn}=m_{Ag}=0,6.108=64,8g\\ BTNT\left(Ag\right):n_{Ag}=n_{AgNO_3}=0,6mol\\ V_{AgNO_3}=\dfrac{0,6}{2}=0,3l\\ BTNT\left(Al\right):n_{Al}=2n_{Al_2O_3}\\ \Leftrightarrow0,1=2n_{Al_2O_3}\\ \Leftrightarrow n_{Al_2O_3}=0,05mol\\ BTNT\left(Fe\right):n_{Fe}=2n_{Fe_2O_3}\\ \Leftrightarrow0,1=2n_{Fe_2O_3}\\ \Leftrightarrow n_{Fe_2O_3}=0,05mol \\ b=m_{oxit.bazo}=0,05.\left(160+102\right)=13,1g\)