PTHH: \(Mg+2HCl\rightarrow MgCl_2+H_2\uparrow\)

               2a_____4a______2a____2a      (mol)

            \(Fe+2HCl\rightarrow FeCl_2+H_2\uparrow\)

               a_____2a______a_____a      (mol)

            \(2Al+6HCl\rightarrow2AlCl_3+3H_2\uparrow\)

                b______3b______b______\(\dfrac{3}{2}\)b    (mol)

Ta lập HPT: \(\left\{{}\begin{matrix}2a+a+\dfrac{3}{2}b=\dfrac{13,44}{22,4}=0,6\\24\cdot2a+56a+27b=15,8\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=0,1\\b=0,2\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{Fe}=\dfrac{0,1\cdot56}{15,8}\cdot100\%=35,44\%\\\%m_{Al}=\dfrac{0,2\cdot27}{15,8}=34,18\%\\\%m_{Mg}=30,38\%\end{matrix}\right.\)

Theo các PTHH: \(n_{HCl}=2n_{H_2}=1,2\left(mol\right)\)

\(\Rightarrow m_{ddHCl}=\dfrac{1,2\cdot36,5}{200}\cdot100\%=21,9\%\)

a. \(n_{H_2}=\dfrac{5,6}{22,4}=0,25\left(mol\right)\)

\(Mg+2HCl\rightarrow MgCl_2+H_2\)

0,25 ..... 0,5 ................... 0,25 (mol) 

\(m_{Mg}=0,25.24=6\left(g\right)\)

\(\rightarrow\left\{{}\begin{matrix}\%m_{Mg}=\dfrac{6}{10}.100\%=60\%\\\%m_{MgO}=100\%-60\%=40\%\end{matrix}\right.\)

\(MgO+2HCl\rightarrow MgCl_2+H_2O\)

0,1 ....... 0,2 (mol) 

\(n_{HCl}=0,25+0,1=0,35\left(mol\right)\)

\(C_M\left(HCl\right)=\dfrac{0,35}{0,1}=3,5\left(M\right)\)

\(n_{H_2}=\dfrac{2,24}{22,4}=0,1(mol)\\ Mg+2HCl\to MgCl_2+H_2\\ MgO+2HCl\to MgCl_2+H_2O\\ \Rightarrow n_{Mg}=0,1(mol)\\ \Rightarrow \%_{Mg}=\dfrac{0,1.24}{6,4}.100\%=37,5\%\\ \Rightarrow \%_{MgO}=100\%-37,5\%=62,5\%\)

\(b,n_{MgO}=\dfrac{6,4-0,1.24}{40}=0,1(mol)\\ \Rightarrow n_{HCl}=2.0,1+2.0,1=0,4(mol)\\ \Rightarrow V_{dd_{HCl}}=\dfrac{0,4}{0,5}=0,8(l)\\ c,n_{MgCl_2}=0,1+0,1=0,2(mol)\\ \Rightarrow C_{M_{MgCl_2}}=\dfrac{0,2}{0,8}=0,25M\)

a) \(Fe+2HCl->FeCl_2+H_2\) (1)

\(2M+2xHCl->2MCl_x+xH_2\) (2)

=> \(n_{HCl}=2.n_{H_2}=2.\dfrac{1,008}{22,4}=0,09\left(mol\right)\)

=> m_HCl = 0,09.36,5 = 3,285 (g)

Theo ĐLBTKL: \(m_A+m_{HCl}=m_{Muối}+m_{H_2}\)

=> \(m_A=4,575+0,045.2-3,285=1,38\left(g\right)\)

b) Đặt số mol Fe, M là a, b

=> 56a + M.b = 1,38 (***)

(1)(2) => a+ 0,5bx = 0,045 (*)

\(\left\{{}\begin{matrix}\dfrac{46.n_{NO_2}+64.n_{SO_2}}{n_{NO_2}+n_{SO_2}}=50,5\\n_{NO_2}+n_{SO_2}=\dfrac{1,8816}{22,4}=0,084\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}n_{NO_2}=0,063\\n_{SO_2}=0,021\end{matrix}\right.\)

Fe⁰ - 3e --> Fe⁺³

a---->3a

M⁰ -xe --> M^+x

b-->bx

N⁺⁵ +1e--> N⁺⁴

___0,063<-0,063

S⁺⁶ + 2e --> S⁺⁴

___0,042<-0,021

Bảo oàn e: 3a + bx = 0,105 (**)

(*)(**) => \(\left\{{}\begin{matrix}a=0,015\\bx=0,06=>b=\dfrac{0,06}{x}\end{matrix}\right.\)

(***) => 0,015.56 + \(M.\dfrac{0,06}{x}\) = 1,38

=> M = 9x (g/mol)

Xét x = 1 => M = 9(L)

Xét x = 2 => M = 18(L)

Xét x = 3 => M = 27(Al)

Coi hỗn hợp Y gồm : Kim loại và Oxi

$n_O = \dfrac{2,71-2,23}{16}= 0,03(mol)$

Gọi $n_{H_2SO_4\ pư}=  a(mol)$

$n_{SO_2} = \dfrac{1,008}{22,4} = 0,045(mol)$

Bảo toàn nguyên tố với H : $n_{H_2O} = n_{H_2SO_4\ pư} = a(mol)$

Bảo toàn nguyên tố với S : 

$n_{SO_4(trong\ muối)} = n_{H_2SO_4} - n_{SO_2} = a - 0,045(mol)$

Bảo toàn nguyên tố với O : 

$0,03 + 4a = (a - 0,045).4 + 0,045.2 + a$
$\Rightarrow a = 0,12(mol)$

\(n_{Cu\left(NO_3\right)_2}=0,5.0,2=0,1\left(mol\right)\)

\(n_{NO_3^-}=0,1.2=0,2\left(mol\right)\)

\(n_{Cu^{2+}}=0,1\left(mol\right)\)

\(n_{HCl}=n_{H^+}=0,5.1,8=0,9\left(mol\right)\)

\(n_{NO}=\dfrac{n_{H^+}}{4}=\dfrac{0,9}{4}=0,225\left(mol\right)\)

Sau phản ứng thu được hỗn hợp kim loại \(\Rightarrow\) Cu và Fe \(\Rightarrow\) \(Fe^{2+}\)

Bảo toàn e:

\(2n_{Fe.pứ}=3n_{NO}+2n_{Cu^{2+}}\)

\(\Rightarrow n_{Fe.pứ}=0,4375\left(mol\right)\)

Có: \(a-m_{Fe.pứ}+m_{Cu}=m_{hh.kl}=0,5\)

\(\Leftrightarrow a-0,4375.56+64.0,1=0,5\\ \Rightarrow a=18,6\)