a) Đặt \(\left\{{}\begin{matrix}n_{Mg}=a\left(mol\right)\\n_{Al}=b\left(mol\right)\end{matrix}\right.\) \(\Rightarrow24a+27b=5,1\)  (1)

Ta có: \(n_{H_2}=\dfrac{5,6}{22,4}=0,25\left(mol\right)\)

Bảo toàn electron: \(2a+3b=0,5\)  (2)

Từ (1) và (2) \(\Rightarrow\left\{{}\begin{matrix}a=0,1\\b=0,1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{Mg}=\dfrac{0,1\cdot24}{5,1}\cdot100\%\approx47,06\%\\\%m_{Al}=52,94\%\end{matrix}\right.\)

b) Bảo toàn nguyên tố: \(n_{HCl}=2n_{H_2}=0,5\left(mol\right)\)

\(\Rightarrow m_{ddHCl}=\dfrac{0,5\cdot36,5}{7,3\%}=250\left(g\right)\)

\(\Rightarrow V_{HCl}=\dfrac{250}{1,2}\approx208,33\left(ml\right)\)

PTHH:  \(CaO+2HNO_3\rightarrow Ca\left(NO_3\right)_2+H_2O\)

            \(MgCO_3+2HNO_3\rightarrow Mg\left(NO_3\right)_2+CO_2\uparrow+H_2O\)

Ta có: \(n_{CO_2}=\dfrac{2,24}{22,4}=0,1\left(mol\right)=n_{MgCO_3}=n_{Mg\left(NO_3\right)_2}\) \(\Rightarrow n_{CaO}=\dfrac{18-0,1\cdot84}{56}=\dfrac{6}{35}\left(mol\right)=n_{Ca\left(NO_3\right)_2}\)

\(\Rightarrow\left\{{}\begin{matrix}\%m_{MgCO_3}=\dfrac{0,1\cdot84}{18}\cdot100\%\approx46,67\%\\\%m_{CaO}=53,33\%\end{matrix}\right.\)

Theo đề bài, ta có: \(m_{ddHNO_3}=500\cdot1,08=540\left(g\right)\) \(\Rightarrow\Sigma n_{HNO_3}=\dfrac{540\cdot12,6\%}{63}=1,08\left(mol\right)\)

Theo PTHH: \(n_{HNO_3\left(p.ứ\right)}=2n_{CaO}+2n_{MgCO_3}=\dfrac{19}{35}\left(mol\right)\) \(\Rightarrow n_{HNO_3\left(dư\right)}=\dfrac{94}{175}\left(mol\right)\)

Mặt khác: \(m_{CO_2}=0,1\cdot44=4,4\left(g\right)\)

\(\Rightarrow m_{dd\left(sau.pư\right)}=m_A+m_{ddHNO_3}-m_{CO_2}=553,6\left(g\right)\)

\(\Rightarrow\left\{{}\begin{matrix}C\%_{Mg\left(NO_3\right)_2}=\dfrac{0,1\cdot148}{553,6}\cdot100\%\approx2,67\%\\C\%_{Ca\left(NO_3\right)_2}=\dfrac{\dfrac{6}{35}\cdot164}{553,6}\cdot100\%\approx5,08\%\\C\%_{HNO_3\left(dư\right)}=\dfrac{\dfrac{19}{35}\cdot63}{553,6}\cdot100\%\approx6,18\%\end{matrix}\right.\)

$Na_2CO_3 + BaCl_2 \to BaCO_3 + 2NaCl$
$n_{Na_2CO_3} = n_{BaCO_3} = \dfrac{39,4}{197} = 0,2(mol)$
$n_{NaOH} = 0,2.2,5 = 0,5(mol)$

$MgCO_3 + 2HCl \to MgCl_2 + CO_2 + H_2O$
$RCO_3 + 2HCl \to RCl_2 +C O_2 + H_2O$

TH1 : NaOH dư

$2NaOH + CO_2 \to Na_2CO_3 + H_2O$

$n_{CO_2} = n_{Na_2CO_3} = 0,2(mol)$
$\Rightarrow n_{MgCO_3} = n_{RCO_3} = n_{CO_2}  :2 = 0,1(mol)$

Ta có : 

0,1.84 + 0,1(R + 60) = 20

=> R = 56(Fe)

Vậy : 

$m_{MgCO_3} = 0,1.84 = 8,4(gam)$
$m_{FeCO_3} = 0,1.116 = 11,6(gam)$

-TH2 : có muối $NaHCO_3$
2NaOH + CO₂ → Na₂CO₃ + H₂O

0,4............0,2...........0,2........................(mol)

NaOH + CO₂ → NaHCO₃

0,1..........0,1.....................(mol)

$n_{CO_2}  = 0,2 + 0,1 = 0,3(mol)$
$n_{MgCO_3} = n_{RCO_3} = n_{CO_2} : 2  = 0,15(mol)$

Suy ra: 

0,15.84 + 0,15(R + 60) = 20

=> R = -10,6 (Loại)

Giả sử: n_MgCO3 = n_RCO3 = x (mol)

⇒ 84x + x(M_R + 60) = 20

⇔ (M_R + 144)x = 20 (1)

PT: \(MgCO_3+2HCl\rightarrow MgCl_2+H_2O+CO_2\)

\(RCO_3+2HCl\rightarrow RCl_2+H_2O+CO_2\)

Theo PT: \(n_{CO_2}=n_{MgCO_3}+n_{RCO_3}=2x\left(mol\right)\)

Ta có: \(n_{NaOH}=0,2.2,5=0,5\left(mol\right)\)

\(n_{BaCO_3}=\dfrac{39,4}{197}=0,2\left(mol\right)=n_{Na_2CO_3}\)

PT: \(BaCl_2+Na_2CO_3\rightarrow BaCO_3+2NaCl\)

TH1: NaOH dư.

PT: \(CO_2+2NaOH\rightarrow Na_2CO_3+H_2O\)

____0,2 ________________0,2 (mol)

⇒ 2x = 0,2 ⇔ x = 0,1 (mol)

Thay vào (1), ta được M_R = 56 (g/mol)

Vậy: R là Fe.

⇒ m_MgCO3 = 0,1.84 = 8,4 (g)

m_FeCO3 = 20 - 8,4 = 11,6 (g)

TH2: NaOH hết.

PT: \(CO_2+2NaOH\rightarrow Na_2CO_3+H_2O\)

____0,2____0,4________0,2 (mol)

\(CO_2+NaOH\rightarrow NaHCO_3\)

_0,1_____0,1 (mol)

⇒ n_CO2 = 0,2 + 0,1 = 0,3 (mol)

⇒ 2x = 0,3 ⇔ x = 0,15 (mol)

Thay vào (1), ta được M_R = -10,67 (loại)

Vậy...

Bạn tham khảo nhé!

\(n_{HCl}=0,3.2=0,6\left(mol\right)\\ n_{H_2}=\dfrac{5,6}{22,4}=0,25\left(mol\right)\\ 2Al+6HCl\rightarrow2AlCl_3+3H_2\\ Fe+2HCl\rightarrow FeCl_2+H_2\\ Vì:\dfrac{0,6}{2}>\dfrac{0,25}{1}\Rightarrow HCldư\\ Đặt:n_{Al}=t\left(mol\right);n_{Fe}=r\left(mol\right)\\ \left(t,r>0\right)\\ \Rightarrow\left\{{}\begin{matrix}27t+56r=8,3\\1,5t+r=0,25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}t=0,1\\r=0,1\end{matrix}\right.\\ \Rightarrow m_{Al}=0,1.27=2,7\left(g\right);m_{Fe}=0,1.56=5,6\left(g\right)\\ b,n_{AlCl_3}=n_{Al}=0,1\left(mol\right)\Rightarrow m_{AlCl_3}=0,1.133,5=13,35\left(g\right)\\ n_{Fe}=n_{FeCl_2}=0,1\left(mol\right)\Rightarrow m_{ddFeCl_2}=127.0,1=12,7\left(g\right)\\ m_{ddHCl}=300.1,15=345\left(g\right)\\ m_{ddsau}=8,3+345-0,25.2=352,8\left(g\right)\)

\(n_{HCl\left(dư\right)}=0,6-0,25.2=0,1\left(mol\right)\\ \Rightarrow m_{ddHCl}=0,1.36,5=3,65\left(g\right)\\ C\%_{ddHCl\left(dư\right)}=\dfrac{3,65}{352,8}.100\approx1,035\%\\ C\%_{ddAlCl_3}=\dfrac{13,35}{352,8}.100\approx3,784\%\\ C\%_{ddFeCl_2}=\dfrac{12,7}{352,8}.100\approx3,6\%\)