Bài 1 : 

a) Gọi $n_{Mg} = a ; n_{Ca} = b \Rightarrow 24a + 40b = 20,8(1)$

Ta có : 

$\%m_{Mg} = \dfrac{24a + 24a}{20,8 + 24a}.100\% = 37,5\%(2)$

Từ (1)(2) suy ra a = 0,2 ; b = 0,4

b)

Bảo toàn Ca : $n_{Ca_3(PO_4)_2} = \dfrac{1}{3}n_{Ca} = \dfrac{0,4}{3}(mol)$

$\Rightarrow m_{Ca_3(PO_4)_2} = \dfrac{0,4}{3}.310 = 41,33(gam)$

\(n_{SO_2}=\dfrac{13,644}{22,4}=0,61\left(mol\right)\)

Đặt n _Fe = x (mol) =>\(m_{Fe}=56x\)

Vì m _Fe = m_Mg => \(n_{Mg}=\dfrac{56x}{24}=\dfrac{7}{3}x\)

n_Al = y(mol)

=> 56x + 56x + 27y = 16,14 (1)

\(Fe\rightarrow Fe^{3+}+3e\)                                       \(S^{+6}+2e\rightarrow S^{+4}\)

\(Mg\rightarrow Mg^{2+}+2e\)

\(Al\rightarrow Al^{3+}+3e\)

Bảo toàn e : 3x + \(\dfrac{7}{3}.2x\) + 3y = 0,61.2 (2)

Từ (1), (2) => x=0,12 ; y=0,1

=> m_Fe =m_Mg=0,12.56 = 6,72(g)

m _Al = 0,1.27=2,7(g)

Gọi $n_{Fe} = a ; n_{Mg} = b; n_{Al} = c$

Ta có : 

$24b = 56a(1)$
$56a + 24b + 27c = 16,14(2)$

$n_{SO_2} = 0,61(mol)$
Bảo toàn electron : $3n_{Fe} + 2n_{Mg} + 3n_{Al} = 2n_{SO_2}$
$\Rightarrow 3a + 2b + 3c = 0,61.2(3)$

Từ (1)(2)(3) suy ra a = 0,12 ; b = 0,28 ; c = 0,1

$m_{Fe} = m_{Mg} = 0,12.56 = 6,72(gam)$

$m_{Al} = 0,1.27 = 2,7(gam)$

a) \(n_{MgO}=\dfrac{16}{40}=0,4\left(mol\right)\)

=> n_Mg = 0,4 (mol)

=> m_Mg = 0,4.24 = 9,6 (g)

b) n_Mg = 0,4 (mol) => n_X = 0,6 (mol)

m_X = 33,6 - 9,6 = 24 (g)

=> \(M_X=\dfrac{24}{0,6}=40\left(g/mol\right)\)

=> X là Ca

c) 

PTHH: 2Mg + O₂ --t^o--> 2MgO

             2Ca + O₂ --t^o--> 2CaO

\(m_{O_2}=49,6-33,6=16\left(g\right)\)

=> \(n_{O_2}=\dfrac{16}{32}=0,5\left(mol\right)\)

=> V_O2 = 0,5.22,4 = 11,2 (l)

=> V_kk = 11,2.5 = 56 (l)

a)\(n_{MgO}=\dfrac{16}{40}=0,4mol\Rightarrow n_{Mg}=0,4mol\Rightarrow m_{Mg}=9,6g\)

\(\Rightarrow m_X=33,6-9,6=24g\)

b)Theo bài: \(\dfrac{n_{Mg}}{n_X}=\dfrac{2}{3}\Rightarrow\dfrac{0,4}{n_X}=\dfrac{2}{3}\Rightarrow n_X=0,6mol\)

\(\Rightarrow M_X=\dfrac{24}{0,6}=40\Rightarrow X:Ca\)

c)\(2Mg+O_2\underrightarrow{t^o}2MgO\)

     \(x\)                    \(x\)

   \(2Ca+O_2\underrightarrow{t^o}2CaO\)

    \(y\)                      \(y\)

\(\Rightarrow\left\{{}\begin{matrix}24x+40y=33,6\\40x+56y=49,6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0,4\\y=0,6\end{matrix}\right.\)

\(\Sigma n_{O_2}=\dfrac{1}{2}n_{Mg}+\dfrac{1}{2}n_{Ca}=0,2+0,3=0,5mol\)

\(m_{O_2}=0,5\cdot32=16g\)

\(V_{kk}=5V_{O_2}=5\cdot0,5\cdot22,4=56l\)

a) \(n_{MgO}=\dfrac{16}{40}=0,4\left(mol\right)\)

=> n_Mg = 0,4 (mol)

=> m_Mg = 0,4.24 = 9,6 (g)

b)

Có: n_Mg : n_X = 2 : 3

Mà n_Mg = 0,4 (mol)

=> n_X = 0,6 (mol)

m_X = 33,6 - 9,6 = 24 (g)

=> \(M_X=\dfrac{24}{0,6}=40\left(g/mol\right)\)

=> X là Ca

c)

PTHH: 2Mg + O₂ --t^o--> 2MgO

            0,4->0,2

             2Ca + O₂ --t^o--> 2CaO

              0,6->0,3

=> \(m_{O_2}=\left(0,2+0,3\right).32=16\left(g\right)\)

\(V_{O_2}=\left(0,2+0,3\right).22,4=11,2\left(l\right)\)

=> V_kk = 11,2.5 = 56 (l)

a) MX=240,6=40(g/mol)MX=240,6=40(g/mol)

=> X là Ca

c PTHH: 2Mg + O₂ --t^o--> 2MgO

            0,4->0,2

             2Ca + O₂ --t^o--> 2CaO

              0,6->0,3

=> mO2=(0,2+0,3).32=16(g)mO2=(0,2+0,3).32=16(g)

VO2=(0,2+0,3).22,4=11,2(l)VO2=(0,2+0,3).22,4=11,2(l)

=> V_kk = 11,2.5 = 56 (l)

\(m_{H_2} = m -(m-2,4) = 2,4(gam)\\ \Rightarrow n_{H_2} = \dfrac{2,4}{2} = 1,2(mol)\\ Gọi : n_{Mg} = a ;n_{Zn} = 2a;n_{Fe}= 3a(mol)\\ Mg + 2HCl \to MgCl_2 + H_2\\ Zn + 2HCl \to ZnCl_2 + H_2\\ Fe + 2HCl \to FeCl_2 + H_2\\ n_{H_2} = n_{Mg} + n_{Zn} + n_{Fe} = a + 2a + 3a = 1,2(mol)\\ \Rightarrow a = 0,2;\\ \Rightarrow m = 0,2.24 + 0,2.2.65 + 0,2.3.56 = 64,4(gam)\)

Gọi x, 2x, 3x tương ứng là số mol của Mg, Zn và Fe: 24x + 65.2x + 56.3x = m ---> m = 322x.

Khối lượng dd tăng = khối lượng kim loại - mH2

m - 2,4 = m - (2x + 4x + 9x) ---> 15x = 2,4 hay x = 0,16 mol.

Thay vào trên thu được: m = 322.0,16 = 51,52 gam.

Đặt \(\left\{{}\begin{matrix}n_{Mg}=a\left(mol\right)\\n_{Zn}=2a\left(mol\right)\\n_{Fe}=3a\left(mol\right)\end{matrix}\right.\)

Ta có: \(m_{t\text{ăng}}=m_{KL}-m_{H_2}\)

\(\Rightarrow m-m_{H_2}=m-2,4\\ \Leftrightarrow m_{H_2}=2,4\left(g\right)\Rightarrow n_{H_2}=\dfrac{2,4}{2}=1,2\left(mol\right)\)

PTHH:
`Mg + 2HCl -> MgCl_2 + H_2`

`Zn + 2HCl -> ZnCl_2 + H_2`

`Fe + 2HCl -> FeCl_2 + H_2`

Theo PTHH: 

\(n_{H_2}=n_{Mg}+n_{Zn}+n_{Fe}=a+2a+3a=6a\left(mol\right)\\ \Rightarrow6a=1,2\Leftrightarrow a=0,2\left(mol\right)\\ \Rightarrow\left\{{}\begin{matrix}n_{Mg}=0,2\left(mol\right)\\n_{Zn}=0,2.2=0,4\left(mol\right)\\n_{Fe}=0,2.3=0,6\left(mol\right)\end{matrix}\right.\)

Vậy \(m=0,2.24+0,4.65+0,6.56=64,4\left(g\right)\)

$$\begin{array}{c}{\Delta }_m=m_Y-m_{H_2}\\ \Rightarrow m-2,4=m-m_{H_2}\\ \iff m_{H_2}=2,4gam\\ \Rightarrow n_{H_2}=\frac{2,4}{2}=1,2mol\end{array}$$

Gọi n_Mg là A => n_Zn là 2a, n_Fe là 3a

$$\begin{array}{c}Mg+2HCl\to MgC{l}_2+H_2\\ \mathrm{a\; a}\end{array}$$

$$\begin{array}{c}Zn+2HCl\to ZnC{l}_2+H_2\\ \mathrm{2a\; 2a}\end{array}$$$$\begin{array}{c}Fe+2HCl\to FeC{l}_2+H_2\\ 3a\; 3a\end{array}$$

$$\begin{array}{c}\Rightarrow n_{H_2}=a+2a+3a=1,2mol\\ \Rightarrow a=0,2mol\\ \Rightarrow m=0,2\cdot 24+0,2\cdot 2\cdot 65+0,2\cdot 3\cdot 56=64,4gam\end{array}$$