\(a.n_{Al}=a;n_{Fe}=b\left(mol\right)\\ m_{hh}=27a+56b=4,17\left(1\right)\\ 4Al+3O_2\underrightarrow{t^{^{ }0}}2Al_2O_3\\ 3Fe+2O_2\underrightarrow{t^{^{ }0}}Fe_3O_4\\ m_{oxit}=\dfrac{1}{2}\cdot102a+\dfrac{1}{3}\cdot232b=6,17\left(2\right)\\ \left(1\right)\left(2\right)\Rightarrow a=0,03;b=0,06\\ \Rightarrow n_{O_2}=\dfrac{3}{4}a+\dfrac{2}{3}b=0,0625mol\\ 2KMnO_4\underrightarrow{t^{^{ }0}}K_2MnO_4+MnO_2+O_2\\ n_{KMnO_4}=2n_{O_2}=0,125mol\\ m_{KMnO_4}=0,125\cdot158=19,75g\\ b.\%m_{Al}=\dfrac{0,03\cdot27}{4,17}.100\%=19,42\%\\ \%m_{Fe}=80,58\%\)

a.\(n_{KMnO_4}=\dfrac{m}{M}=\dfrac{31,6}{158}=0,2mol\)

\(PTHH:2KMnO_4\underrightarrow{np}K_2MnO_4+MnO_2+O_2\)

                     2                 1                1          1           ( mol )

                   0,2                                             0,1

\(V_{O_2}=n.22,4=0,1.22,4=2,24l\)

b.\(n_{Fe}=\dfrac{m}{M}=\dfrac{11,2}{56}=0,2mol\) 

\(3Fe+2O_2\underrightarrow{t^o}Fe_3O_4\)

      3         2        1     ( mol )

    0,2      0,1

      0,1    0,1      0,05     ( mol )

\(m_{Fe_3O_4}=n.M=0,05.232=11,6g\)

Có lẽ đề cho "Đốt cháy hoàn toàn 5,4 g Al" bạn nhỉ?

a, PT: \(4Al+3O_2\underrightarrow{t^o}2Al_2O_3\)

Ta có: \(n_{Al}=\dfrac{5,4}{27}=0,2\left(mol\right)\)

Theo PT: \(n_{O_2}=\dfrac{3}{4}n_{Al}=0,15\left(mol\right)\)

\(\Rightarrow V_{O_2}=0,15.22,4=3,36\left(l\right)\)

b, PT: \(2KMnO_4\underrightarrow{t^o}K_2MnO_4+MnO_2+O_2\)

Theo PT: \(n_{KMnO_4}=2n_{O_2}=0,3\left(mol\right)\)

\(\Rightarrow m_{KMnO_4}=0,3.158=47,4\left(g\right)\)

\(n_{Fe}=\dfrac{11.2}{56}=0.2\left(mol\right)\)

\(3Fe+2O_2\underrightarrow{t^0}Fe_3O_4\)

\(0.2.......\dfrac{2}{15}\)

\(V_{O_2}=\dfrac{2}{15}\cdot22.4=2.987\left(l\right)\)

\(2KMnO_4\underrightarrow{t^0}K_2MnO_4+MnO_2+O_2\)

\(\dfrac{4}{15}..............................\dfrac{2}{15}\)

\(m_{KMnO_4}=\dfrac{4}{15}\cdot158=42.13\left(g\right)\)

a) PTHH: 3 Fe + 2 O2 -to-> Fe3O4

b) nFe=0,2(mol) -> nO2= 2/3. 0,2= 2/15 (mol)

=> V(O2,đktc)=22,4. 2/15 \(\approx\) 2,987(l)

c) 2 KMnO4 -to-> K2MnO4 + MnO2  + O2

nKMnO4= 2/15. 2= 4/15(mol)

=>mKMnO4=4/15 x 158 \(\approx\) 42,133(g)

\(n_C=\dfrac{1.2}{12}=0.1\left(mol\right)\\ n_S=\dfrac{4}{32}=0.125\left(mol\right)\)

\(2KMnO_4\underrightarrow{t^0}K_2MnO_4+MnO_2+O_2\)

\(C+O_2\underrightarrow{t^0}CO_2\)

\(S+O_2\underrightarrow{t^0}SO_2\)

\(\sum n_{O_2}=n_C+n_S=0.1+0.125=0.225\left(mol\right)\)

\(\Rightarrow n_{KMnO_4}=2n_{O_2}=0.225\cdot2=0.45\left(mol\right)\)

\(m_{KMnO_4}=0.45\cdot158=71.1\left(g\right)\)

2KMnO4 -to>K2MnO4+O2+MnO2

0,45------------------------0,225

C+O2-to>CO2

0,1--0,1

S+O2-to>SO2

0,125-0,125

n C=1,2\12=0,1 mol

n S=4\32=0,125 mol

=>m KMnO4=0,45.158=77,1g

PTHH: \(4Al+3O_2\xrightarrow[]{t^o}2Al_2O_3\)

           \(2KMnO_4\xrightarrow[]{t^o}K_2MnO_4+MnO_2+O_2\uparrow\)

Ta có: \(n_{Al}=\dfrac{5,4}{27}=0,2\left(mol\right)\) \(\Rightarrow\left\{{}\begin{matrix}n_{O_2}=0,15\left(mol\right)\\n_{KMnO_4}=0,3\left(mol\right)\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}V_{O_2}=0,15\cdot22,4=3,36\left(l\right)\\m_{KMnO_4}=0,3\cdot158=47,4\left(g\right)\end{matrix}\right.\)

con cc

\(n_{Al}=\dfrac{5.4}{27}=0.2\left(mol\right)\)

\(4Al+3O_2\underrightarrow{^{^{t^0}}}2Al_2O_3\)

\(0.2..........0.15\)

\(V_{O_2}=0.15\cdot22.4=3.36\left(l\right)\)

\(2KMnO_4\underrightarrow{^{^{t^0}}}K_2MnO_4+MnO_2+O_2\)

\(0.3...............................................0.15\)

\(m_{KMnO_4}=0.3\cdot158=47.4\left(g\right)\)

a) PTHH: \(4Al+3O_2\xrightarrow[]{t^o}2Al_2O_3\)

Ta có: \(n_{Al}=\dfrac{2,7}{27}=0,1\left(mol\right)\)

\(\Rightarrow n_{O_2}=0,075\left(mol\right)\) \(\Rightarrow V_{O_2}=0,075\cdot22,4=1,68\left(l\right)\)

b) PTHH: \(2KMnO_4\xrightarrow[]{t^o}K_2MnO_4+MnO_2+O_2\uparrow\)

Theo PTHH: \(n_{KMnO_4}=2n_{O_2}=0,15\left(mol\right)\) \(\Rightarrow m_{KMnO_4}=0,15\cdot138=23,7\left(g\right)\)

a,  n_Al = 2,7 : 27 = 0,1 mol

     PTHH :       4Al   +   3O₂   ->   2Al₂O₃

                     0,1mol -->0,075mol

      => \(V_{O_2}\) cần dùng = 0,075 . 22,4 = 1,68 lít            (đktc)

b, PTHH :   2KMnO₄ -> K₂MnO₄ + MnO₂ + O₂

                         _{0,15 mol        <--                               0,075mol}

=> \(m_{KMnO_4}\) cần dùng = 0,15 . ( 39 + 55 + 16 . 4 ) = 23,7 gam

PTHH :

\(2KClO_3\underrightarrow{t^o}2KCl+3O_2\)

    1/3                        0,5

\(2MnO_4\underrightarrow{t^o}K_2MnO_4+MnO_2+O_2\uparrow\)

     1                                           0,5

Vậy khi điều chế cùng lượng O₂ ta dùng KClO₃ lợi hơn vì với 1 mol KClO₃ sẽ cho ra 1,5 mol O2 còn KMnO₄ chỉ cho ra 0,5 mol O2 

\(n_{O_2}=\dfrac{11,2}{22,4}=0,5\left(mol\right)\)

\(m_{KClO_3}=122,5.\dfrac{1}{3}=\dfrac{245}{6}\approx40,8\left(g\right)\)

\(m_{KMnO_4}=158.1=158\left(g\right)\)