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

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

0,2                 0,1              0,1        0,1

a)\(V_{O_2}=0,1\cdot22,4=2,24l\)

b)\(m_{CRắn}=m_{K_2MnO_4}+m_{MnO_2}=0,1\cdot197+0,1\cdot87=28,4g\)

c)\(n_{CH_4}=\dfrac{11,2}{22,4}=0,5mol\)

\(CH_4+2O_2\underrightarrow{t^o}CO_2+2H_2O\)

0,5        0,1    0              0

0,05      0,1    0,05         0,1

0,45       0      0,05         0,1

\(V_{CO_2}=0,05\cdot22,4=1,12l\)

\(m_{H_2O}=0,1\cdot18=1,8g\)

PTHH: 2KMnO4--t^o-> K2MnO4+MnO2+O2

              0,2----------------0,1---------0,1-----0,1

b, n_KMnO4= \(\dfrac{31,6}{158}\)=0,2 mol

Theo pt: n_O2=\(\dfrac{1}{2}\).0,2=0,1 mol

=> V_O2= 0,1.22,4= 2,24 l

=>m cr=0,1.197+0,1.87=28,4g

CH4+2O2-to>CO2+2H2O

            0,5-----0,25-----0,5

n CH4=\(\dfrac{11,2}{22,4}\)=0,5 mol

=>Oxi du

=>V CO2=0,25.22,4=5,6l

=>m H2O=0,5.18=9g

n_CaCO3 = \(\dfrac{15}{100}=0,15\left(mol\right)\)

PTHH: CaCO3 -> CaO + CO2

PT:          1              1            1   (mol)

ĐB:          0,15       0,15       0,15 (mol)

m_CaO = 0,15.56 = 8,4 (g)

V_CO2  = 0,15.22,4 = 3,36(l)

\(1.a.CaCO_3.t^o\rightarrow CaO+CO_2\\ b.m_{CaCO_3}=m_{CaO}+m_{CO_2}\\ \Rightarrow m_{CO_2}=m_{CaCO_3}-m_{CaO}=20-11,2=8,8\left(g\right)\)

CaCO₃-to>CaO+CO₂

3-----------------3------3 mol

n _CaO=\(\dfrac{168}{56}\)=3 mol

=>m _CaCO3=3.100=300g

=>V_CO2=3.22,4=67,2g

\(m_{CaCO_3}=90\%.400=360\left(g\right)\\ \rightarrow n_{CaCO_3}=\dfrac{360}{100}=3,6\left(mol\right)\)

PTHH: CaCO₃ --t^o--> CaO + CO₂

             3,6 ----------> 3,6 -----> 3,6

\(\rightarrow n_{CaO}=3,6.75\%=2,7\left(mol\right)\\ \rightarrow n_{CaCO_3\left(chưa.pư\right)}=3,6-2,7=0,9\left(mol\right)\)

\(\rightarrow m_X=0,9.100+2,7.56=241,2\left(g\right)\\ \%m_{CaO}=\dfrac{0,9.100}{241,2}=37,31\%\)

\(V_Y=V_{CO_2}=3,6.75\%.22,4=60,48\left(l\right)\)

\(m_{CaCO_3}=\dfrac{400\cdot90\%}{100\%}=360g\Rightarrow n_{CaCO_3}=\dfrac{360}{100}=3,6mol\)

\(CaCO_3\underrightarrow{t^o}CaO+CO_2\)

3,6           3,6       3,6

Thực tế: \(n_{CaO}=3,6\cdot75\%=2,7mol\)

\(\Rightarrow m_{CaO}=2,7\cdot56=151,2g\)

a) \(n_{CaCO_3\left(bđ\right)}=\dfrac{400.90\%}{100}=3,6\left(mol\right)\)

=> \(n_{CaCO_3\left(pư\right)}=\dfrac{3,6.75}{100}=2,7\left(mol\right)\)

PTHH: CaCO₃ --t^o--> CaO + CO₂

              2,7---------->2,7---->2,7

=> m_X = m_{đá vôi} - m_CO2 = 400 - 2,7.44 = 281,2 (g)

b) 

m_CaO = 2,7.56 = 151,2 (g)

=> \(\%CaO=\dfrac{151,2}{281,2}.100\%=53,77\%\)

V_CO2 = 2,7.22,4 = 60,48 (l)

\(m_{CaCO_3}=400\cdot90\%=360\left(g\right)\)

\(m_{trơ}=400-360=40\left(g\right)\)

\(n_{CaCO_3}=\dfrac{360}{100}=3.6\left(mol\right)\)

\(a.\)

\(n_{CaCO_3\left(pư\right)}=3.6\cdot75\%=2.7\left(mol\right)\)

\(CaCO_3\underrightarrow{^{^{t^0}}}CaO+CO_2\)

\(2.7........2.7...........2.7\)

\(m_X=m_{CaO}+m_{CaCO_3\left(dư\right)}+m_{trơ}=2.7\cdot56+\left(3.6-2.7\right)\cdot100+40=281.2\left(g\right)\)

\(b.\)

\(\%CaO=\dfrac{2.7\cdot56}{281.2}\cdot100\%=53.77\%\)

\(V_{CO_2}=2.7\cdot22.4=60.48\left(l\right)\)

$n_{Kali} = \dfrac{21,65.36,03\%}{39} = 0,2(mol)$

Gọi $n_{KMnO_4} = a ; n_{KClO_3} = b$
$2KMnO_4 \xrightarrow{t^o} K_2MnO_4 + MnO_2 + O_2$
$2KClO_3 \xrightarrow{t^o} 2KCl + 3O_2$

Bảo toàn Kali : $a + b = 0,2$

$n_{O_2} = 0,5a + 1,5b(mol)$
Bảo toàn khối lượng : $158a + 122,5b = 21,65 + (0,5a + 1,5b).32$

Suy ra:  a = b = 0,1

$n_{O_2} = 0,5a + 1,5b = 0,2(mol)$
$V_{O_2} = 0,2.22,4 = 4,48(lít)$

\(Đặt:m_{Al_2O_3}=g\left(g\right)\Rightarrow m_{CaCO_3}+m_{MgCO_3}=8g\left(g\right)\\ PTHH:CaCO_3\rightarrow\left(t^o\right)CaO+CO_2\\ MgCO_3\rightarrow\left(t^o\right)CO_2+MgO\\ Đặt:n_{CaCO_3}=a\left(mol\right);n_{MgCO_3}=b\left(mol\right)\left(a,b>0\right)\\ \Rightarrow\left\{{}\begin{matrix}100a+84b=8g\\56a+40b+g=60\%.9g=5,4g\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{31}{440}g\\b=\dfrac{1}{88}g\end{matrix}\right.\\ \Rightarrow\%m_{Al_2O_3}=\dfrac{g}{9g}.100\%=11,111\%\)

\(\%m_{MgCO_3}=\dfrac{\dfrac{1}{88}g.84}{9g}.100\%\approx10,606\%\\ \%m_{CaCO_3}=\dfrac{\dfrac{31}{440}g.100}{9g}.100\approx78,283\%\)

\(b,\%m_{\dfrac{Al_2O_3}{A}}=\dfrac{g}{\dfrac{1}{88}.40g+\dfrac{31}{440}.56g+g}.100\approx18,5185\%\\ \%m_{\dfrac{MgO}{A}}=\dfrac{\dfrac{1}{88}.40g}{\dfrac{1}{88}.40g+\dfrac{31}{440}.56g+g}.100\approx8,4175\%\\ \Rightarrow m_{Al_2O_3}=18,5185\%.2=0,37037\left(g\right)\Rightarrow n_{Al_2O_3}=\dfrac{0,37037}{102}\left(mol\right)\\ m_{MgO}=8,4175\%.2=0,16835\left(g\right)\\ \Rightarrow n_{MgO}=\dfrac{0,16835}{40}\left(mol\right)\\ m_{CaO}=2-\left(0,37037+0,16835\right)=1,46128\left(g\right)\\ \Rightarrow n_{CaO}=\dfrac{1,46128}{56}\left(mol\right)\)

\(PTHH:Al_2O_3+6HCl\rightarrow2AlCl_3+3H_2O\\ CaO+2HCl\rightarrow CaCl_2+H_2O\\ MgO+2HCl\rightarrow MgCl_2+H_2O\\ n_{HCl}=2.\left(\dfrac{1,46128}{56}+\dfrac{0,16835}{40}\right)+6.\dfrac{0,37037}{102}\approx0,0824\left(mol\right)\\ \Rightarrow V_{ddHCl}\approx\dfrac{0,0824}{0,5}\approx0,1648\left(lít\right)\approx164,8\left(ml\right)\)