Đốt cháy hoàn toàn 39 gam hỗn hợp gồm Al và Fe, người ta phải dùng 12,32 lít khí oxi ở đktc. Hãy tính khối lượng mỗi chất trong hỗn hợp ban đầu và khỗi lượng hỗn hợp hai chất rắn sinh ra sau phản ứng.
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Đặt \(\left\{{}\begin{matrix}n_{Mg}=x\left(mol\right)\\n_{Fe}=y\left(mol\right)\end{matrix}\right.\)
Theo đề: \(m_{hh}=36\left(g\right)\)
\(\Rightarrow m_{Mg}+m_{Fe}=36\\ \Rightarrow24x+56y=36\left(1\right)\)
\(PTHH:2Mg+O_2\underrightarrow{t^o}2MgO\\ \left(mol\right)....x\rightarrow...0,5x.....x\\ PTHH:3Fe+2O_2\underrightarrow{t^o}Fe_3O_4\\ \left(mol\right)....y\rightarrow...\dfrac{2}{3}y....\dfrac{1}{3}y\)
Theo đề: \(n_{O_2}=\dfrac{13,44}{22,4}=0,6\left(mol\right)\)
\(\Rightarrow0,5x+\dfrac{2}{3}y=0,6\left(2\right)\)
\(\xrightarrow[\left(2\right)]{\left(1\right)}\left\{{}\begin{matrix}24x+56y=36\\0,5x+\dfrac{2}{3}y=0,6\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=0,8\\y=0,3\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}m_{Mg}=0,8.24=19,2\left(g\right)\\m_{Fe}=0,3.56=16,8\left(g\right)\end{matrix}\right.\\ m_r=m_{MgO}+m_{Fe_3O_4}=0,8.40+\dfrac{1}{3}.0,3.232=55,2\left(g\right)\)
PTHH: C+O2→CO20,3mol:0,3mol→0,3molC+O2→CO20,3mol:0,3mol→0,3mol
S+O2→SO20,2mol:0,2mol→0,2molS+O2→SO20,2mol:0,2mol→0,2mol
mC=36%10100%=3,6(g)⇔nC=3,612=0,3(mol)mC=36%10100%=3,6(g)⇔nC=3,612=0,3(mol)
mS=10−3,6=6,4(g)⇔nS=6,432=0,2(mol)mS=10−3,6=6,4(g)⇔nS=6,432=0,2(mol)
VO2=(0,3+0,2)22,4=11,2(l)VO2=(0,3+0,2)22,4=11,2(l)
mhh=mCO2+mSO2=0,3.44+0,2.64=26(g)
PTHH: \(C+O_2\xrightarrow[]{t^o}CO_2\)
a___a______a (mol)
\(S+O_2\xrightarrow[]{t^o}SO_2\)
b___b_______b (mol)
Ta lập HPT: \(\left\{{}\begin{matrix}12a+32b=10\\a+b=\dfrac{11,2}{22,4}=0,5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=0,3\\b=0,2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}m_C=0,3\cdot12=3,6\left(g\right)\\m_S=6,4\left(g\right)\\V_{khí}=0,5\cdot22,4=11,2\left(l\right)\end{matrix}\right.\)
a: \(C+O_2\rightarrow CO_2\)(ĐK: t độ)
x x x
\(S+O_2\rightarrow SO_2\)(ĐK: t độ)
y y y
b: \(n_{O_2}=\dfrac{11.2}{22.4}=0.5\left(mol\right)\)
Theo đề, ta có hệ:
12x+32y=10 và x+y=0,5
=>x=0,3 và y=0,2
\(m_C=0.3\cdot12=3.6\left(g\right)\)
\(m_S=0.2\cdot32=6.4\left(g\right)\)
c: \(n_{CO_2}=n_C=0.3\left(mol\right)\)
\(n_{SO_2}=n_S=0.2\left(mol\right)\)
\(V_{khí}=22.4\left(0.3+0.2\right)=11.2\left(lít\right)\)
\(n_{O_2}=\dfrac{11,2}{22,4}=0,5\left(mol\right)\)
PTHH :
\(C+O_2\rightarrow\left(t^o\right)CO_2\)
x x x
\(S+O_2\rightarrow\left(t^o\right)SO_2\)
y y y
Gọi n C = x
n S = y (mol)
Ta có hệ PT :
\(\left\{{}\begin{matrix}12x+32y=10\\x+y=0,5\end{matrix}\right.\)
\(\rightarrow x=0,3;y=0,2\)
\(m_C=0,3.12=3,6\left(g\right)\)
\(m_S=0,2.32=6,4\left(g\right)\)
\(c,V_{hhk}=\left(0,3+0,2\right).22,4=11,2\left(l\right)\)
PTHH: \(2Mg+O_2\underrightarrow{t^o}2MgO\)
\(3Fe+2O_2\underrightarrow{t^o}Fe_3O_4\)
\(n_{O_2}=\frac{13,44}{22,4}=0,6\left(mol\right)\)
Đặt số mol Mg là x, số mol Fe là y, ta có hệ:
\(\left\{\begin{matrix}\frac{1}{2}x+\frac{2}{3}y=0,6\\24x+56y=36\end{matrix}\right.\)
giải pt, ta được x=0,8,y=0,3
\(m_{Mg}=0,8.24=19,2g\)
\(m_{Fe}=0,3.56=16,8g\)
\(n_{MgO}=n_{Mg}=0,8mol\)
\(m_{MgO}=0,8.40=32g\)
\(n_{Fe_3O_4}=\frac{1}{3}.n_{Fe}=\frac{1}{3}.0,3=0,1mol\)
\(m_{Fe_3O_4}=0,1.232=23,2g\)
Khối lượng hh thu đc: 32+23,2=55,2g
\(2Mg\left(x\right)+O_2\left(0,5x\right)\rightarrow2MgO\left(x\right)\)
\(3Fe\left(y\right)+2O_2\left(\frac{2y}{3}\right)\rightarrow Fe_3O_4\left(\frac{y}{3}\right)\)
Gọi số mol của Mg, Fe lần lược là x, y thì ta có
\(24x+56y=36\left(1\right)\)
\(n_{O_2}=\frac{13,44}{22,4}=0,6\)
\(\Rightarrow0,5x+\frac{2y}{3}=0,6\left(2\right)\)
Từ (1) và (2) ta có hệ : \(\left\{\begin{matrix}0,5x+\frac{2y}{3}=0,6\\24x+56y=36\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}x=0,8\\y=0,3\end{matrix}\right.\)
\(\Rightarrow m_{Mg}=0,8.24=19,2\)
\(\Rightarrow m_{Fe}=0,3.56=16,8\)
\(\Rightarrow m_{O_2}=0,6.32=19,2\)
\(\Rightarrow m_{hh}=19,2+36=55,2\)
\(n_{Al} = a ; n_{Fe} = b\Rightarrow 27a + 56b = 27,6(1)\\ 4Al + 3O_2 \xrightarrow{t^o} 2Al_2O_3\\ 3Fe + 2O_2 \xrightarrow{t^o} Fe_3O_4\\ n_{Al_2O_3} = \dfrac{1}{2}n_{Al} = 0,5a(mol)\\ n_{Fe_3O_4} = \dfrac{1}{3}n_{Fe} = \dfrac{b}{3}(mol)\\ \Rightarrow 0,5a.102 + \dfrac{b}{3}232 = 43,6(2)\\ (1)(2) \Rightarrow a = 0,4 ; b = 0,3\\ m_{Al} = 0,4.27 = 10,8(gam) ; m_{Fe} = 0,3.56 = 16,8(gam)\)
a)
\(n_{O_2}=\dfrac{3,36}{22,4}=0,15\left(mol\right)\)
\(n_{H_2O}=\dfrac{1,8}{18}=0,1\left(mol\right)\)
PTHH: 2H2 + O2 --to--> 2H2O
0,1<-0,05<-------0,1
2CO + O2 --to--> 2CO2
0,2<--0,1-------->0,2
=> \(\left\{{}\begin{matrix}V_{H_2}=0,1.22,4=2,24\left(l\right)\\V_{CO}=0,2.22,4=4,48\left(l\right)\end{matrix}\right.\)
b) \(m_{CO_2}=0,2.44=8,8\left(g\right)\)
\(n_{O_2}=\dfrac{3,36}{22,4}=0,15mol\)
\(n_{H_2O}=\dfrac{1,8}{18}=0,1mol\)
\(2CO+O_2\rightarrow2CO_2\)
a 0,5a a
\(2H_2+O_2\rightarrow2H_2O\)
0,1 0,05 \(\leftarrow\) 0,1
\(\Sigma n_{O_2}=0,5a+0,05=0,15\)
\(\Rightarrow a=n_{O_2\left(CO\right)}=0,2mol\)
\(V_{CO}=2\cdot0,2\cdot22,4=8,96l\)
\(V_{H_2}=0,1\cdot22,4=2,24l\)
\(m_{CO_2}=0,2\cdot44=8,8g\)
Gọi số mol Al, Na trong a gam hỗn hợp là x, y (mol)
=> 27x + 23y = a (1)
PTHH: 4Al + 3O2 --to--> 2Al2O3
x---------------->0,5x
4Na + O2 --to--> 2Na2O
y---------------->0,5y
=> 102.0,5x + 62.0,5y = 1,64.a
=> 51x + 31y = 1,64a (2)
(1)(2) => 51x + 31y = 1,64(27x + 23y)
=> 6,72x = 6,72y
=> x = y
\(\left\{{}\begin{matrix}\%m_{Al}=\dfrac{27x}{27x+23y}.100\%=54\%\\\%m_{Na}=\dfrac{23y}{27x+23y}.100\%=46\%\end{matrix}\right.\)
Đặt \(\left\{{}\begin{matrix}n_{Al}=x\left(mol\right)\\n_{Fe}=y\left(mol\right)\end{matrix}\right.\)
Theo đề: \(m_{hh}=39\left(g\right)\)
\(\Rightarrow m_{Al}+m_{Fe}=39\\ \Rightarrow27x+56y=39\left(1\right)\)
\(PTHH:4Al+3O_2\underrightarrow{t^o}2Al_2O_3\\ \left(mol\right)....x\rightarrow..0.75x....0,5x\\ PTHH:3Fe+2O_2\underrightarrow{t^o}Fe_3O_4\\ \left(mol\right)....y\rightarrow..\dfrac{2}{3}y.....\dfrac{1}{3}y\)
Theo đề: \(n_{O_2}=\dfrac{V}{22,4}=\dfrac{12,32}{22,4}=0,55\left(mol\right)\)
\(\Rightarrow0,75x+\dfrac{2}{3}y=0,55\left(2\right)\)
\(\xrightarrow[\left(1\right)]{\left(2\right)}\left\{{}\begin{matrix}27x+56y=39\\0,75x+\dfrac{2}{3}y=0,55\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=0,2\\y=0,6\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}m_{Al}=0,2.27=5,4\left(g\right)\\m_{Fe}=0,6.56=33,6\left(g\right)\end{matrix}\right.\\ m_r=m_{Al_2O_3}+m_{Fe_3O_4}=0,5.0,2.102+\dfrac{1}{3}.0,6.232=56,6\left(g\right)\)