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\(a,V_{C_2H_5OH}=\dfrac{10.96}{100}=9,6\left(ml\right)\\ m_{C_2H_5OH}=9,6.0,8=7,68\left(g\right)\\ n_{C_2H_5OH}=\dfrac{7,68}{46}=\dfrac{96}{575}\left(mol\right)\)
PTHH: 2C2H5OH + 2Na ---> 2C2H5ONa + H2
\(\dfrac{96}{575}\)------------------------------------->\(\dfrac{48}{575}\)
\(V_{H_2}=\dfrac{48}{575}.22,4=1,87\left(l\right)\)
\(b,V_{dd}=12+10,6=20,6\left(ml\right)\\ Đ_r=\dfrac{9,6}{20,6}.100=46,6^o\)
Gọi \(\left\{{}\begin{matrix}n_{C_2H_5OH}=a\left(mol\right)\\n_{H_2O}=b\left(mol\right)\end{matrix}\right.\)
\(n_{H_2}=\dfrac{5,6}{22,4}=0,25\left(mol\right)\)
PTHH:
2C2H5OH + 2Na ---> 2C2H5ONa + H2
a --------------------------------------------> 0,5a
2H2O + 2Na ---> 2NaOH + H2
b --------------------------------> 0,5b
Hệ pt \(\left\{{}\begin{matrix}46a+18b=20,2\\0,5a+0,5b=0,25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=0,4\left(mol\right)\\b=0,1\left(mol\right)\end{matrix}\right.\)
\(\rightarrow\left\{{}\begin{matrix}m_{C_2H_5OH}=0,4.46=18,4\left(g\right)\\m_{H_2O}=0,1.18=1,8\left(g\right)\end{matrix}\right.\rightarrow\left\{{}\begin{matrix}V_{C_2H_5OH}=\dfrac{18,4}{0,8}=23\left(ml\right)\\V_{H_2O}=\dfrac{1,8}{1}=1,8\left(ml\right)\end{matrix}\right.\)
=> Độ rượu là: \(\dfrac{23}{23+1,8}=92,74^o\)
\(V_{C_2H_5OH\left(\text{nguyên chất}\right)}=16.71,875\%=11,5\left(ml\right)\\ \rightarrow m_{C_2H_5OH\left(\text{nguyên chất}\right)}=11,5.0,8=9,2\left(g\right)\\ \rightarrow n_{C_2H_5OH\left(\text{nguyên chất}\right)}=\dfrac{9,2}{46}=0,2\left(mol\right)\)
PTHH: 2C2H5OH + 2K ---> 2C2H5OK + H2
0,2 0,1
=> VH2 = 0,1.22,4 = 2,24 (l)
nH2 = 85,12 : 22,4 = 3,8 (mol) ; nH2O = VH2O.D = 108 (g) => nH2O = 108/18 = 6 (mol)
PTHH:
2Na + 2C2H5OH → 2C2H5ONa + H2↑
x → 0,5x (mol)
2Na + 2H2O → 2NaOH + H2↑
6 → 3 (mol)
Ta có: nH2 = 0,5x + 3 = 3,8
=> x = 1,6 (mol) = nC2H5OH
mC2H5OH = 1,6.46 = 73,6 (g)
Vì dd rượu gồm rượu etylic và nước nên ta gọi :
\(\left\{{}\begin{matrix}n\left(nước\right)=x\\n\left(rượu-etylic\right)=x\end{matrix}\right.\left(mol\right)\)
PTHH :
2Na + 2H2O - > 2NaOH + H2\(\uparrow\) (1)
..........xmol.........................1/2xmol
2Na + 2C2H5OH - > 2C2H5ONa + H2\(\uparrow\) (2)
............ymol......................................1/2ymol
Ta có HPT : \(\left\{{}\begin{matrix}18x+46y=10,1\\\dfrac{1}{2}x+\dfrac{1}{2}y=0,125\end{matrix}\right.\) => x = 0,05 ; y = 0,2
Ta có :
V(rượu nguyên chất) = \(\dfrac{m}{D}=\dfrac{0,2.46}{0,8}=11,5\left(ml\right)\)
V(nước) = \(\dfrac{m}{D}=\dfrac{10,1-9,2}{1}=0,9\left(ml\right)\)
=> V(dd rượu) = V(nước) + V(rượu nguyên chất) = 0,9 + 11,5
=> độ rượu = \(\dfrac{V\left(rượu-nguyên-chất\right)}{Vdd\left(rượu\right)}.100=\dfrac{11,5}{12,4}.100\approx92,74^o\)