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PTHH: Al2O3+6HCl➝2AlCl3+3H2O(1)
a)nAl2O3=\(\dfrac{10,2}{102}\)=0,1(mol)
mHCl=\(\dfrac{5\%.219}{100\%}\)=10,95(g)
⇒nHCl=\(\dfrac{10,95}{36,5}\)=0,3(mol)
Xét tỉ lệ Al2O3:\(\dfrac{0,1}{1}\)=0,1
Xét tỉ lệ HCl:\(\dfrac{0,3}{6}\)=0,05
⇒HCl pứng hết,Al2O3 còn dư
Theo PTHH(1) ta có nAl2O3 pứng=\(\dfrac{nHCl}{6}\)=\(\dfrac{0,3}{6}\)=0,05(mol)
⇒nAl2O3 dư=nAl2O3ban đầu-nAl2O3 pứng=0,1-0,05=0,05(mol)
⇒mAl2O3 dư=0,05.102=5,1(g)
b) C%HCl=\(\dfrac{0,3.36,5}{219+10,2}\).100%=4,8%
nAlCl3=0,1(mol)
⇒C%AlCl3=\(\dfrac{0,1.136,5}{10,2+219}\).100%=6%
Bài 4 :
\(n_{H2}=\dfrac{V_{H2}}{22,4}=\dfrac{3,36}{22,4}=0,15\left(mol\right)\)
Pt : \(2Al+3H_2SO_4\rightarrow Al_2\left(SO_4\right)_3+3H_2|\)
2 3 1 3
0,1 0,15 0,05 0,15
a) \(n_{Al}=\dfrac{0,15.2}{3}=0,1\left(mol\right)\)
⇒ \(m_{Al}=n_{Al}.M_{Al}\)
= 0,1 . 27
= 2,7 (g)
\(m_{Cu}=10-2,7=7,3\left(g\right)\)
0/0Al = \(\dfrac{m_{Al}.100}{m_{hh}}=\dfrac{2,7.100}{10}=27\)0/0
0/0Cu = \(\dfrac{m_{Cu}.100}{m_{hh}}=\dfrac{7,3.100}{10}=13\)0/0
b) \(n_{Al2\left(SO4\right)3}=\dfrac{0,15.1}{3}=0,05\left(mol\right)\)
⇒ \(m_{Al2\left(SO4\right)3}=n_{Al2\left(SO4\right)3.}M_{Al2\left(SO4\right)3}\)
= 0,05 . 342
= 17,1 (g)
\(n_{H2SO4}=\dfrac{0,1.3}{2}=0,15\left(mol\right)\)
⇒ \(m_{H2SO4}=n_{H2SO4}.M_{H2SO4}\)
= 0,15 .98
= 14,7 (g)
\(C_{H2SO4}=\dfrac{m_{ct}.100}{m_{dd}}\Rightarrow m_{dd}=\dfrac{m_{ct}.100}{C}=\)\(\dfrac{14,7.100}{15}=98\left(g\right)\)
mdung dịch sau phản ứng = (mAl + mCu) + mH2SO4 - mH2
= 10 + 98 - (0,15 . 2)
=107,7 (g)
\(C_{Al2\left(SO4\right)3}=\dfrac{m_{ct}.100}{m_{dd}}=\dfrac{17,1.100}{107,7}=15,88\)0/0
Chúc bạn học tốt
Bài 1:
a: \(\sqrt{\left(\sqrt3-1\right)^2}\cdot\sqrt3=\sqrt3\left(\sqrt3-1\right)=3-\sqrt3\)
b: \(\sqrt{6+2\sqrt5}-\sqrt{6-2\sqrt5}\)
\(=\sqrt{\left(\sqrt5+1\right)^2}-\sqrt{\left(\sqrt5-1\right)^2}\)
\(=\sqrt5+1-\left(\sqrt5-1\right)=\sqrt5+1-\sqrt5+1=1+1=2\)
c: \(\sqrt{\left(2-\sqrt3\right)^2}+\sqrt{\left(1-\sqrt3\right)^2}\)
\(=2-\sqrt3+\left|1-\sqrt3\right|\)
\(=2-\sqrt3+\sqrt3-1=2-1=1\)
d: \(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\)
\(=\sqrt{9^2-17}\)
\(=\sqrt{81-17}=\sqrt{64}=8\)
Bài 2:
a: ĐKXĐ: x<=4/5
\(\sqrt{4-5x}=12\)
=>\(4-5x=12^2=144\)
=>5x=4-144=-140
=>x=-28(nhận)
b: \(\sqrt{4\left(1-x\right)^2}-6=0\)
=>\(2\cdot\left|x-1\right|-6=0\)
=>2|x-1|=6
=>|x-1|=3
=>\(\left[\begin{array}{l}x-1=3\\ x-1=-3\end{array}\right.\Longrightarrow\left[\begin{array}{l}x=4\\ x=-2\end{array}\right.\)
c: \(\sqrt{4x^2+4x+1}=6\)
=>\(\sqrt{\left(2x+1\right)^2}=6\)
=>|2x+1|=6
=>\(\left[\begin{array}{l}2x+1=6\\ 2x+1=-6\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=5\\ 2x=-7\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac52\\ x=-\frac72\end{array}\right.\)
Bài 3:
Xét ΔABC vuông tại A có AH là đường cao
nên \(AH^2=HB\cdot HC\)
=>\(HC=\frac{3^2}{2}=4,5\left(\operatorname{cm}\right)\)
BC=BH+CH=2+4,5=6,5(cm)
Xét ΔABC vuông tại A có AH là đường cao
nên \(AB^2=BH\cdot BC=2\cdot6,5=13\)
=>\(AB=\sqrt{13}\) (cm)
Xét ΔABC vuông tại A có AH là đường cao
nên \(CA^2=CH\cdot CB=4,5\cdot6,5=\frac92\cdot\frac{13}{2}=\frac{117}{4}\)
=>\(CA=\sqrt{\frac{117}{4}}=\frac{3\sqrt{13}}{2}\left(\operatorname{cm}\right)\)
khi cho Natri vào cốc nước
mẩu Natri mặt xung quanh bề mặt nước , có khí thoát ra , mẩu Natri tan dần
pthh : 2Na + 2H2O -> 2NaOH + H2
PTHH: \(Al_2O_3+3H_2SO_4\rightarrow Al_2\left(SO_4\right)_3+3H_2O\)
Ta có: \(\left\{{}\begin{matrix}m_{H_2SO_4}=588\cdot5\%=29,4\left(g\right)\Rightarrow n_{H_2SO_4}=\dfrac{29,4}{98}=0,3\left(mol\right)\\n_{Al_2O_3}=\dfrac{20,4}{102}=0,2\left(mol\right)\end{matrix}\right.\)
Xét tỉ lệ: \(\dfrac{0,2}{1}>\dfrac{0,3}{3}\) \(\Rightarrow\) Al2O3 còn dư
\(\Rightarrow n_{Al_2\left(SO_4\right)_3}=0,1\left(mol\right)=n_{Al_2O_3\left(dư\right)}\)
\(\Rightarrow C\%_{Al_2\left(SO_4\right)_3}=\dfrac{0,1\cdot342}{20,4+588-0,1\cdot102}\cdot100\%\approx5,72\%\)
a: \(x^4+2x^2-3\)
\(=x^4+3x^2-x^2-3\)
\(=x^2\left(x^2+3\right)-\left(x^2+3\right)=\left(x^2+3\right)\left(x^2-1\right)=\left(x^2+3\right)\left(x-1\right)\left(x+1\right)\)
b: \(\left(2x+1\right)^4-3\left(2x+1\right)^2+2\)
\(=\left(2x+1\right)^4-\left(2x+1\right)^2-2\left(2x+1\right)^2+2\)
\(=\left\lbrack\left(2x+1\right)^2-1\right\rbrack\left\lbrack\left(2x+1\right)^2-2\right\rbrack\)
\(=\left(2x+1+1\right)\left(2x+1-1\right)\left(4x^2+4x+1-2\right)\)
\(=2x\left(2x+2\right)\left(4x^2+4x-1\right)=4x\left(x+1\right)\left(4x^2+4x-1\right)\)
c: x(x+1)(x+2)(x+3)-24
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)-24\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)-24\)
\(=\left(x^2+3x+6\right)\left(x^2+3x-4\right)=\left(x^2+3x+6\right)\left(x+4\right)\left(x-1\right)\)
d: (x+1)(x+2)(x+4)(x+5)-4
\(=\left(x^2+6x+5\right)\left(x^2+6x+8\right)-4\)
\(=\left(x^2+6x+5\right)^2+3\left(x^2+6x+5\right)-4\)
\(=\left(x^2+6x+5+4\right)\left(x^2+6x+5-1\right)=\left(x^2+6x+9\right)\left(x^2+6x+4\right)\)
\(=\left(x+3\right)^2\cdot\left(x^2+6x+4\right)\)