Áp dụng sơ đồ đường chéo ta có:

Do đó: \(\dfrac{V_{ddA}}{V_{ddB}}=\dfrac{3-C_{M_B}}{C_{M_A}-3}\)

mà \(\dfrac{V_{ddA}}{V_{ddB}}=\dfrac{3}{5}\left(gt\right)\)

nên \(\dfrac{3-C_{M_B}}{C_{M_A}-3}=\dfrac{3}{5}\left(1\right)\)

Lại có: \(C_{M_A}=2.C_{M_B}\left(gt\right)\left(2\right)\)

Suy ra: \(\left(1\right)\Leftrightarrow\dfrac{3-C_{M_B}}{2.C_{M_B}-3}=\dfrac{3}{5}\)

\(\Leftrightarrow5\left(3-C_{M_B}\right)=3\left(2.C_{M_B}-3\right)\)

\(\Leftrightarrow15-5.C_{M_B}=6.C_{M_B}-9\)

\(\Leftrightarrow-5.C_{M_B}-6.C_{M_B}=-9-15\)

\(\Leftrightarrow-11.C_{M_B}=-24\)

\(\Leftrightarrow C_{M_B}=\dfrac{-24}{-11}\approx2,18\left(M\right)\)

Từ (2) \(\Rightarrow C_{M_A}\approx2.2,18\approx4,36\left(M\right)\)

Gọi nồng độ mol của dung dịch B là \(x\left(mol\right)\)

=> Nồng độ mol của dung dịch A là \(2x\left(mol\right)\)

Áp dụng qui tắc đường chéo ta có

\(2x\)----->3

___3___

\(x\)------>5

=> \(2x=5-3=2\)

=> \(x=1\)

=> Nồng độ mol của dung dịch A là 2M

Nồng độ mol của dung dịch B là 1M

Gọi \(\left\{{}\begin{matrix}C\%\left(A\right)=a\%\\C\%\left(B\right)=2a\%\end{matrix}\right.\)

Giả sử trộn 600 gam dd A với 400 gam dd B:

\(m_{H_2SO_4\left(A\right)}=\dfrac{600a}{100}=6a\left(g\right)\)

\(m_{H_2SO_4\left(B\right)}=\dfrac{400.2a}{100}=8a\left(g\right)\)

=> \(C\%=\dfrac{6a+8a}{600+400}.100\%=20\%\)

=> a = 14,2857

=> \(\left\{{}\begin{matrix}C\%\left(A\right)=14,2857\%\\C\%\left(B\right)=28,5714\%\end{matrix}\right.\)
 

1, \(n_{NaOH}=0,3.1+1,5.0,2=0,6\left(mol\right)\)

\(V_{NaOH}=0,2+0,3=0,5\left(l\right)\)

\(\rightarrow\left\{{}\begin{matrix}C_{MNaOH}=\dfrac{0,6}{0,5}=1,2M\\C\%=1,2.\dfrac{40}{10.1,05}=4,57\%\end{matrix}\right.\)

2, \(m_{H_2SO_4}=200.9,8\%=19,6\left(g\right)\\ m_{ddH_2SO_4\left(39,2\%\right)}=\dfrac{19,6}{39,2\%}=50\left(g\right)\\ \rightarrow m_{H_2O\left(thêm\right)}=200-50=150\left(g\right)\)

Cách pha: ta cân lấy 50 g ddH₂SO₄ 39,2% và 150 g H₂O, rót nước vào bình ống nghiệm rồi từ từ rót ddH₂SO₄ vào rồi khuấy đều 

a,nA=\(\dfrac{18,25}{36,5}\)=0,5(mol)

nB=\(\dfrac{10,95}{36,5}\)=0,3(mol)

→nC=0,3+0,5=0,8(mol)

→CM(C)=\(\dfrac{0,8}{2}\)=0,4M

b,CM(A)=\(\dfrac{0,5}{V1}\)

CM(B)=\(\dfrac{0,3}{V2}\)

→\(\dfrac{0,5}{V1}\)=\(\dfrac{0,3}{V2}\)=0,8

=>V1=0,625  l

=>V2=0,375 l 

=>CmV1=\(\dfrac{0,5}{0,625}\)=0,8M

=>CmV2=\(\dfrac{0,3}{0,375}\)=0,8M

\(a,n_A=\dfrac{18,25}{36,5}=0,5\left(mol\right)\\ n_B=\dfrac{10,95}{36,5}=0,3\left(mol\right)\)

\(\rightarrow n_C=0,3+0,5=0,8\left(mol\right)\\ \rightarrow C_{M\left(C\right)}=\dfrac{0,8}{2}=0,4M\)

\(b,C_{M\left(A\right)}=\dfrac{0,5}{V_1}\\ C_{M\left(B\right)}=\dfrac{0,3}{V_2}\\ \rightarrow\dfrac{0,5}{V_1}:\dfrac{0,3}{V_2}=0,8\\ \rightarrow\dfrac{0,5}{V_1}=\dfrac{0,24}{V_2}=\dfrac{0,5+0,24}{V_1+V_2}=\dfrac{0,74}{2}=0,37\\ \rightarrow\left\{{}\begin{matrix}V_1=\dfrac{0,5}{0,34}=1,4\left(l\right)\\V_2=\dfrac{0,24}{0,34}=0.6\left(l\right)\end{matrix}\right.\\ \rightarrow\left\{{}\begin{matrix}C_{M\left(A\right)}=\dfrac{0,5}{1,4}=0,36M\\C_{M\left(B\right)}=\dfrac{0,5}{0,6}=0,83M\end{matrix}\right.\)

a, \(n_{OH^-}=10^{-1}.V_A\left(mol\right)\)

\(n_{H^+}=10^{-2}.V_B\left(mol\right)\)

\(n_{OH^-dư}=10^{-2}.\left(V_A+V_B\right)\left(mol\right)\)

Ta có: \(n_{OH^-}-n_{OH^-dư}=n_{H^+}\)

\(\Leftrightarrow10^{-1}.V_A-10^{-2}.\left(V_A+V_B\right)=10^{-2}.V_B\)

\(\Leftrightarrow0,09V_A=0,02V_B\)

\(\Rightarrow\dfrac{V_A}{V_B}=\dfrac{2}{9}\)

b, Ta có: \(\left\{{}\begin{matrix}V_A+V_B=0,55\\\dfrac{V_A}{V_B}=\dfrac{2}{9}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}V_A=0,1\left(l\right)\\V_B=0,45\left(l\right)\end{matrix}\right.\)

\(n_{BaCl_2}=\dfrac{1}{2}n_{Cl^-}=\dfrac{1}{2}n_{H^+}=\dfrac{1}{2}.10^{-2}.0,1=0,0005\left(mol\right)\Rightarrow m_{BaCl_2}=0,104\left(g\right)\)

\(n_{Ba\left(OH\right)_2}=\dfrac{1}{2}n_{OH^-dư}=\dfrac{1}{2}.10^{-2}.0,55=0,00275\left(mol\right)\Rightarrow m_{Ba\left(OH\right)_2}=0,047025\left(g\right)\)

\(\Rightarrow\%m_{Ba\left(OH\right)_2}=\dfrac{0,047025}{0,047025+0,104}.100\%=31,14\%\)

\(\Rightarrow\%m_{BaCl_2}=62,86\%\)