Ta có:  V A : V B  = 2:3

Số mol  H 2 S O 4  có trong 2V (l) dung dịch A:

n H 2 S O 4  =  C M . V A  = 0,2 . 2V = 0,4V (mol)

Số mol  H 2 S O 4  có trong 3V (l) dung dịch B:

n H 2 S O 4  =  C M . V B   = 0,5 . 3V = 1,5V (mol)

Nồng độ mol của dung dịch  H 2 S O 4  sau khi pha trộn:

Vậy nồng độ mol của dung dịch C là 0,38M.

a) 

Coi V A = 2(lít) => V B = 3(lít)

Trong dung dịch C, ta có :

V C = V A + V B = 2 + 3 = 5(lít)

n H2SO4 = n H2SO4(trong A) + n H2SO4(trong B) = 2.0,2 + 3.0,5 = 1,9(mol)

Suy ra :

CM H2SO4 = 1,9/5 = 0,38M

b)

Sau khi trộn :

V C =  V A + V B

n H2SO4 = 0,2V A + 0,5V B

Suy ra : 

CM H2SO4 = (0,2V A + 0,5V B)/(V A + V B ) = 0,3

<=> 0,2V A + 0,5V B = 0,3V A + 0,3V B

<=> 0,1V A = 0,2V B

<=> V A / V B = 0,2/0,1 = 2 / 1

Vậy phải trộn A và B theo tỉ lệ 2 : 1 về thể tích

\(GS:\)

\(V_A=2\left(l\right),V_B=3\left(l\right)\)

\(n_{H_2SO_4\left(1\right)}=0.2\cdot2=0.4\left(mol\right)\)

\(n_{H_2SO_4\left(2\right)}=0.5\cdot3=1.5\left(mol\right)\)

\(C_{M_{H_2SO_4}}=\dfrac{0.4+1.5}{2+3}=0.38\left(M\right)\)

\(b.\)

\(V_{H_2SO_4\left(1\right)}=a\left(l\right)\)

\(V_{H_2SO_4\left(2\right)}=b\left(l\right)\)

\(C_{M_{H_2SO_4}}=\dfrac{0.2a+0.5b}{a+b}=0.3\left(M\right)\)

\(\Leftrightarrow0.2a+0.5b-0.3a-0.3b=0\)

\(\Leftrightarrow0.2b=0.1a\)

\(\Leftrightarrow\dfrac{a}{b}=\dfrac{0.2}{0.1}=2\)

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

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

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

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

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

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