\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)

diluted solution ?:  w_dil = 50 weight % = 50g product/100g solution
                      make = 1000ml from this solution
------------------------------------------------------------------
product = H(2)SO4 'acid sulfuric' MW=(S)32+4*16(O)+2*H(1)    = 98g
                                (M)olecular(W)eight H(2)SO4 = 98g
product = H(2)O   ' aqua        ' MW=(H)2*1+1*16(O)          = 18g
------------------------------------------------------------------
solution  = soln

peter.vlasschaert@gmail,03/11/2016,version 1.0

Products : labo flask 1 : 'acid sulfuric' ,rho_acid =density = 1,84g/ml, w_acid = 96% weight
               flask 2 : ' aqua        ' ,rho_aq   =density = 1,00g/ml,

How to find  (y) ml flask 1 , (make - y) ml flask 2  ? find y

info : rho_* w_ * y = (g product/ml)*(g product/100g soln)*y

(%i1) kill(all);
\[\tag{\%{}o0}\label{o0} \mathit{done}\]
(%i1) p1 : rho_acid*w_acid * y = (rho_acid*y+rho_aq*(make-y))*w_dil;
\[\tag{p1}\label{p1}\mathit{rho\_ acid}{{w}_{\mathit{acid}}}y={{w}_{\mathit{dil}}}\left( \mathit{rho\_ acid}y+\mathit{rho\_ aq}\left( \mathit{make}-y\right) \right) \]
(%i2) p2:solve(p1,y);
\[\tag{p2}\label{p2}[y=\frac{\mathit{make}\,\mathit{rho\_ aq}{{w}_{\mathit{dil}}}}{\left( \mathit{rho\_ aq}-\mathit{rho\_ acid}\right) {{w}_{\mathit{dil}}}+\mathit{rho\_ acid}{{w}_{\mathit{acid}}}}]\]
(%i3) p3:part(p2,1);
\[\tag{p3}\label{p3}y=\frac{\mathit{make}\,\mathit{rho\_ aq}{{w}_{\mathit{dil}}}}{\left( \mathit{rho\_ aq}-\mathit{rho\_ acid}\right) {{w}_{\mathit{dil}}}+\mathit{rho\_ acid}{{w}_{\mathit{acid}}}}\]
(%i4) p4:ev(p3,make=1000);
\[\tag{p4}\label{p4}y=\frac{1000\mathit{rho\_ aq}{{w}_{\mathit{dil}}}}{\left( \mathit{rho\_ aq}-\mathit{rho\_ acid}\right) {{w}_{\mathit{dil}}}+\mathit{rho\_ acid}{{w}_{\mathit{acid}}}}\]
(%i8) p5:rho_acid = 1.84;
p6:rho_aq   = 1;
p7:w_acid   = 0.96;
p8:w_dil    = 0.5;
\[\tag{p5}\label{p5}\mathit{rho\_ acid}=1.84\] \[\tag{p6}\label{p6}\mathit{rho\_ aq}=1\] \[\tag{p7}\label{p7}{{w}_{\mathit{acid}}}=0.96\] \[\tag{p8}\label{p8}{{w}_{\mathit{dil}}}=0.5\]
(%i12) p9:ev(p4,p5,p6,p7,p8);
\[\tag{p9}\label{p9}y=371.3606654783125\]
(%i15) p10:y_aq=ev(make - part(p9,2),make = 1000);
\[\tag{p10}\label{p10}{{y}_{\mathit{aq}}}=628.6393345216875\]

We get diluted soln 50 wt% ,take y ml =371.4ml flask 1 and
put other flask and take y_aq from flask 2 ⇒ total volume = make = 1000

(%i16) p11:vol_tot = ev(y+y_aq,p9,p10);
\[\tag{p11}\label{p11}\mathit{vol\_ tot}=1000.0\]
Created with wxMaxima.