Calculate the molarity and molality of a solution made by mixing equal volumes of 30% by weight of H2SO4 (density = 1 218 g/ml) and 70% by weight of H2SO4 (density = 1 610 g/ml)

Assume y ml of each solution, a and b, are mixed

Calculate mass of solution using formula,  mass = density(d)  × Volume (V)

Mass of solution a, ma =  1.218  × y  = 1.218y
Mass  H2SO4, msolute a = 30% or 30×1.218y100 
msolute a =  0.3654y g 
Moles H2SO4, nsolute a  = 0;3654y98or 0.003729y mol   (Using formula, moles =  mass, m /Molar mass) 
Mass of water, msolvent a = mA- msolute a 
msolvent a  = 1.281y – 0.3654y 
msolvent a= = 0.8526y  g  or  0.8526 X 10-3y  kg
 
Similarly for solution B
 mb = 1.610y  g   
msolute b = 70×1.610y100or 1.127y  g 

 nsolute b  =   1.127y98 or 11.5y mol
 msolvent b  = 1.610y – 1.127y = 0.483y g  or  0.483 × 10-3y kg
 
When y ml of each solution is mixed
Total volume, V = y + y = 2y ml or  2y × 10-3 L
Total moles of H2SO4, nsolute  = nsolute a   + nsolute b
 nsolute=   0.003729y + 11.5y = 0.015229y mol
 Total mass of solvent  in kg, msolvent =  msolvent a + msolvent b
msolvent =  1.3356y×10-3 kg
Molarity, M =nsolute/V

M  = 0.015229y2y×10-3

 M = 7.614M

Molality, m =  nsolutemsolvent in kg=0.015229y1.3356y×10-3=11.402m

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