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Question

Find the molality of a solution made by mixing equal volumes of 60% (w/w) H2SO4 (density = 1.84 g/mL) and 40% (w/w) of H2SO4 (density = 1.52 g/mL) solutions.

A
10.6 m
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B
12.5 m
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C
19.2 m
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D
15.7 m
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Solution

The correct option is A 10.6 m
Assuming V mL of H2SO4 is mixed together.
60% (w/w) means 60 g of solute is present in 100 g of the solution.
Since, density of solution = mass of the solutionvolume of the solution
Mass of H2SO4 solution = 1.84 ×V = 1.84V g
100 g of the solution contains 60 g of H2SO4
1.84V g of the solution will contain = 60100×1.84V = 1.104V g...(i)
Similarly,
40% (w/w) means 40 g of solute is present in 100 g of the solution.
Since, density = mass of the solutionvolume of the solution
Mass of H2SO4 solution = 1.52 ×V = 1.52V g
100 g of the solution contains 40 g of H2SO4
1.52V g of the solution will contain = 40100×1.52V = 0.608V g...(ii)
Total mass of the solution = 1.84V + 1.52V = 3.36V g
Total mass of the solute = 1.104V + 0.608V = 1.712V g
Moles of H2SO4 = given massmolar mass=1.712V98 mol
Total mass of the solvent (water) = 3.36V - 1.712V = 1.648V g
Molarity = moles of solutemass of solution in kg
Molality = 1.712V/981.648V×1000 = 10.6 m

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