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How many mL of sulphuric acid of density 1.84 g mL1 containing 95.6 mass % of H2SO4 should be added to one litre of 40 mass % solution of H2SO4 of density 1.31 g mL1 in order to prepare 50 mass % solution of sulphuric acid of density 1.40 g mL1?

A
66.2 ml
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B
55.2 ml
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C
95.5 ml
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D
105.2 ml
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Solution

The correct option is C 95.5 ml
Let mass of solution be 100 gm
​Therefore amount of solute in it = 95.6 gm
Volume of solution = massdensity = 1001.84 = 54.3478 ml
Volume = 1 L =1000 ml
Density = 1.31 g/ml
Mass of solution = 1310 g
Mass % of solute = 40 %

Let mass of solute in it be X g

Mass % = massofsolutemassofsolution×100

40 = X1300×100

X = 40×1310 = 524 gm

For solution to make 50 % mass percent and density 1.40 g/ml
Volume of solution =1400 ml
Amount of solute present should be,

Y gm = 50×1400100 = 700 g
​Thus
Amount of solute needed to be added to the 40 % to make it 50% by mass =700-524 = 176 g
Volume of H2SO4 of density 1.84 g/ml required to be added to 40 % = massdensity = 1761.84 =95.6521 ml
so the answer is C

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