Question

# 250 mL of a ‘x′ M solution and 500 mL of a ‘y′ M solution of a solute A are mixed and diluted to 2 litres to produce a solution with the final concentration 1.6 M. If x:y=5:4, then the value of x and y respectively are:

A
4.92 and 4.92
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B
3.94 and 3.152
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C
4.92 and 3.94
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D
4.92 and 3.936
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Solution

## The correct option is C 4.92 and 3.94Initial conditions of the solution: Solute A: (i) Volume of solution V1 = 250 mL Molarity of solution M1 = x M (ii) Volume of solution V2 = 500 mL Molarity of solution M2 = y M Final conditions of solution : Molarity of solution Mf = 1.6 M Volume of solution Vf = 2 L Also, xy=54 ⇒x=54 y...(i) . We know that, in case of dilution, moles remain conserved. M1V1+M2V2=MfVf ⇒x2501000+y5001000=1.6×2 ⇒(250×x)+(500×y)=3200 On simplifying , x+2y=12.8 ...(ii) From equations (i) and (ii) we get 1.25y+2y=12.8 ⇒3.25y=12.8 ⇒y=3.94 and x=54 y ∴x=1.25×3.94=4.92 Hence, the molarity of the 250 mL solution is 4.92 M and the molarity of the 500 mL solution is 3.94 M

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