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
• B. 3.94 and 4.92
• C. 4.92 and 3.94
• D. 3.94 and 3.94

Answer 1

The correct option is C 4.92 and 3.94

Initial conditions of the solution:
Solute A:
(i) Volume of solution $V_1$ = 250 mL
Molarity of solution $M_1$ = x M

(ii) Volume of solution $V_2$ = 500 mL
Molarity of solution $M_2$ = y M

Final conditions of solution :
Molarity of solution $M_f$ = 1.6 M
Volume of solution $V_f$ = 2 L

Also,
$\frac{x}{y}=\frac{5}{4}$
$\Rightarrow x=\frac{5}{4}y$ ....(i)

We know that, in case of dilution, moles remain conserved.
$M_1{V}_1+M_2{V}_2=M_f{V}_f$
$\Rightarrow x\frac{250}{1000}+y\frac{500}{1000}=1.6\times 2$
$\Rightarrow (250\times x)+(500\times y)=3200$

On simplifying ,
x + 2y = 12.8 ...(ii)

From equations (i) and (ii) we get
$1.25y+2y=12.8$
$\Rightarrow 3.25y=12.8$
$\Rightarrow$ y = 3.94 and $x=\frac{5}{4}y$
$\therefore x=1.25\times 3.94=4.92$

Hence, the molarity of the 250 mL solution is 4.92 M and the molarity of the 500 mL solution is 3.94 M