A) \[0.5L\]of \[A+1.5L\]of B
B) \[1.5\,L\]of \[A+0.5L\]of B
C) \[1L\]of \[A+1L\]of B
D) \[0.75L\]of \[A+1.25L\]of B
Correct Answer: A
Solution :
Let the volume of 0.5 N HCl solution \[\text{=}\,{{\text{V}}_{\text{1}}}\] and the volume of 0.1 N HCl solution \[\text{=}\,{{\text{V}}_{2}}\] Total volume of the mixture = 2 L \[{{\text{V}}_{1}}+{{V}_{2}}=2L\] ?(i) We know that \[\underset{(For0.5\,N\,HCl)}{\mathop{{{N}_{1}}{{V}_{1}}}}\,+\underset{(For\,0.1\,N\,HCl)}{\mathop{{{N}_{2}}{{V}_{2}}}}\,=\underset{(resulting\,solution)}{\mathop{NV}}\,\] \[0.5\times {{V}_{1}}+0.1\times {{V}_{2}}=0.2\times 0.2\] \[0.5\,{{V}_{1}}+0.1\,{{V}_{2}}=0.4\] ?(ii) Multiply Eq (i) with 0.5 and then, subtract Eq (ii) from it, \[\begin{align} & \underline{\begin{align} & 0.5{{V}_{1}}+0.5{{V}_{2}}=0.5\times 2\,\,\,\,\,\,\,\,\,...(iii) \\ & 0.5{{V}_{1}}+0.5{{V}_{2}}=0.4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(ii) \\ \end{align}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0.4{{V}_{2}}=0.6 \\ \end{align}\] \[{{V}_{2L}}=1.5L\] \[{{V}_{1}}=2-1.5=0.5\,L\] Hence, 0.5 L of A + 1.5 L of B are mixed.
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