Question

The volumes of two $ \text{HCl} $ solutions A(0.5 N) and B(0.1 N) to be mixed for preparing 2 L of 0.2 N HCl solution are

• 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

Answer 1

The Correct Option is A

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.