A 0.5 M aqueous \( H_2SO_4 \) solution is diluted from 2 litres to 20 litres. The concentration of the resulting solution will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.1 N
On dilution the amount of solute does not change; only the volume increases. So the molarity falls in proportion:
\( \displaystyle M_1 V_1 = M_2 V_2 \)
\( \displaystyle M_2 = \frac{0.5 \times 2}{20} = 0.05\,\mathrm{M} \)
The options are in normality. Normality = molarity × n-factor, where the n-factor of an acid is the number of \( \ce{H+} \) ions one molecule can give. Sulphuric acid is dibasic:
\( \displaystyle \ce{H2SO4 -> 2H+ + SO4^2-} \quad \Rightarrow \quad n = 2 \)
\( \displaystyle N = 0.05 \times 2 = 0.1\,\mathrm{N} \)
So the concentration of the resulting solution is 0.1 N.
Note: The question is from beyond the NCERT textbook.