Arrange the following mixtures in increasing order of their resultant molarity
(A) 20 mL of 0.5 M HCl + 30 mL of 0.3 M HCl
(B) 30 mL of 0.3 M HCl + 30 mL of 0.3 M HCl
(C) 20 mL of 0.5 M HCl + 20 mL of 0.3 M HCl
(D) 20 mL of 0.3 M HCl + 30 mL of 0.5 M HCl
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B), (A), (C), (D)
When two solutions of the same solute are mixed, the moles of solute add up, and so do the volumes. Since moles = molarity × volume, the resulting molarity is
\( \displaystyle M = \frac{M_1V_1 + M_2V_2}{V_1 + V_2} \)
(With volumes in mL, \( M \times V \) gives millimoles.)
(A) \( \displaystyle M = \frac{20(0.5) + 30(0.3)}{50} = \frac{10 + 9}{50} = 0.38\ \mathrm{M} \)
(B) \( \displaystyle M = \frac{30(0.3) + 30(0.3)}{60} = \frac{9 + 9}{60} = 0.30\ \mathrm{M} \)
(C) \( \displaystyle M = \frac{20(0.5) + 20(0.3)}{40} = \frac{10 + 6}{40} = 0.40\ \mathrm{M} \)
(D) \( \displaystyle M = \frac{20(0.3) + 30(0.5)}{50} = \frac{6 + 15}{50} = 0.42\ \mathrm{M} \)
In increasing order of molarity:
\( \displaystyle 0.30\,(\mathrm{B}) \lt 0.38\,(\mathrm{A}) \lt 0.40\,(\mathrm{C}) \lt 0.42\,(\mathrm{D}) \)
Shortcut: Mixing two 0.3 M solutions leaves the molarity at 0.3 M, the lowest possible value here, so the order starts with (B). Only Option (3) does.