Arrange the following in increasing order of their molarity when their equal weights are dissolved in 250 mL of water.
(A) glucose (\( 180\, g\, mol^{-1} \))
(B) sodium carbonate (\( 106\, g\, mol^{-1} \))
(C) sodium hydroxide (\( 40\, g\, mol^{-1} \))
(D) acetic acid (\( 60\, g\, mol^{-1} \))
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (D), (C)
Molarity is the number of moles of solute per litre of solution, and the number of moles is the mass divided by the molar mass:
\( \displaystyle \text{Molarity} = \frac{n}{V} = \frac{w}{M \times V} \)
where w is the mass of solute, M its molar mass and V the volume of solution in litres. Here the same mass w of each solute is dissolved to give the same volume (250 mL). So the molarity depends only on the molar mass, and it is inversely proportional to the molar mass: the lighter the molecule, the more moles in the same mass.
(A) Glucose, 180 g mol−1: \( n = w/180 \), the fewest moles.
(B) Sodium carbonate, 106 g mol−1: \( n = w/106 \).
(D) Acetic acid, 60 g mol−1: \( n = w/60 \).
(C) Sodium hydroxide, 40 g mol−1: \( n = w/40 \), the most moles.
In increasing order of molarity:
\( \displaystyle \text{glucose} \lt \ce{Na2CO3} \lt \ce{CH3COOH} \lt \ce{NaOH} \)
Shortcut: Increasing molarity is decreasing molar mass: 180 > 106 > 60 > 40, which reads (A), (B), (D), (C).