The following solutions were prepared by dissolving 1 g of solute in 1 L of the solution. Arrange the following solutions in decreasing order of their molarity

(A) Glucose (molar mass = $180\, g\, mol^{-1}$)
(B) NaOH (molar mass = $40\, g\, mol^{-1}$)
(C) NaCl (molar mass = $58.5\, g\, mol^{-1}$)
(D) KCl (molar mass = $74.5\, g\, mol^{-1}$)

Choose the correct answer from the options given below:

(B), (C), (D), (A)

The correct answer is Option (3) → (B), (C), (D), (A)

Molarity Calculation

Molarity ($M$) is defined as the number of moles of solute per liter of solution.

$M = \frac{\text{Moles of Solute}}{\text{Volume of Solution (in L)}}$

The number of moles is calculated as:

$\text{Moles} = \frac{\text{Mass of Solute (in g)}}{\text{Molar Mass of Solute (in } \text{g} \cdot \text{mol}^{-1})}$

Since the mass of solute (1 g) and the volume of solution (1 L) are the same for all solutions, the molarity will be inversely proportional to the molar mass:

$M = \frac{1 \text{ g}}{(\text{Molar Mass})} \times \frac{1}{1 \text{ L}}$

$\text{Molarity} \propto \frac{1}{\text{Molar Mass}}$

To arrange the solutions in decreasing order of molarity, we need to arrange them in increasing order of their molar masses.

1. Calculate Molarities (or compare $\frac{1}{\text{Molar Mass}}$)

2. Arrange in Decreasing Order of Molarity

The order from highest molarity to lowest molarity is:

$\text{NaOH} > \text{NaCl} > \text{KCl} > \text{Glucose}$

$\text{(B)} > \text{(C)} > \text{(D)} > \text{(A)}$

Conclusion

The correct arrangement in decreasing order of molarity is (B), (C), (D), (A).