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:
Answer & explanation
Correct answer: option 3
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 $\frac{1}{\text{Molar Mass}}$)
|
Solute |
Molar Mass (g⋅mol-1) |
Molarity (M) = $\frac{1}{\text{MolarMass1}}$ |
$\frac{1}{\text{MolarMass1}}$ (Approx. Value) |
Rank (1=Highest Molarity) |
|
(A) Glucose |
180.0 |
$\frac{1}{180}$ |
0.0056 |
4 |
|
(B) NaOH |
40.0 |
$\frac{1}{40}$ |
0.0250 |
1 |
|
(C) NaCl |
58.5 |
$\frac{1}{58.5}$ |
0.0171 |
2 |
|
(D) KCl |
74.5 |
$\frac{1}{74.5}$ |
0.0134 |
3 |
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).