Molarity Calculation for Solutions

This question asks us to arrange four different solutions based on their molarity. Molarity is a crucial concept in chemistry that defines the concentration of a solution. It is calculated as the number of moles of solute present in one liter of the solution. The formula is:

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

In this problem, each solution is prepared by dissolving 1 gram of solute in 1 liter of solution. This means the volume of the solution is constant (1 L) for all the substances we are considering. Because the volume is the same, the molarity of each solution will directly depend on the number of moles of the solute dissolved.

Moles Calculation for Solutes

To determine the molarity, we first need to calculate the number of moles for each solute. The formula to calculate moles is:

$$ \text{Moles} = \frac{\text{Mass of Solute}}{\text{Molar Mass of Solute}} $$

We are given that the mass of solute for each case is 1 gram. Let's calculate the moles:

• (A) Glucose: Molar mass = 180 g $mol^{-1}$. Moles = $ \frac{1 \text{ g}}{180 \text{ g mol}^{-1}} $
• (B) NaOH: Molar mass = 40 g $mol^{-1}$. Moles = $ \frac{1 \text{ g}}{40 \text{ g mol}^{-1}} $
• (C) NaCl: Molar mass = 58.5 g $mol^{-1}$. Moles = $ \frac{1 \text{ g}}{58.5 \text{ g mol}^{-1}} $
• (D) KCl: Molar mass = 74.5 g $mol^{-1}$. Moles = $ \frac{1 \text{ g}}{74.5 \text{ g mol}^{-1}} $

Molarity and Molar Mass Relationship

Since the volume of each solution is 1 L, the molarity value is numerically equal to the number of moles calculated:

$$ Molarity \approx \text{Moles of Solute} $$

Observing the formula for moles, we can see that when the mass of the solute is fixed (at 1 g), the number of moles is inversely proportional to the molar mass of the solute:

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

Consequently, the molarity of the solution is also inversely proportional to the molar mass of the solute:

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

This means that the solute with the lowest molar mass will yield the highest number of moles and thus the highest molarity. Conversely, a solute with a higher molar mass will result in fewer moles and a lower molarity.

Ordering Solutes by Molar Mass

To arrange the solutions in decreasing order of molarity, we first need to order the solutes by their molar masses. Let's list the molar masses provided:

Now, let's arrange these molar masses in increasing order:

40 g $mol^{-1}$ (NaOH) < 58.5 g $mol^{-1}$ (NaCl) < 74.5 g $mol^{-1}$ (KCl) < 180 g $mol^{-1}$ (Glucose)

Since molarity is inversely proportional to molar mass, the decreasing order of molarity will be the reverse of this sequence:

Molarity of NaOH > Molarity of NaCl > Molarity of KCl > Molarity of Glucose

Solution Molarity Ranking

Therefore, arranging the solutions in decreasing order of their molarity, we get:

1. (B) NaOH
2. (C) NaCl
3. (D) KCl
4. (A) Glucose

This sequence corresponds to the order (B), (C), (D), (A).