Question

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 = 7(4)5 g mol$^{-1}$)

• A. (A), (D), (C), (B)
• B. (A), (B), (C), (D)
• C. (B), (C), (D), (A)
• D. (D), (C), (A), (B)

Hint:

When comparing the molarity of solutions, focus on the molar mass of the solute. A lower molar mass results in higher molarity when the same mass of solute is used.

Answer 1

The Correct Option is A

Step 1: Formula for molarity.
Molarity is given by the formula: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \] Since we have 1 g of solute in each case, we can calculate the molarity by dividing the number of moles by 1 L of solution.
Step 2: Calculating the number of moles.
The number of moles is given by: \[ \text{moles of solute} = \frac{\text{mass of solute}}{\text{molar mass of solute}} \] Now, let's calculate the moles for each solute:
- For glucose (A): \[ \text{moles of glucose} = \frac{1 \, \text{g}}{180 \, \text{g/mol}} = 0.00556 \, \text{mol} \] Thus, the molarity of glucose is: \[ M = 0.00556 \, \text{mol/L} \] - For NaOH (B): \[ \text{moles of NaOH} = \frac{1 \, \text{g}}{40 \, \text{g/mol}} = 0.025 \, \text{mol} \] Thus, the molarity of NaOH is: \[ M = 0.025 \, \text{mol/L} \] - For NaCl (C): \[ \text{moles of NaCl} = \frac{1 \, \text{g}}{58.5 \, \text{g/mol}} = 0.01709 \, \text{mol} \] Thus, the molarity of NaCl is: \[ M = 0.01709 \, \text{mol/L} \] - For KCl (D): \[ \text{moles of KCl} = \frac{1 \, \text{g}}{7(4)5 \, \text{g/mol}} = 0.01342 \, \text{mol} \] Thus, the molarity of KCl is: \[ M = 0.01342 \, \text{mol/L} \] Step 3: Arranging in decreasing order of molarity.
We can now arrange the molarities in decreasing order:
(1) NaOH (B) has the highest molarity of 0.025 mol/L.
(2) NaCl (C) has the next highest molarity of 0.01709 mol/L.
(3) KCl (D) has a molarity of 0.01342 mol/L.
(4) Glucose (A) has the lowest molarity of 0.00556 mol/L.
Therefore, the correct order is: (A), (D), (C), (B).
Final Answer: \[ \boxed{\text{The correct sequence is (A), (D), (C), (B).}} \]