Arranging Substances by Molarity

The problem asks us to arrange four substances (Glucose, Urea, Benzoic Acid, and Sucrose) in increasing order of their molarities when 0.28 g of each is dissolved in 1 L of water. Molarity is defined as moles of solute per liter of solution.

Calculating Molar Masses

First, we calculate the molar mass (MM) for each substance using their chemical formulas:

• Glucose ($C_6H_{12}O_6$): $MM = (6 \times 12.011) + (12 \times 1.008) + (6 \times 15.999) \approx 180.16$ g/mol
• Urea ($NH_2CONH_2$): $MM = (2 \times 14.007) + (4 \times 1.008) + (1 \times 12.011) + (1 \times 15.999) \approx 60.06$ g/mol
• Benzoic Acid ($C_6H_5COOH$): $MM = (7 \times 12.011) + (6 \times 1.008) + (2 \times 15.999) \approx 122.12$ g/mol
• Sucrose ($C_{12}H_{22}O_{11}$): $MM = (12 \times 12.011) + (22 \times 1.008) + (11 \times 15.999) \approx 342.30$ g/mol

Determining Molarity Order

Molarity (M) is calculated as:

$ M = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}} $

Since the mass (0.28 g) and volume (1 L) are the same for all substances, the number of moles is given by:

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

Therefore, molarity is inversely proportional to the molar mass when mass and volume are constant:

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

Comparing Molar Masses and Molarities

We list the substances and their approximate molar masses:

• Sucrose (D): $\approx 342.30$ g/mol
• Glucose (A): $\approx 180.16$ g/mol
• Benzoic Acid (C): $\approx 122.12$ g/mol
• Urea (B): $\approx 60.06$ g/mol

Arranging the molar masses in increasing order:

Urea (B) < Benzoic Acid (C) < Glucose (A) < Sucrose (D)

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

Molarity(Sucrose) < Molarity(Glucose) < Molarity(Benzoic Acid) < Molarity(Urea)

This corresponds to the order: D < A < C < B.

Final Arrangement

The correct order of increasing molarities is D, A, C, B.