Suppose 60% w`//`w aqueous solution of glucose `( C_(6)H_(12) O_(6)` ) and 20% w `//`w aqueous solution of urea `( NH_(2)CONH_(2)` ) have equal molarity, then which solution has higher density `:`

Options

A. Both have equal density
B. Glucose solution
C. Urea solution
D. Cannot be predicted

Answer

To solve the problem, we need to determine the densities of the two solutions (60% w/w glucose and 20% w/w urea) given that they have equal molarity.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The molarity (M) of a solution can be expressed in terms of weight percentage and density:
\[ M = \left( \frac{\text{Weight \%} \times \text{Density} \times 10}{\text{Molecular Weight}} \right) \]

2. **Calculate the Molecular Weights**:
- For glucose (C₆H₁₂O₆):
- Carbon (C): 12 g/mol × 6 = 72 g/mol
- Hydrogen (H): 1 g/mol × 12 = 12 g/mol
- Oxygen (O): 16 g/mol × 6 = 96 g/mol
- Total = 72 + 12 + 96 = 180 g/mol

- For urea (NH₂CONH₂):
- Nitrogen (N): 14 g/mol × 2 = 28 g/mol
- Carbon (C): 12 g/mol = 12 g/mol
- Oxygen (O): 16 g/mol = 16 g/mol
- Total = 28 + 12 + 16 = 56 g/mol

3. **Set Up the Equations for Molarity**:
Let \( d_g \) be the density of the glucose solution and \( d_u \) be the density of the urea solution.
- For glucose:
\[ M_g = \frac{60 \times d_g \times 10}{180} \]
- For urea:
\[ M_u = \frac{20 \times d_u \times 10}{56} \]

4. **Equate the Molarities**:
Since the molarities are equal:
\[ \frac{60 \times d_g \times 10}{180} = \frac{20 \times d_u \times 10}{56} \]
Simplifying this equation:
\[ \frac{60 \times d_g}{180} = \frac{20 \times d_u}{56} \]
Canceling out the 10s:
\[ \frac{60}{180} d_g = \frac{20}{56} d_u \]
Simplifying further:
\[ \frac{1}{3} d_g = \frac{5}{14} d_u \]

5. **Cross-Multiply to Find the Relationship**:
Cross-multiplying gives:
\[ 14 d_g = 15 d_u \]
Rearranging gives:
\[ d_g = \frac{15}{14} d_u \]

6. **Conclusion**:
Since \( d_g = \frac{15}{14} d_u \), it indicates that the density of the glucose solution is greater than that of the urea solution. Therefore, the glucose solution has a higher density.

### Final Answer:
The glucose solution has more density.