Question

The chemistry teacher asked the students to prepare 20% w/w solution of urea [NH₂CONH₂] in water. Which one of the following solution does not conform to the required composition?

• A. 6g urea dissolved in 24g water
• B. 20g urea dissolved in 80g water
• C. 10g urea dissolved in 40g water
• D. 4g urea dissolved in 16g water
• E. 15g urea dissolved in 30g water

Answer 1

Answer: (E)

Understand Weight by Weight Percentage (% w/w):
A 20% w/w solution means that the mass of the solute (urea) constitutes 20% of the total mass of the solution (urea + water). The formula for weight by weight percentage is: \[ \% \, w/w = \left( \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \right) \times 100\% \] Where, Total Mass of Solution = Mass of Solute + Mass of Solvent. We need to check each option to see if it yields a 20% w/w solution.

Check Option (A): 6g urea dissolved in 24g water
 

Mass of Solute (urea) = 6 g 
Mass of Solvent (water) = 24 g 
Total Mass of Solution = 6 g + 24 g = 30 g 
\[ \% \, w/w = \left( \frac{6 \, \text{g}}{30 \, \text{g}} \right) \times 100\% = \left( \frac{1}{5} \right) \times 100\% = 20\% \] This solution conforms to the required composition.

Check Option (B): 20g urea dissolved in 80g water
 

Mass of Solute (urea) = 20 g 
Mass of Solvent (water) = 80 g 
Total Mass of Solution = 20 g + 80 g = 100 g 
\[ \% \, w/w = \left( \frac{20 \, \text{g}}{100 \, \text{g}} \right) \times 100\% = 0.20 \times 100\% = 20\% \] This solution conforms to the required composition.

Check Option (C): 10g urea dissolved in 40g water
 

Mass of Solute (urea) = 10 g 
Mass of Solvent (water) = 40 g 
Total Mass of Solution = 10 g + 40 g = 50 g 
\[ \% \, w/w = \left( \frac{10 \, \text{g}}{50 \, \text{g}} \right) \times 100\% = \left( \frac{1}{5} \right) \times 100\% = 20\% \] This solution conforms to the required composition.

Check Option (D): 4g urea dissolved in 16g water
 

Mass of Solute (urea) = 4 g 
Mass of Solvent (water) = 16 g 
Total Mass of Solution = 4 g + 16 g = 20 g 
\[ \% \, w/w = \left( \frac{4 \, \text{g}}{20 \, \text{g}} \right) \times 100\% = \left( \frac{1}{5} \right) \times 100\% = 20\% \] This solution conforms to the required composition.

Check Option (E): 15g urea dissolved in 30g water
 

Mass of Solute (urea) = 15 g 
Mass of Solvent (water) = 30 g 
Total Mass of Solution = 15 g + 30 g = 45 g 
\[ \% \, w/w = \left( \frac{15 \, \text{g}}{45 \, \text{g}} \right) \times 100\% = \left( \frac{1}{3} \right) \times 100\% = 33.33...\% \] This solution does not conform to the required 20% w/w composition.

Options (A), (B), (C), and (D) all represent a 20% w/w solution of urea in water. Option (E) represents a 33.33% w/w solution.

Therefore, the solution that does not conform to the required composition is (E).

Answer 2

To prepare a 20% w/w solution of urea, the mass of urea in the solution should be 20% of the total mass of the solution. This can be expressed as:
Mass of urea (g) / Total mass of solution (g) × 100 = 20%

The total mass of the solution is the sum of the mass of urea and the mass of water: Total mass = Mass of urea + Mass of water
 
Let's evaluate each option:

1. 6g urea dissolved in 24g water:
   Total mass = 6g + 24g = 30g
   The percentage of urea = (6g / 30g) × 100 = 20% ✔️
2. 20g urea dissolved in 80g water:
   Total mass = 20g + 80g = 100g
   The percentage of urea = (20g / 100g) × 100 = 20% ✔️
3. 10g urea dissolved in 40g water:
   Total mass = 10g + 40g = 50g
   The percentage of urea = (10g / 50g) × 100 = 20% ✔️
4. 4g urea dissolved in 16g water:
   Total mass = 4g + 16g = 20g
   The percentage of urea = (4g / 20g) × 100 = 20% ✔️
5. 15g urea dissolved in 30g water:
   Total mass = 15g + 30g = 45g
   The percentage of urea = (15g / 45g) × 100 = 33.33% ❌

Therefore, the solution that does not conform to the required composition is: 15g urea dissolved in 30g water