1120 gm of 2 'm' urea solution is mixed with 2480 gm of 4 'm' urea solution. Calculate the molality of the resulting solution ?

Answer

To calculate the molality of the resulting solution when mixing two urea solutions, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula is:
\[ m = \frac{n}{W} \]
where \( n \) is the number of moles of solute and \( W \) is the mass of the solvent in kilograms.

### Step 2: Calculate the number of moles of solute in each solution
1. **For the first solution (2 m urea solution)**:
- Given: Mass of solution = 1120 g, Molarity (m) = 2 m
- Moles of solute (urea) in the first solution:
\[ n_1 = m_1 \times \text{mass of solution} = 2 \times \frac{1120}{1000} = 2 \times 1.12 = 2.24 \text{ moles} \]

2. **For the second solution (4 m urea solution)**:
- Given: Mass of solution = 2480 g, Molarity (m) = 4 m
- Moles of solute (urea) in the second solution:
\[ n_2 = m_2 \times \text{mass of solution} = 4 \times \frac{2480}{1000} = 4 \times 2.48 = 9.92 \text{ moles} \]

### Step 3: Calculate the total number of moles of solute
Now, we can find the total number of moles of urea in the resulting solution:
\[ n_{total} = n_1 + n_2 = 2.24 + 9.92 = 12.16 \text{ moles} \]

### Step 4: Calculate the total mass of the solvent
To find the mass of the solvent, we need to subtract the mass of the solute from the total mass of the solutions:
- Total mass of the solutions = 1120 g + 2480 g = 3600 g
- Mass of solute (urea) can be calculated using the number of moles and the molar mass of urea (approximately 60 g/mol):
\[ \text{Mass of solute} = n_{total} \times \text{Molar mass of urea} = 12.16 \times 60 = 729.6 \text{ g} \]
- Mass of solvent = Total mass of solutions - Mass of solute
\[ \text{Mass of solvent} = 3600 \text{ g} - 729.6 \text{ g} = 2870.4 \text{ g} = 2.8704 \text{ kg} \]

### Step 5: Calculate the molality of the resulting solution
Now we can calculate the molality using the total number of moles of solute and the mass of the solvent in kilograms:
\[ m = \frac{n_{total}}{W} = \frac{12.16}{2.8704} \approx 4.24 \text{ mol/kg} \]

### Final Answer
The molality of the resulting solution is approximately **4.24 mol/kg**.

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