The molarity of solution containing `15.20 g` of urea, (molar mass = 60) dissolved in `150 g` of water is

Options

A. `1.689 " mol kg " ^(-1)`
B. `0.1689 " mol kg " ^(-1)`
C. `0.5922 " mol kg " ^(-1)`
D. `0.2533 " mol kg " ^(-1)`

Answer

To find the molarity of the solution containing 15.20 g of urea dissolved in 150 g of water, we can follow these steps:

### Step 1: Calculate the number of moles of urea
To find the number of moles of urea, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of urea = 15.20 g
- Molar mass of urea = 60 g/mol

\[ \text{Number of moles of urea} = \frac{15.20 \, \text{g}}{60 \, \text{g/mol}} = 0.2533 \, \text{mol} \]

### Step 2: Convert the mass of water to kilograms
Since molarity is defined in terms of liters of solution and moles of solute, we need to convert the mass of water from grams to kilograms:

\[ \text{Mass of water} = 150 \, \text{g} = 0.150 \, \text{kg} \]

### Step 3: Calculate the molality
Molarity (M) is defined as the number of moles of solute per liter of solution. However, since we are given the mass of water, we can calculate molality (which is moles of solute per kg of solvent) first and then convert it to molarity if needed.

\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}} \]

Substituting the values we calculated:

\[ \text{Molarity} = \frac{0.2533 \, \text{mol}}{0.150 \, \text{kg}} = 1.6887 \, \text{mol/kg} \]

### Step 4: Final result
The molarity of the solution is approximately:

\[ \text{Molarity} \approx 1.689 \, \text{mol/kg} \]

### Conclusion
Thus, the molarity of the solution containing 15.20 g of urea dissolved in 150 g of water is **1.689 mol/kg**.