Dissolving `120g` of urea (mol wt `= 60)` in 1000g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

Options

A. `1.78M`
B. `2.00M`
C. `2.05M`
D. `2.22M`

Explanation

To find the molarity of the solution, we will follow these steps:

### Step 1: Calculate the number of moles of urea
We are given:
- Mass of urea (solute) = 120 g
- Molar mass of urea = 60 g/mol

To find the number of moles of urea, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass of solute}}{\text{Molar mass of solute}} \]
Substituting the values:
\[ \text{Number of moles of urea} = \frac{120 \, \text{g}}{60 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 2: Calculate the mass of the solution
The mass of the solution is the sum of the mass of the solute and the mass of the solvent.
- Mass of water (solvent) = 1000 g
- Mass of urea (solute) = 120 g

So, the mass of the solution is:
\[ \text{Mass of solution} = \text{Mass of solute} + \text{Mass of solvent} = 120 \, \text{g} + 1000 \, \text{g} = 1120 \, \text{g} \]

### Step 3: Calculate the volume of the solution
We are given the density of the solution:
- Density = 1.15 g/mL

Using the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
We can rearrange this to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1120 \, \text{g}}{1.15 \, \text{g/mL}} \approx 973.91 \, \text{mL} \]

To convert this volume to liters:
\[ \text{Volume in liters} = \frac{973.91 \, \text{mL}}{1000} \approx 0.974 \, \text{L} \]

### Step 4: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} = \frac{2 \, \text{moles}}{0.974 \, \text{L}} \approx 2.05 \, \text{mol/L} \]

Thus, the molarity of the solution is approximately **2.05 mol/L**.

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