25 g of a solute of molar mass `250 g mol^(-1)` is dissolved in 100 ml of water to obtain a solution whose density is `1.25 g ml^(-1)`. The molarity and molality of the solution are respectively

Options

A. 0.75 and 1
B. 0.8 and 1
C. 1 and 0.8
D. 1 and 0.75

Explanation

To calculate the molarity and molality of the solution, we can follow these steps:

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

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

Given:
- Mass of solute = 25 g
- Molar mass = 250 g/mol

\[ \text{Number of moles} = \frac{25 \, \text{g}}{250 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 2: Calculate the volume of the solution in liters
Since the volume of the solution is given in milliliters, we need to convert it to liters:

\[ \text{Volume in liters} = \frac{100 \, \text{ml}}{1000} = 0.1 \, \text{L} \]

### Step 3: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:

\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in L}} \]

Substituting the values:

\[ \text{Molarity (M)} = \frac{0.1 \, \text{mol}}{0.1 \, \text{L}} = 1 \, \text{M} \]

### Step 4: Calculate the mass of the solution
To find the mass of the solution, we need to consider the mass of the solute and the mass of the solvent (water).

The density of the solution is given as 1.25 g/ml. Therefore, the mass of the solution can be calculated as:

\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 1.25 \, \text{g/ml} \times 100 \, \text{ml} = 125 \, \text{g} \]

### Step 5: Calculate the mass of the solvent (water)
To find the mass of the solvent, we subtract the mass of the solute from the mass of the solution:

\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute} = 125 \, \text{g} - 25 \, \text{g} = 100 \, \text{g} \]

### Step 6: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent:

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

Converting the mass of the solvent to kilograms:

\[ \text{Mass of solvent in kg} = \frac{100 \, \text{g}}{1000} = 0.1 \, \text{kg} \]

Now we can calculate the molality:

\[ \text{Molality (m)} = \frac{0.1 \, \text{mol}}{0.1 \, \text{kg}} = 1 \, \text{m} \]

### Final Answer:
The molarity and molality of the solution are both 1 M and 1 m, respectively.