100 mL aqueous solution of glucose with osmotic pressure 1.2 atm at `25^(@)C` is mixed with 300 mL aqueous solution of urea at 2.4 atm at `25^(@)C`. Calculate the osmotic pressure of mixture.

Options

A. 1.37 atm
B. 2.59 atm
C. 1.85 atm
D. 2.13 atm

Answer

To solve the problem of finding the osmotic pressure of the mixture of glucose and urea solutions, we can follow these steps:

### Step 1: Identify the given values
- Volume of glucose solution, \( V_1 = 100 \, \text{mL} \)
- Osmotic pressure of glucose solution, \( \pi_1 = 1.2 \, \text{atm} \)
- Volume of urea solution, \( V_2 = 300 \, \text{mL} \)
- Osmotic pressure of urea solution, \( \pi_2 = 2.4 \, \text{atm} \)

### Step 2: Calculate the total volume of the mixture
The total volume \( V \) of the mixture is the sum of the volumes of the two solutions:
\[ V = V_1 + V_2 = 100 \, \text{mL} + 300 \, \text{mL} = 400 \, \text{mL} \]

### Step 3: Use the formula for osmotic pressure of the mixture
The osmotic pressure of the mixture can be calculated using the formula:
\[ \pi = \frac{\pi_1 V_1 + \pi_2 V_2}{V} \]
Where:
- \( \pi \) is the osmotic pressure of the mixture,
- \( \pi_1 \) and \( \pi_2 \) are the osmotic pressures of the individual solutions,
- \( V_1 \) and \( V_2 \) are the volumes of the individual solutions,
- \( V \) is the total volume of the mixture.

### Step 4: Substitute the values into the formula
Substituting the known values into the equation:
\[ \pi = \frac{(1.2 \, \text{atm} \times 100 \, \text{mL}) + (2.4 \, \text{atm} \times 300 \, \text{mL})}{400 \, \text{mL}} \]

### Step 5: Calculate the numerator
Calculate the contributions from both solutions:
\[ \pi = \frac{(120 \, \text{atm} \cdot \text{mL}) + (720 \, \text{atm} \cdot \text{mL})}{400 \, \text{mL}} = \frac{840 \, \text{atm} \cdot \text{mL}}{400 \, \text{mL}} \]

### Step 6: Calculate the osmotic pressure of the mixture
Now, divide to find the osmotic pressure:
\[ \pi = \frac{840}{400} = 2.1 \, \text{atm} \]

### Step 7: Final result
The osmotic pressure of the mixture is:
\[ \pi = 2.1 \, \text{atm} \]