The osmotic pressure of a decimolar solution of glucose at `30^(@)C` is :

Options

A. 24.88 atm
B. 2.48 atm
C. 12.44 atm
D. 124.4 atm

Answer

To calculate the osmotic pressure of a decimolar solution of glucose at \(30^\circ C\), we can follow these steps:

### Step 1: Understand the formula for osmotic pressure
The formula for osmotic pressure (\(\Pi\)) is given by:
\[ \Pi = CRT \]
where:
- \(C\) = molarity of the solution
- \(R\) = gas constant
- \(T\) = temperature in Kelvin

### Step 2: Identify the molarity of the solution
The problem states that the solution is decimolar. This means:
\[ C = 0.1 \, \text{mol/L} \]

### Step 3: Convert the temperature from Celsius to Kelvin
To convert the temperature from Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
For \(30^\circ C\):
\[ T = 30 + 273 = 303 \, K \]

### Step 4: Identify the value of the gas constant
The gas constant \(R\) is given as:
\[ R = 0.082 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \]

### Step 5: Substitute the values into the osmotic pressure formula
Now we can substitute the values of \(C\), \(R\), and \(T\) into the osmotic pressure formula:
\[ \Pi = (0.1 \, \text{mol/L}) \times (0.082 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1}) \times (303 \, K) \]

### Step 6: Calculate the osmotic pressure
Now we perform the calculation:
\[ \Pi = 0.1 \times 0.082 \times 303 \]
Calculating this step-by-step:
1. Calculate \(0.1 \times 0.082 = 0.0082\)
2. Then multiply \(0.0082 \times 303 = 2.4866\)

Rounding this to two decimal places, we get:
\[ \Pi \approx 2.49 \, \text{atm} \]

### Step 7: Final answer
Thus, the osmotic pressure of the decimolar solution of glucose at \(30^\circ C\) is approximately:
\[ \Pi \approx 2.48 \, \text{atm} \]