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 find the osmotic pressure of a decimolar solution of glucose at 30°C, we can use the formula for osmotic pressure:

\[ \Pi = C \cdot R \cdot T \]

Where:
- \(\Pi\) = osmotic pressure
- \(C\) = concentration in molarity (M)
- \(R\) = universal gas constant
- \(T\) = temperature in Kelvin (K)

### Step 1: Identify the concentration
The problem states that the solution is decimolar, which means:
\[ C = 0.1 \, \text{M} \, \text{(decimolar)} \]

### Step 2: Convert temperature to Kelvin
The temperature given is 30°C. To convert this to Kelvin:
\[ T = 30 + 273 = 303 \, \text{K} \]

### Step 3: Use the value of the gas constant
The value of the gas constant \(R\) is:
\[ R = 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \]

### Step 4: Substitute the values into the osmotic pressure formula
Now we can substitute the values into the osmotic pressure formula:
\[ \Pi = C \cdot R \cdot T \]
\[ \Pi = 0.1 \, \text{mol/L} \cdot 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \cdot 303 \, \text{K} \]

### Step 5: Calculate the osmotic pressure
Calculating this gives:
\[ \Pi = 0.1 \cdot 0.0821 \cdot 303 \]
\[ \Pi = 2.488 \, \text{atm} \]

### Final Answer
The osmotic pressure of the decimolar solution of glucose at 30°C is:
\[ \Pi \approx 2.488 \, \text{atm} \]