The osmotic pressure of 5% (mass/volume) solution of cane sugar at 50-C is

Options

A. 2.51 atm
B. 3 atm
C. 3.88 atm
D. 3.45 atm

Answer

To calculate the osmotic pressure of a 5% (mass/volume) solution of cane sugar at 50°C, we can follow these steps:

### Step 1: Understand the Given Information
- We have a 5% (mass/volume) solution of cane sugar.
- The temperature is given as 50°C.

### Step 2: Convert Temperature to Kelvin
To use the ideal gas law, we need to convert the temperature from Celsius to Kelvin.
\[ T(K) = T(°C) + 273 \]
\[ T = 50 + 273 = 323 \, K \]

### Step 3: Calculate the Mass of the Solute
In a 5% (mass/volume) solution, this means there are 5 grams of cane sugar in 100 mL of solution. Therefore:
- Mass of cane sugar (W) = 5 g

### Step 4: Determine the Molar Mass of Cane Sugar
The molar mass of cane sugar (sucrose, C₁₂H₂₂O₁₁) is approximately 342 g/mol.

### Step 5: Calculate the Number of Moles of Cane Sugar
Using the formula for moles:
\[ N = \frac{mass}{molar \, mass} \]
\[ N = \frac{5 \, g}{342 \, g/mol} \approx 0.0146 \, mol \]

### Step 6: Use the Osmotic Pressure Formula
The formula for osmotic pressure (π) is given by:
\[ \pi = \frac{NRT}{V} \]
Where:
- \(N\) = number of moles
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin
- \(V\) = volume of the solution in liters (0.1 L for 100 mL)

### Step 7: Substitute the Values into the Osmotic Pressure Formula
\[ \pi = \frac{(0.0146 \, mol) \times (0.0821 \, L·atm/(K·mol)) \times (323 \, K)}{0.1 \, L} \]

### Step 8: Perform the Calculation
\[ \pi = \frac{(0.0146) \times (0.0821) \times (323)}{0.1} \]
Calculating the numerator:
\[ 0.0146 \times 0.0821 \times 323 \approx 0.373 \]
Now divide by 0.1:
\[ \pi \approx 3.73 \, atm \]

### Final Answer
The osmotic pressure of the 5% (mass/volume) solution of cane sugar at 50°C is approximately **3.73 atm**.

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