The osmotic pressure in atmosphere of `10%`solution of cane sugar at `69^(@)C`is

Options

A. 724 atm
B. 824 atm
C. 8.21 atm
D. 7.21 atm

Answer

To find the osmotic pressure of a 10% solution of cane sugar at 69°C, we can follow these steps:

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = iCRT \]
where:
- \(i\) = van 't Hoff factor (for cane sugar, which is a non-electrolyte, \(i = 1\))
- \(C\) = molarity of the solution
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin

### Step 2: Calculate the molarity of the solution
A 10% solution of cane sugar means there are 10 grams of cane sugar in 100 mL of solution.

1. **Calculate the number of moles of cane sugar**:
The molar mass of cane sugar (sucrose) is approximately 342 g/mol.
\[ \text{Moles of cane sugar} = \frac{\text{mass}}{\text{molar mass}} = \frac{10 \text{ g}}{342 \text{ g/mol}} \approx 0.02924 \text{ mol} \]

2. **Convert volume from mL to L**:
\[ 100 \text{ mL} = 0.1 \text{ L} \]

3. **Calculate molarity (C)**:
\[ C = \frac{\text{moles}}{\text{volume in L}} = \frac{0.02924 \text{ mol}}{0.1 \text{ L}} = 0.2924 \text{ mol/L} \]

### Step 3: Convert temperature to Kelvin
To convert Celsius to Kelvin:
\[ T(K) = T(°C) + 273 = 69 + 273 = 342 \text{ K} \]

### Step 4: Substitute values into the osmotic pressure formula
Now, substituting the values into the osmotic pressure formula:
\[ \pi = iCRT = (1)(0.2924 \text{ mol/L})(0.0821 \text{ L·atm/(K·mol)})(342 \text{ K}) \]

### Step 5: Calculate the osmotic pressure
Calculating the above expression:
\[ \pi = 0.2924 \times 0.0821 \times 342 \approx 7.84 \text{ atm} \]

### Step 6: Round to significant figures
Rounding to three significant figures, we get:
\[ \pi \approx 7.84 \text{ atm} \]

### Final Answer
The osmotic pressure of a 10% solution of cane sugar at 69°C is approximately **7.84 atm**.

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