The osmotic pressure of 5% (mass/volume) solution of cane sugar at 50 degree celsius 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 (C12H22O11) at 50 degrees Celsius, we can follow these steps:

### Step 1: Understand the concentration of the solution
A 5% (mass/volume) solution means that there are 5 grams of cane sugar in 100 mL of solution.

### Step 2: Convert the volume from mL to L
Since osmotic pressure is typically calculated using liters, we need to convert 100 mL to liters:
\[ \text{Volume (L)} = \frac{100 \text{ mL}}{1000} = 0.1 \text{ L} \]

### Step 3: Calculate the number of moles of cane sugar
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of cane sugar (C12H22O11) is approximately 342 g/mol. Thus, the number of moles is:
\[ \text{Number of moles} = \frac{5 \text{ g}}{342 \text{ g/mol}} \approx 0.0146 \text{ moles} \]

### Step 4: Calculate the concentration (C)
The concentration (C) in moles per liter is given by:
\[ C = \frac{\text{Number of moles}}{\text{Volume (L)}} = \frac{0.0146 \text{ moles}}{0.1 \text{ L}} = 0.146 \text{ M} \]

### Step 5: Use the osmotic pressure formula
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = CRT \]
Where:
- \(C\) is the concentration in moles per liter,
- \(R\) is the ideal gas constant (0.0821 L·atm/(K·mol)),
- \(T\) is the temperature in Kelvin.

### Step 6: Convert the temperature to Kelvin
To convert 50 degrees Celsius to Kelvin:
\[ T(K) = 50 + 273 = 323 \text{ K} \]

### Step 7: Calculate the osmotic pressure
Now substituting the values into the osmotic pressure formula:
\[ \pi = (0.146 \text{ M}) \times (0.0821 \text{ L·atm/(K·mol)}) \times (323 \text{ K}) \]
Calculating this gives:
\[ \pi \approx 3.88 \text{ atm} \]

### Conclusion
The osmotic pressure of the 5% (mass/volume) solution of cane sugar at 50 degrees Celsius is approximately **3.88 atm**.

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