If 3.42 g of sugar (molar mass=342) are dissolved in 500ml of an aqueous solution at 300K, what will be its osmotic pressure?

Explanation

To calculate the osmotic pressure of the solution, we can use the formula:

\[ \pi = \frac{WRT}{MV} \]

Where:
- \(\pi\) = osmotic pressure
- \(W\) = mass of the solute (in grams)
- \(R\) = universal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)
- \(M\) = molar mass of the solute (in g/mol)
- \(V\) = volume of the solution (in liters)

### Step-by-step solution:

1. **Identify the given values:**
- Mass of sugar (W) = 3.42 g
- Molar mass of sugar (M) = 342 g/mol
- Volume of solution (V) = 500 mL = 0.5 L (conversion from mL to L)
- Temperature (T) = 300 K
- Universal gas constant (R) = 0.0821 L·atm/(K·mol)

2. **Substitute the values into the osmotic pressure formula:**
\[ \pi = \frac{3.42 \, \text{g} \times 0.0821 \, \text{L·atm/(K·mol)} \times 300 \, \text{K}}{342 \, \text{g/mol} \times 0.5 \, \text{L}} \]

3. **Calculate the numerator:**
\[ 3.42 \times 0.0821 \times 300 = 84.30906 \]

4. **Calculate the denominator:**
\[ 342 \times 0.5 = 171 \]

5. **Now divide the numerator by the denominator:**
\[ \pi = \frac{84.30906}{171} \approx 0.493 \]

6. **Round the answer:**
\[ \pi \approx 0.50 \, \text{atm} \]

### Final Answer:
The osmotic pressure of the solution is approximately **0.50 atm**.