Calculate the osmotic pressure at14°C of a solution of naphthalene (C10H8) in benzene containing0.156mol naphthalene per liter of solution. The osmotic pressure equation is

Π = 

*n*

*V*

·*R*·*T*
 
where Π is osmotic pressure, *n* is number of moles of solute, *V* is volume of solution, *R* is the ideal gas constant, and *T* is temperature.

To calculate the osmotic pressure \(\Pi\) of the solution, we'll use the formula:

\[
\Pi = \frac{n}{V} \cdot R \cdot T
\]

Where:
- \(\Pi\) is the osmotic pressure.
- \(n\) is the number of moles of solute.
- \(V\) is the volume of the solution in liters.
- \(R\) is the ideal gas constant (\(R = 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1}\)).
- \(T\) is the temperature in Kelvin.

### Given:
- Number of moles of naphthalene (\(n\)) = 0.156 mol/L
- Volume (\(V\)) = 1 L (since the concentration is given per liter)
- Temperature (\(T\)) = 14°C = 287.15 K (converted from Celsius to Kelvin by adding 273.15)

Now we can plug these values into the osmotic pressure formula:

\[
\Pi = \left(\frac{0.156 \, \text{mol}}{1 \, \text{L}}\right) \cdot 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \cdot 287.15 \, \text{K}
\]

Now, calculate:

\[
\Pi = 0.156 \cdot 0.0821 \cdot 287.15
\]

\[
\Pi \approx 3.67 \, \text{atm}
\]

### Final Answer:
The osmotic pressure \(\Pi\) of the solution at 14°C is approximately **3.67 atm**.

Would you like more details, or do you have any questions about this calculation? 

Here are five related questions:
1. How does the osmotic pressure change with temperature?
2. What effect does increasing the concentration of naphthalene have on osmotic pressure?
3. How would you calculate osmotic pressure for a solution with multiple solutes?
4. What assumptions are made in the ideal gas law when calculating osmotic pressure?
5. How does osmotic pressure relate to colligative properties?

**Tip:** Always ensure the temperature is in Kelvin when applying the osmotic pressure formula to avoid errors.

Learn how to calculate the osmotic pressure at 14°C of a solution of naphthalene in benzene using the ideal gas law formula. Understand the components involved: number of moles of solute, volume of solution, ideal gas constant, and temperature.

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