Seawater contains 34 g of salts for every liter of solution. Assuming that the solute consists entirely of NaCl (in fact, over 90% of the salt is indeed NaCl), calculate the osmotic pressure of seawater at 20 °C

Verified step by step guidance

1. Identify the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. Determine the van't Hoff factor \( i \) for NaCl. Since NaCl dissociates into two ions (Na^+ and Cl^-), \( i = 2 \).
3. Convert the temperature from Celsius to Kelvin: \( T = 20 + 273.15 = 293.15 \text{ K} \).
4. Calculate the molarity \( M \) of the NaCl solution. First, find the molar mass of NaCl (Na: 22.99 g/mol, Cl: 35.45 g/mol), then use the given mass of NaCl (34 g/L) to find \( M = \frac{\text{mass of solute}}{\text{molar mass} \times \text{volume of solution in liters}} \).
5. Substitute the values into the osmotic pressure formula: \( \Pi = iMRT \), using \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \), and solve for \( \Pi \).

Key Concepts

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution, as described by the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molar concentration of the solute, R is the ideal gas constant, and T is the temperature in Kelvin.

Van 't Hoff Factor (i)

The van 't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution. For NaCl, which dissociates into two ions (Na⁺ and Cl⁻), the van 't Hoff factor is 2. This factor is crucial for calculating osmotic pressure, as it affects the total concentration of solute particles in the solution.

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. To calculate osmotic pressure, it is essential to convert the mass of solute (in this case, NaCl) into moles using its molar mass, and then determine the molarity of the solution. This concentration is a key component in the osmotic pressure equation.