Which of the following solutions will give rise to a greater osmotic pressure at equilibrium: 5.00 g of NaCl in 350.0 mL water or 35.0 g of glucose in 400.0 mL water? For NaCl, MW = 58.5 amu; for glucose, MW = 180 amu.

Verified step by step guidance

1. Calculate the number of moles of NaCl using its mass (5.00 g) and molar mass (58.5 g/mol).
2. Determine the number of moles of glucose using its mass (35.0 g) and molar mass (180 g/mol).
3. Calculate the molarity of the NaCl solution by dividing the number of moles of NaCl by the volume of the solution in liters (0.350 L).
4. Calculate the molarity of the glucose solution by dividing the number of moles of glucose by the volume of the solution in liters (0.400 L).
5. Use the van 't Hoff factor to determine the effective concentration of particles in each solution, considering NaCl dissociates into two ions (Na^+ and Cl^-), and compare the osmotic pressures using the formula \( \pi = iMRT \), where \( i \) is the van 't Hoff factor, \( M \) is molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

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. The formula for osmotic pressure (π) is π = iCRT, where 'i' is the van 't Hoff factor (number of particles the solute dissociates into), 'C' is the molarity of the solution, 'R' is the ideal gas constant, and 'T' is the temperature in Kelvin.

Van 't Hoff Factor

The van 't Hoff factor (i) indicates the number of particles a solute dissociates into in solution. For example, NaCl dissociates into two ions (Na+ and Cl-), giving it an i value of 2, while glucose does not dissociate and has an i value of 1. This factor is crucial for calculating osmotic pressure, as it affects the total concentration of solute particles in the solution.

Molarity and Mass Calculations

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. To compare the osmotic pressures of the two solutions, one must first convert the mass of each solute into moles using their molar masses (MW). For NaCl, 5.00 g corresponds to approximately 0.0855 moles, while 35.0 g of glucose corresponds to about 0.194 moles, which will influence the osmotic pressure calculations.