A 0.505-g sample of a compound is dissolved in enough water to form 100.0 mL of solution. This solution has an osmotic pressure of 2.56 atm at 25°C. If each molecule of the solute dissociates into two particles (in this solvent), what is the molar mass of this solute?
pi = inRT
pi = 2.56 atm
i = 2
R = 0.08206
T = 298K
Solve for n, then n = grams/molar mass
You know grams and n, solve for molar mass.
To find the molar mass of the solute, we can use the formula:
Molar mass (g/mol) = (0.0821 * T * V) / (π * i * P)
Where:
- 0.0821 is the ideal gas constant (atm * L / mol * K)
- T is the temperature in Kelvin (25°C = 298K)
- V is the volume of the solution in liters (100.0 mL = 0.100 L)
- π is a mathematical constant, approximately equal to 3.14159
- i is the van't Hoff factor (the number of particles the solute dissociates into, in this case, 2)
- P is the osmotic pressure in atm (2.56 atm)
Now let's substitute these values into the formula:
Molar mass (g/mol) = (0.0821 * 298K * 0.100 L) / (π * 2 * 2.56 atm)
Calculating this expression will give us the molar mass of the solute.