Final answer:
The temperature at which a 0.0411 M solution of calcium nitrate exhibits an osmotic pressure of 3.14 atm is calculated using the formula II = MRT, where dissociation of the compound into three ions is considered.
Step-by-step explanation:
Calculating Osmotic Pressure of a Calcium Nitrate Solution
To answer the question of determining the temperature at which a 0.0411 M solution of calcium nitrate (Ca(NO₃)₂) will exhibit an osmotic pressure of 3.14 atm, we must use the formula for osmotic pressure:
II = MRT
Where:
- II is the osmotic pressure
- M is the molarity of the solution after accounting for dissociation
- R is the ideal gas constant (0.08206 L·atm/K·mol)
- T is the temperature in Kelvin
Since we know that calcium nitrate completely dissociates into three ions (1 Ca²⁺ and 2 NO₃⁻), the actual molarity (M) of particles is 0.0411 M × 3 = 0.1233 M.
Now, solving the formula for T:
T = II / (MR)
Plug in the values:
T = 3.14 atm / (0.1233 M × 0.08206 L·atm/K·mol)
Calculating this gives us the temperature in Kelvin. Be sure to convert it to degrees Celsius if needed by subtracting 273.15.