What is the freezing point of a solution of 5grams of CaCO3 and 10ml of H20?
The freezing point depression equation is
delta T = Kf*molality where Kf is 1.86 degrees/m for water. However, CaCO3 is not very soluble in water, certainly not to the extent of 5 g/10 mL water so one would need to go through the Ksp equation to determine the solubility, then apply delta T = i*Kf*m where i = 2.
To determine the freezing point of a solution, we need to know the total concentration of solute particles in the solution. In this case, we have 5 grams of CaCO3 dissolved in 10 ml of H2O.
1. Convert grams of CaCO3 to moles:
- The molar mass of CaCO3 is 100.09 g/mol.
- Divide 5 grams by the molar mass to get the number of moles: 5 g / 100.09 g/mol = 0.04995 moles.
2. Convert milliliters of H2O to liters:
- Divide 10 ml by 1000 to get the volume in liters: 10 ml / 1000 = 0.01 liters.
3. Calculate the concentration of solute particles:
- For each CaCO3 molecule, we get one Ca2+ ion and one CO32- ion, so there are a total of 0.04995 x 2 = 0.0999 moles of solute particles.
- The concentration is the number of moles divided by the volume: 0.0999 moles / 0.01 liters = 9.99 mol/L.
4. Use the equation for freezing point depression:
- The freezing point depression (ΔTf) is given by the formula: ΔTf = Kf * m.
- Kf is the cryoscopic constant, which depends on the solvent. For water, Kf is approximately 1.86 °C/m.
- m is the molal concentration, which is the concentration expressed in moles of solute per kilogram of solvent.
- We need to convert the concentration from mol/L to mol/kg. Since the density of water is about 1 kg/L, the concentration in mol/kg is the same as the concentration in mol/L.
- Plug in the values to calculate the freezing point depression: ΔTf = 1.86 °C/m * 9.99 mol/kg = 18.53 °C.
5. Determine the freezing point of the solution:
- Subtract the freezing point depression from the freezing point of pure water, which is 0 °C: 0 °C - 18.53 °C = -18.53 °C.
Therefore, the freezing point of the solution of 5 grams of CaCO3 and 10 ml of H2O is approximately -18.53 °C.