how many grams of calcium nitrate need to be dissolved in 250 mL of water to form a solution that has a freezing temperature of -3.2 degrees C
delta T =i*Kf*molality
Solve for molality. i = 3
m = mols/kg solvent
Solve for moles.
moles = grams/molar mass
Solve for grams.
To determine the number of grams of calcium nitrate needed to form a solution with a freezing temperature of -3.2 degrees Celsius, you need to use the concept of molality and the freezing point depression constant.
Here's the step-by-step process:
1. Identify the freezing point depression constant (Kf) for water. For water, the Kf value is 1.86 °C/m. This means that for every 1 molal (1 mol/kg) solution, the freezing point decreases by 1.86 °C.
2. Calculate the molality (m) of the solution using the freezing point depression formula: ΔT = Kf * m. Rearrange the formula to solve for molality: m = ΔT / Kf.
ΔT is the change in freezing point temperature, which is (-3.2 °C - 0 °C) = -3.2 °C.
Kf is the freezing point depression constant for water, which is 1.86 °C/m.
m = -3.2 °C / 1.86 °C/m = -1.72 m.
3. Determine the molar mass of calcium nitrate (Ca(NO3)2). The molar mass of calcium (Ca) is 40.08 g/mol, the molar mass of nitrogen (N) is 14.01 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol.
Ca(NO3)2 = 1 * (40.08 g/mol) + 2 * (14.01 g/mol) + 6 * (16.00 g/mol) = 164.09 g/mol.
4. Calculate the mass of calcium nitrate required using the molality of the solution.
Mass (g) = m * molar mass (g/mol) * solvent mass (kg).
In this case, the solvent mass is given as 250 mL, which is 0.25 kg (since 1 mL of water is roughly equal to 1 g).
Mass (g) = -1.72 m * 164.09 g/mol * 0.25 kg = -111.97 g.
Since you cannot have a negative mass, the result is only the absolute value: 111.97 g of calcium nitrate would need to be dissolved in 250 mL of water to form a solution with a freezing temperature of -3.2 degrees Celsius.