1 solution containing 1.23 gram of Ca(NO3)2 in 10 gm of water boils at 100.975 celcious at 760 m.m. Calculate the degree of dissociation of Ca(No3)2. Hints- Kb(H2O)=0.468Kmol

To determine the degree of dissociation of calcium nitrate, Ca(NO3)2, in the given solution, we need to analyze the boiling point elevation caused by the solute. The boiling point elevation can be calculated using the formula:

Boiling Point Elevation Formula

The formula for boiling point elevation is:

ΔT_b = i * K_b * m

• ΔT_b = change in boiling point
• i = van 't Hoff factor (degree of dissociation)
• K_b = ebullioscopic constant of the solvent (for water, K_b = 0.468 K kg/mol)
• m = molality of the solution

Step 1: Calculate the Change in Boiling Point

The boiling point of pure water is 100°C, and the boiling point of the solution is 100.975°C. Therefore, the change in boiling point (ΔT_b) is:

ΔT_b = 100.975°C - 100°C = 0.975°C

Step 2: Calculate the Molality of the Solution

Next, we need to find the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. First, we calculate the number of moles of Ca(NO3)2:

The molar mass of Ca(NO3)2 is calculated as follows:

• Calcium (Ca): 40.08 g/mol
• Nitrogen (N): 14.01 g/mol × 2 = 28.02 g/mol
• Oxygen (O): 16.00 g/mol × 6 = 96.00 g/mol

Total molar mass = 40.08 + 28.02 + 96.00 = 164.10 g/mol

Now, we can find the number of moles of Ca(NO3)2 in 1.23 g:

Number of moles = mass / molar mass = 1.23 g / 164.10 g/mol ≈ 0.00749 moles

Since we have 10 g of water, we convert this to kilograms:

10 g = 0.010 kg

Now we can calculate the molality:

m = moles of solute / kg of solvent = 0.00749 moles / 0.010 kg = 0.749 mol/kg

Step 3: Substitute Values into the Boiling Point Elevation Formula

Now we can substitute the values into the boiling point elevation formula:

0.975°C = i * 0.468 K kg/mol * 0.749 mol/kg

Step 4: Solve for the van 't Hoff Factor (i)

Rearranging the equation to solve for i gives us:

i = 0.975°C / (0.468 K kg/mol * 0.749 mol/kg)

Calculating this yields:

i ≈ 2.77

Step 5: Determine the Degree of Dissociation

Calcium nitrate dissociates in solution as follows:

Ca(NO3)2 → Ca²⁺ + 2 NO3⁻

This means that one formula unit of Ca(NO3)2 produces three particles in solution (1 Ca²⁺ and 2 NO3⁻). Therefore, the theoretical van 't Hoff factor (i) for complete dissociation is 3.

The degree of dissociation (α) can be calculated using the relationship:

i = 1 + α(n - 1)

Where n is the number of particles produced per formula unit (which is 3 for Ca(NO3)2):

2.77 = 1 + α(3 - 1)

2.77 = 1 + 2α

1.77 = 2α

α = 1.77 / 2 = 0.885

Final Result

The degree of dissociation of Ca(NO3)2 in this solution is approximately 0.885, or 88.5%. This indicates that a significant portion of the calcium nitrate has dissociated into its constituent ions in the solution.