A complex is represented as CoCl3.xNH3.

Its 0.1 molal soln in aq.solution shows depression in F.P of 0.558 degrees celsius.

Kf for H2O is 1.86

Assuming 100% ionisation of complex and coordination no. is 6, calculate formula of complex?

To determine the formula of the complex represented as CoCl3.xNH3, we can use the information provided about the depression in freezing point and the properties of the solution. Let’s break this down step by step.

Understanding Freezing Point Depression

Freezing point depression is a colligative property, which means it depends on the number of solute particles in a solution rather than their identity. The formula for freezing point depression is given by:

ΔTf = Kf × m × i

Where:

• ΔTf = depression in freezing point (in degrees Celsius)
• Kf = freezing point depression constant of the solvent (for water, Kf = 1.86 °C kg/mol)
• m = molality of the solution (in mol/kg)
• i = van 't Hoff factor, which represents the number of particles the solute dissociates into in solution

Calculating the Van 't Hoff Factor

Given that the depression in freezing point (ΔTf) is 0.558 °C and the molality (m) is 0.1 mol/kg, we can rearrange the formula to find the van 't Hoff factor (i):

i = ΔTf / (Kf × m)

Substituting the values:

i = 0.558 / (1.86 × 0.1) = 0.558 / 0.186 = 3

Interpreting the Van 't Hoff Factor

The van 't Hoff factor of 3 indicates that the complex dissociates into three particles in solution. Since we have CoCl3.xNH3, we need to consider how this complex dissociates.

Dissociation of the Complex

Assuming complete ionization, CoCl3.xNH3 can dissociate as follows:

CoCl3.xNH3 → Co^3+ + 3Cl^- + xNH3

This means that for every formula unit of CoCl3.xNH3, we get one cobalt ion (Co^3+), three chloride ions (Cl^-), and x ammonia molecules (NH3). Therefore, the total number of particles (i) can be expressed as:

i = 1 (for Co^3+) + 3 (for Cl^-) + x (for NH3)

Setting this equal to the calculated van 't Hoff factor:

1 + 3 + x = 3

Solving for x

From the equation above, we can solve for x:

x = 3 - 4 = -1

This result suggests that our assumption about the dissociation might need to be reconsidered. Since x cannot be negative, we need to reassess the coordination number and the actual dissociation.

Revising the Coordination Number

Given that the coordination number is 6, it is likely that the ammonia molecules are not dissociating but are part of the complex. Therefore, we can consider that the complex does not dissociate ammonia in the solution.

Thus, the correct dissociation would be:

CoCl3.xNH3 → Co^3+ + 3Cl^- + xNH3

In this case, we can assume that x = 3, which means there are three ammonia molecules coordinated to cobalt.

Final Formula of the Complex

Putting it all together, the formula of the complex can be represented as:

CoCl3·3NH3

This indicates that cobalt is coordinated with three ammonia molecules and three chloride ions, maintaining a coordination number of 6. Thus, the final formula of the complex is CoCl3·3NH3.