Calculation of Degree of Dissociation of K3[Fe(CN)6]

The Vant Hoff factor of a solution is defined as the ratio of the actual number of particles formed in a solution to the number of particles that would be present if the solute were completely dissociated in the solution. In this case, the Vant Hoff factor of K3[Fe(CN)6] is given as 3.333, which means that each formula unit of K3[Fe(CN)6] dissociates into 3.333 particles in the solution.

The degree of dissociation (α) of a solute is defined as the fraction of the total number of solute molecules that dissociate into ions in a solution. It is given by the formula:

α = (number of ions formed / initial number of solute molecules) x 100%

To calculate the degree of dissociation of K3[Fe(CN)6], we need to know the initial number of solute molecules in the solution. This can be obtained by dividing the number of moles of K3[Fe(CN)6] by the volume of the solution in liters.

Let us assume that we have a solution of K3[Fe(CN)6] with a concentration of 1 mol/L. The molar mass of K3[Fe(CN)6] is 329.26 g/mol, which means that 1 mol of K3[Fe(CN)6] weighs 329.26 g.

Therefore, the number of moles of K3[Fe(CN)6] in 1 liter of the solution is given as:

n = mass / molar mass = 1000 g / 329.26 g/mol = 3.038 mol

Now, we can calculate the initial number of solute molecules as:

N = n x Avogadro's number = 3.038 mol x 6.022 x 10^23/mol = 1.828 x 10^24 molecules

Next, we need to calculate the number of ions formed in the solution. Since each formula unit of K3[Fe(CN)6] dissociates into 3 ions, the total number of ions formed in the solution is:

nions = Vant Hoff factor x N = 3.333 x 1.828 x 10^24 = 6.094 x 10^24 ions

Finally, we can calculate the degree of dissociation as:

α = (number of ions formed / initial number of solute molecules) x 100%
= (6.094 x 10^24 / 1.828 x 10^24) x 100%
= 333.33%

Therefore, the degree of dissociation of K3[Fe(CN)6] is 333.33%. This means that about one-third of the K3[Fe(CN)6] molecules in the solution dissociate into ions.