A decimolar solution of potassium ferrocyanide K4[Fe(CN)6] is 50% dissociated at 300K. Calculate the value of van't Hoff factor for potassium ferrocyanide.?

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Calculation of van't Hoff factor for potassium ferrocyanide

Step 1: Understanding van't Hoff factor

Van't Hoff factor (i) is defined as the ratio of the observed colligative property to the calculated colligative property. It is a measure of the degree of dissociation of a solute in a solution.

Step 2: Calculation of degree of dissociation

Given, a decimolar solution of potassium ferrocyanide K4[Fe(CN)6] is 50% dissociated at 300K.

Degree of dissociation (α) = 50/100 = 0.5

Step 3: Calculation of van't Hoff factor

The formula to calculate van't Hoff factor is:

i = 1 + α(n-1)

where n is the number of particles into which the solute dissociates.

Potassium ferrocyanide dissociates into four ions in solution: K+ and Fe(CN)6-4, each of which carries a charge of 1, and two CN- ions, each of which carries a charge of -1.

Therefore, n = 4

Substituting the values in the formula, we get:

i = 1 + 0.5(4-1) = 2.5

Therefore, the van't Hoff factor for potassium ferrocyanide is 2.5.

Step 4: Interpretation of result

The van't Hoff factor of 2.5 indicates that potassium ferrocyanide undergoes significant dissociation in solution. This is because the number of particles into which it dissociates is higher than the number of particles in a non-dissociating solute. The value of 2.5 is also consistent with the fact that potassium ferrocyanide is an electrolyte and therefore dissociates in solution.

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