MHT CET · Chemistry · Solutions

Relationship between van’t Hoff’s factor (i) and degree of dissociation $(α)$ is

A $i = \frac{α - 1}{n' - 1}$
B $i = \frac{α - 1}{1 - n'}$
C $α = \frac{1 - i}{n' - 1}$
D $α = \frac{i - 1}{n' - 1}$

Verified Solution

Answer & Solution

Correct Answer

(D) $α = \frac{i - 1}{n' - 1}$

Step-by-step Solution

Detailed explanation

Relationship between vant Hoff factor (i) and degree of dissociation

(α)

is given by

α = \frac{1 - i}{n' - 1}

Where, n is the number of ions formed after dissociation. The relationship can be obtained as follows: For the reaction,

A ⇌ n' B

Initially 1 mole 0
After dissociation

(1 - α)

mole n’

α

Total number of moles present in the solution

= (1 - α) + n^{'} α = 1 + (n^{'} - 1) α

Van’t Hoff factor,

i = 1 + (n^{'} - 1), α >

1 if

n' \geq 2

∴ α = \frac{i - 1}{n' - 1}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Relationship between van’t Hoff’s factor (i) and degree of dissociation α is

Step-by-step Solution

Relationship between van’t Hoff’s factor (i) and degree of dissociation $(α)$ is