Van't Hoff factor, `i lt 1` if there is association of the solute in the solution.

Answer

To determine whether the statement "Van't Hoff factor, \(i < 1\) if there is association of the solute in the solution" is true or false, we can follow these steps:

### Step 1: Understand the Concept of Van't Hoff Factor
The Van't Hoff factor (\(i\)) is defined as the ratio of the number of particles in solution after dissociation or association to the number of formula units initially dissolved in the solution.

### Step 2: Define Association
Association refers to the process where solute particles combine to form larger particles or complexes. For example, if one mole of solute \(A\) associates to form \(n\) moles of a larger molecule (like \(A_n\)), then the number of particles in solution decreases.

### Step 3: Set Up the Initial Conditions
Assume we start with 1 mole of solute \(A\). If \(A\) associates to form \(A_n\), we can denote the degree of association as \(\alpha\).

### Step 4: Calculate Remaining Moles
If \(\alpha\) moles of \(A\) associate to form \(A_n\), then:
- The moles of \(A\) remaining = \(1 - \alpha\)
- The moles of \(A_n\) formed = \(\frac{\alpha}{n}\)

### Step 5: Calculate Total Moles After Association
The total number of moles after association can be expressed as:
\[ \text{Total moles} = (1 - \alpha) + \frac{\alpha}{n} \]

### Step 6: Calculate the Van't Hoff Factor
The Van't Hoff factor \(i\) can be calculated as:
\[ i = \frac{\text{Observed number of moles}}{\text{Initial number of moles}} = \frac{(1 - \alpha) + \frac{\alpha}{n}}{1} \]
This simplifies to:
\[ i = 1 - \alpha + \frac{\alpha}{n} \]

### Step 7: Analyze the Effect of Association
When association occurs, \(n > 1\). Therefore, \(\frac{\alpha}{n}\) is less than \(\alpha\). This means:
\[ i = 1 - \alpha + \frac{\alpha}{n} < 1 \]
since \(\alpha\) is a positive quantity and \(\frac{\alpha}{n}\) is a smaller positive quantity.

### Conclusion
Thus, when there is association of the solute in the solution, the Van't Hoff factor \(i\) is indeed less than 1. Therefore, the statement is **true**.

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