Derive an expression relating the van't Hoff factor and the degree of dissociation.

The van't Hoff factor (i) is defined as the ratio of the actual number of particles formed in a solution to the number of formula units initially dissolved.

Let's consider a generic salt, AB, that dissociates into A+ and B- ions in solution. If the initial concentration of AB is C, and the degree of dissociation is α, then the concentration of A+ and B- ions formed will be αC each.

Therefore, the total number of particles formed in solution is 1 + α + α = 1 + 2α.

The van't Hoff factor is then given by:

i = (total number of particles formed) / (number of formula units initially dissolved)
i = (1 + 2α) / 1
i = 1 + 2α

Therefore, the van't Hoff factor is directly related to the degree of dissociation by the expression:

i = 1 + 2α

The van 't Hoff factor (i) is a measure of the number of particles a solute produces when it dissociates in a solvent. It is defined as the ratio of the observed osmotic pressure of a solution to the osmotic pressure that would be expected if the solute did not dissociate.

The degree of dissociation (α) is the fraction of solute molecules that have dissociated. It can be expressed as:

```
α = (i - 1) / (n - 1)
```

where n is the number of ions produced by each solute molecule.

For example, if a solute dissociates into two ions (n = 2), then the degree of dissociation would be:

```
α = (i - 1) / (2 - 1) = (i - 1) / 1 = i - 1
```

Therefore, the van 't Hoff factor can be expressed in terms of the degree of dissociation as:

```
i = 1 + α
```