Question

what would be the value of vant hoff's factor for a dilute solution of k2SO4 in water?

Answer 1

The dilute solution of K2SO4 dissociates into 2K+ and SO42-. Thus Vant Hoff factor is approximately 3. But in actual situation this value is less than 3 because in dilute solution salts do not ionize completely. 
approximate value for a very dilute solution is 3

Answer 2

Given:

Given ion is $K_2SO_4$.

To find:

We have to find the vant Hoff's factor.

Solution:

The vant Hoff's factor is denoted by the term "i".

In dilute solution $K_2SO_4$ dissociates as follows-

$K_2SO_4\rightarrow 2K^++SO_4^{2-}$

Change in number of moles after a time is given as-

For $K_2SO_4$= (1-a).

Number of moles of $K^+$ formed is 2a.

Number of moles of $SO_4^{2-}$ formed is a.

Where a is called dissociation factor.

Thus the vant Hoff factor can be given as-

$i = 1 - a + 2a + a \\ i = 1 + 2a$

For dilute solution a is 1.

Thus we can write-

$i = 1 + 2 \times 1 \\ i = 3$

Thus, the vant Hoff factor for $K_2SO_4$ is 3.