Question

The answer to this question is a single digit integer ranging from 0 to 9 the van't Hoff factor for aqueous solution of $CuS{O_4}.5{H_2}O$ will be

Answer 1

in the given question we have to find out the van’t Hoff factor of an aqueous solution. The van’t Hoff factor is a relationship in between the ideal value of a solution’s binding properties and the observed binding properties.

Complete step by step solution:
We can understand van’t Hoff factor as a factor which is relating to the binding of atoms and molecules. It is denoted by $i$ and is the number of particles produced in a solution from only one formula unit of solute.
Van’t Hoff factor = the total number of dissociated ions
The van’t Hoff factor for aqueous $CuS{O_4}.5{H_2}O$ solution –
$CuS{O_4}.5{H_2}O\xrightarrow{\Delta } CuS{O_4} + 5{H_2}O$
Further on heating CuSO4 we get ${Cu^{+2}}$ and ${{SO_4}^{-2}}$
Thus van’t Hoff factor is 2 for the aqueous solution of $CuS{O_4}.5{H_2}O$

Hence, the answer is 2.

Note: When solute particles associate in solution, then $i < 1$ for example, carboxylic acids such as acetic acid form dimers in benzene, in a form that the number of solute particles is half the number of acid molecules. When solute particles dissociate in solution, then $i > 1$ for example sodium chloride in water. When solute particles neither dissociate nor associate in solution, then $i = 1$ for example glucose in water.
The value of $i$ is the actual number of particles in solution after dissociation divided by the number of formula units initially dissolved in solution. That means the number of particles per formula unit of the solute when a solution is dilute.