Question

Question #7517e

Answer 1

`i = 5/4`

Explanation:

The van't Hoff factor, `i`, tells you the ratio that exists between the number of moles of solute dissolved in solution and the number of moles of particles of solute present in solution.

`i = "total number of moles of particles of solute"/"number of moles of solute dissolved in solution"`

Now, you know that `50%` of the electrolyte dissociates completely to produce ions

`"AB"_ ((aq)) -> "A"_ ((aq))^(+) + "B"_ ((aq))^(-)`

Notice that ever mole of `"AB"` that dissociates produces `1` mole of `"A"^(+)` and `1` mole of `"B"^(-)`, or

`"1 mole A"^(+) + "1 mole B"^(-) = color(red)(2)color(white)(.)"moles ions"`

If we take `x` to be the total number of moles of `"AB"` dissolved in solution, you can say that

• `color(blue)(x * 0.5) ->` the number of molecules that dissociate
• `color(purple)(x * 0.5) ->` the number of molecules that dimerise

For every mole of `"AB"` that dissociates, you have `color(red)(2)` moles of ions, so the solution will contain

`color(red)(2) * color(blue)(x * 0.5) = x ->` the number of moles of ions

Now, the other `50%` of the molecules dimerise, i.e. the bond together to form a dimer.

`"AB"_ ((aq)) + "AB"_ ((aq)) -> ("AB")_ (2(aq))`

This means that for every `1` mole of molecules that dimerise, you get `1/2` moles of dimers in the resulting solution, so

`1/2 * color(purple)(x * 0.5) = (1/4 * x) ->` the number of moles of dimers

This means that the total number of moles of particles of solute present in the solution will be

`x + 1/4 * x = 5/4 * x`

This means that the van't Hoff factor will be

`i = (5/4 * color(red)(cancel(color(black)(x))))/(color(red)(cancel(color(black)(x)))) = 5/4`