Question #410dd

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

#i = "what you get in solution"/"what you dissolve to make the solution"#

Potassium hydroxide, #"KOH"#, is a soluble ionic compound, which means that it dissociates completely to form potassium cations and hydroxide anions

#"KOH"_ ((aq)) -> "K"_ ((aq))^(+) + "OH"_ ((aq))^(-)#

Notice that every #1# mole of potassium hydroxide that dissolves in solution produces

• one mole of potassium cations, #1 xx "K"^(+)#
• one mole of hydroxide anions, #1 xx "OH"^(-)#

This means that for every mole of potassium hydroxide you dissolve in solution, you get #2# moles of particles of solute.

Therefore, the van't Hoff factor will be equal to #2#

#i = (1 color(red)(cancel(color(black)("mole K"^(+)))) + 1 color(red)(cancel(color(black)("mole OH"^(-)))))/(1color(red)(cancel(color(black)("mole KOH")))) = 2#

You can thus say that

#color(darkgreen)(ul(color(black)(i = 2))) -># you get twice as many moles of particles of solute in solution than the number of moles of solute you dissolved to make the solution