The degree of dissociation α is the fraction of the original solute molecules that have dissociated.
If you have a solution of "HCN" with a concentration of c color(white)(l)"mol/L" and degree of dissociation α, then at equilibrium you have
color(white)(mmmmmml)"HCN + H"_2"O" ⇌ "H"_3"O"^"+" + "CN"^"-"
"I/mol·L"^"-1": color(white)(mm)c color(white)(mmmmmmmll)0color(white)(mmml)0
"C/mol·L"^"-1":color(white)(m)"-"αc color(white)(mmmmmml) "+"αc color(white)(mll) "+"αc
"E/mol·L"^"-1": color(white)(m) c"-"αc color(white)(mmmmmmll) αc color(white)(mmll) αc
Thus, at equilibrium, the total concentration of all particles is
c "-" αc + αc + αc = c + αc = c(1+α)
The van't Hoff i factor is the number of moles of particles obtained from 1 mol of solute. That is,
i = (color(red)(cancel(color(black)(c)))(1+α))/color(red)(cancel(color(black)(c))) = 1 + α
i = "1.000 02" = 1 + α
α = "1.000 02 - 1" = "0.000 02"
"Percent dissociation" = α × 100 % = "0.000 02" × 100 % = 0.002 %
