Given that isotonic solutions have the same osmotic pressure, we equate the osmotic pressures of the K
2SO
4 and glucose solutions :
i×0.004M=0.01M
Here,
i is the van't Hoff factor, which accounts for the number of ions the compound dissociates into in the solution. Solving this equation for
i, we get
i=2.5.
For the compound K
2SO
4, which dissociates into 3 ions (2K
+ and 1 SO
42-), the formula for
i is given by
i=1+(n−1)α
where
n is the number of ions the solute dissociates into and
α is the degree of dissociation.
Substituting
n=3 and
i=2.5 into this formula and solving for
α gives
α=n−1i−1=3−12.5−1=0.75
To convert this into a percentage, we multiply by 100, yielding a percentage dissociation of 75%.