The hydrolysis reaction for the salt NaIO is:
NaIO + H2O → HIO + NaOH
In this reaction, the sodium ion (Na+) is a spectator ion and does not participate in the reaction. The iodate ion (IO3-) reacts with water to form the iodic acid (HIO) and hydroxide ion (OH-). Since the hydroxide ion is produced in the reaction, the solution is basic.
The dissociation of HIO in water can be written as follows:
HIO + H2O ⇌ H3O+ + IO3-
The equilibrium constant expression for this reaction is:
Ka = [H3O+][IO3-]/[HIO]
Since the concentration of NaIO is given, we can assume that the initial concentration of HIO is equal to the concentration of NaIO. Let x be the concentration of H3O+ and IO3- that is formed when HIO dissociates. Then, we have:
Ka = x^2 / (0.050 - x)
Assuming that x is much smaller than 0.050, we can simplify this expression to:
Ka = x^2 / 0.050
Solving for x, we get:
x = sqrt(Ka * 0.050) = 1.52 * 10^-6 M
The pH of the solution is given by:
pH = -log[H3O+] = -log(x) = 5.82
Therefore, the pH of the solution is 5.82