Final answer:
The hydronium ion concentration in a 0.160 M solution of formic acid is determined by calculating the square root of the product of the dissociation constant, Ka, and the formic acid concentration, assuming x is much less than the initial concentration of the acid.
Step-by-step explanation:
To determine the concentration of hydronium ions ([H3O+]) in a 0.160 M solution of formic acid with a known Ka of 1.8×10−4, we use the equilibrium expression for the dissociation of a weak acid:
HA ⇌ H+ + A−
Ka = [H+][A−]/[HA]
Since [H+] and [A−] are equal and the acid dissociates slightly, we can simplify the Ka expression:
Ka = x2 / (0.160 − x)
Assuming x << 0.160, we can approximate it as follows:
Ka ≈ x2 / 0.160
Solving for x (which is equal to [H3O+]), we get:
x = √(Ka × 0.160) = √(1.8×10−4 × 0.160)
After calculation, the x value is found and represents the concentration of H3O+.