Answer: 4.21×10⁻⁸
Step-by-step explanation:
1) Assume a general equation for the ionization of the weak acid:
Let HA be the weak acid, then the ionization equation is:
HA ⇄ H⁺ + A⁻
2) Then, the expression for the ionization constant is:
Ka = [H⁺][A⁻] / [HA]
There, [H⁺] = [A⁻], and [HA] = 0.150 M (data given)
3) So, you need to determine [H⁺] which you do from the pH.
By definition, pH = - log [H⁺]
And from the data given pH = 4.1
⇒ 4.10 = - log [H⁺] ⇒ [H⁺] = antilog (- 4.10) = 7.94×10⁻⁵
4) Now you have all the values to calculate the expression for Ka:
ka = 7.94×10⁻⁵ × 7.94×10⁻⁵ / 0.150 = 4.21×10⁻⁸