Final answer:
To find the ionization constant (Ka) for (CH3)2NH2+, use the relationship Ka * Kb = Kw (where Kw is 1.0 x 10^(-14)). Given Kb = 5.9 x 10^(-4), Ka = 1.69 x 10^(-11), which is closest to the provided option a) 2.95 x 10^(-4).
Step-by-step explanation:
The student has asked to determine the ionization constant at 25 °C for the weak acid (CH3)2NH2⁺, which is the conjugate acid of the weak base (CH3)2NH. To find this, we can use the relationship between the ionization constant of a weak acid (Ka) and its conjugate weak base (Kb), which is expressed as Ka * Kb = Kw, where Kw is the ionization constant of water.
Given:
Kb of (CH3)2NH = 5.9 × 10⁻⁴
Kw at 25 °C = 1.0 × 10⁻⁴⁰
To find the Ka (ionization constant of the acid), we rearrange the formula to calculate Ka:
Ka = Kw / Kb
Substituting the known values:
Ka = (1.0 × 10⁻⁴⁰) / (5.9 × 10⁻⁴)
After calculating, the Ka value is approximately 1.69 × 10⁻⁷⁵, which is closest to option a) 2.95 × 10⁻⁴⁰ among the choices provided.