What is the H3O+ ion concentration in a 0.1 M NH3 solution with Kb = 1.8 x 10-5? (a) 7.5 x 10-12 (b) 3.0 x 10-10 (c) 1.8 x 10-6 (d) 1.3 x 10-3 (e) none of these
Chemistry · Sun Jul 10 2022
Answered on
To find the H3O+ ion concentration in a 0.1 M NH3 solution, we need to use the concept of the ionization of water and the Kb value of NH3.
First, let's write out the balanced equation for the ionization of NH3 in water: NH3 + H2O ⇌ NH4+ + OH-
The Kb value represents the equilibrium constant for the reaction. It can be given by the equation: Kb = [NH4+][OH-] / [NH3]
Given that the Kb value for NH3 is 1.8 x 10-5, we can set up the equation: 1.8 x 10-5 = [NH4+][OH-] / [NH3]
Since we are interested in the H3O+ ion concentration, we can use the relationship: [H3O+] = Kw / [OH-] where Kw is the ionization constant of water and it is equal to 1.0 x 10-14 at 25°C.
Using the equation above, we need to find the [OH-] concentration. To do this, we can rearrange the equation for Kb: Kb = [NH4+][OH-] / [NH3] [OH-] = Kb * [NH3] / [NH4+]
Now, we can substitute the values into the equation: [OH-] = (1.8 x 10-5) * (0.1) / (0.1) [OH-] = 1.8 x 10-5
Lastly, we can calculate the H3O+ ion concentration: [H3O+] = Kw / [OH-] [H3O+] = (1.0 x 10-14) / (1.8 x 10-5) [H3O+] = 5.56 x 10-10
Therefore, the H3O+ ion concentration in a 0.1 M NH3 solution is approximately 5.56 x 10-10 M.
The question involves the concept of acid-base equilibria and the ionization of weak bases. NH3 is a weak base that can accept a proton (H+) to form NH4+. The equilibrium constant Kb is a measure of how well NH3 can accept a proton, and a higher Kb value indicates a stronger base. In this case, NH3 has a relatively small Kb value, which means it is a weak base.
To find the H3O+ ion concentration in the NH3 solution, we can use the Kb value and the concept of the ionization of water. Water can dissociate into H3O+ and OH- ions, and their concentrations are related by the ionization constant of water, Kw. By calculating the OH- concentration using the Kb value, we can then determine the H3O+ ion concentration using the relationship between H3O+ and OH- concentrations.
It is important to understand the concepts of equilibrium constant, acid-base equilibrium, and the ionization of water to solve this type of question accurately.