Calculate the H3O+ ion concentration and the pH at the equivalence point when 45.0 mL of 0.4000 M NH3 is mixed with 45.0 mL of 0.4000 M HCl.

Ka=5.6x10-10

To calculate the H3O+ ion concentration and the pH at the equivalence point, we need to determine the number of moles of NH3 and HCl.

First, let's determine the number of moles of NH3. We can use the formula:

moles = concentration (M) * volume (L)

moles of NH3 = 0.4000 M * 0.0450 L = 0.0180 moles

Similarly, let's calculate the number of moles of HCl:

moles of HCl = 0.4000 M * 0.0450 L = 0.0180 moles

Since NH3 and HCl react in a 1:1 ratio according to the balanced chemical equation:

NH3 + HCl -> NH4Cl

At the equivalence point, all of the NH3 will react, leaving no excess NH3 in the solution. Therefore, the number of moles of HCl used will be equal to the number of moles of NH3 initially present (0.0180 moles).

Now, let's calculate the concentration of NH4+ ions formed as a result of the reaction:

moles of NH4+ = moles of NH3 = 0.0180 moles

We can find the concentration of NH4+ ions by dividing the number of moles by the total volume of the solution (0.0450 L + 0.0450 L = 0.0900 L):

concentration of NH4+ ions = moles of NH4+ / volume (L) = 0.0180 moles / 0.0900 L = 0.2000 M

At the equivalence point, NH4+ is a weak acid that will dissociate to form H3O+ ions and NH3. Since the reaction is occurring in water, we can assume that the concentration of water (H2O) remains constant.

Using the balanced chemical equation for the dissociation of NH4+:

NH4+ + H2O -> H3O+ + NH3

We can say that at the equivalence point, the concentration of H3O+ ions will be equal to the concentration of NH4+ ions, which is 0.2000 M.

The pH of a solution can be calculated using the formula:

pH = -log[H3O+]

So, let's calculate the pH using the concentration of H3O+:

pH = -log(0.2000) = 0.6990

Therefore, at the equivalence point, the H3O+ ion concentration is 0.2000 M, and the pH of the solution is 0.6990.