Compute the pH of 1.0x10^-5 M NH4NO3.

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To calculate the pH of a solution, we need to look at the dissociation of the given compound. In this case, NH4NO3 is a salt that is produced by the combination of a weak acid (NH4+) and a strong base (NO3-).

Since NH4+ is a weak acid, it can undergo partial dissociation in water, while NO3- will remain as an ion. The dissociation equation for NH4NO3 can be written as:
NH4NO3 → NH4+ + NO3-

Since NH4+ is a weak acid, it will donate a proton (H+) to the water molecules, resulting in the formation of hydronium ions (H3O+). This process can be represented as:
NH4+ + H2O → NH3 + H3O+

Now we need to consider the equilibrium constant, which is the ratio of the concentration of the products to the concentration of the reactant. For this reaction, the equilibrium constant is represented as Ka.

To simplify our calculations, we will assume that NH3, the product of the reaction, does not undergo further reaction with water. This allows us to write the equilibrium expression as:
Ka = [NH3] * [H3O+] / [NH4+]

The concentration of NH4+ is given as 1.0 × 10^-5 M. Since NH3 is a weak base, we can assume that it will not significantly contribute to the H3O+ concentration. Therefore, the concentration of H3O+ can be considered negligibly small.

Thus, we can simplify the equation to:
Ka = [NH3] / [NH4+]

Now, we need to find the concentration of NH3. Since NH4+ and NH3 are a conjugate acid-base pair, they form a buffer solution. In a buffer solution, the concentration of the weak acid (NH4+) and its conjugate base (NH3) are related by the Henderson-Hasselbalch equation:

pH = pKa + log([A-] / [HA])

In this case, NH3 is the weak base and NH4+ is its conjugate acid. The equilibrium constant can be expressed as pKa = -log(Ka).

Given that Ka = [NH3] / [NH4+], you can rearrange the equation to determine [NH3] in terms of Ka and [NH4+]:
[NH3] = Ka * [NH4+]

Substituting this into the Henderson-Hasselbalch equation:
pH = pKa + log(Ka * [NH4+] / [NH4+])

Since [NH4+] is the same in both the numerator and denominator, they cancel out:
pH = pKa + log(Ka)

Now, you can calculate the pH using the given data. If you have the value of the pKa for the ammonium ion (NH4+), substitute that value into the equation and solve for pH.