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Chapter 15: Problem 86

Hydrazoic acid, HN \(_{3},\) is a weak acid. A 0.01 M solution of hydrazoic acid contained a concentration of 0.0005 \(\mathrm{M}\) of the \(\mathrm{N}_{3}^{-}\) ion. Find the acid-ionization constant of hydrazoic acid.

Short Answer

Expert verified
The acid-ionization constant \(Ka\) of hydrazoic acid is 0.000025.

Step by step solution

01

Identify given quantities

The molar concentration of hydrazoic acid is given as 0.01 M and that of the \(N_3^-\) ion is 0.0005 M.
02

Express \(Ka\)

The ionization constant of acid \(Ka\) is represented by the formula \[Ka = \frac{[N_3^-][H^+]}{[HN_3]}\] It's important to note that because hydrazoic acid is a weak acid, the concentrations of \(N_3^-\) and \(H^+\) after dissociation should be equal.
03

Substitute the values

Substitute the given values into the \(Ka\) equation. \[Ka = \frac{(0.0005)^2}{0.01}\] This is because [\(H^+\)] is equal to the concentration of the \(N_3^-\) ion, which is 0.0005 M.
04

Evaluate to find \(Ka\)

Use the rules of arithmetic to solve for \(Ka\). \[Ka = \frac{0.00000025}{0.01} = 0.000025\]

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