To calculate the percent ionization of hydrazoic acid (HN3) in solutions of different concentrations, we need to use the given Ka value for hydrazoic acid and the equilibrium expression for ionization:
HN3 โ H+ + N3-
The equation for the ionization constant (Ka) is:
Ka = [H+][N3-]/[HN3]
Now, let's calculate the percent ionization for each given concentration:
A) Concentration = 0.377 M
First, we need to find the initial concentration of HN3 that will be used in the denominator of the Ka expression. Assuming HN3 fully ionizes, the initial concentration of HN3 at equilibrium will be equal to the given concentration:
[HN3] = 0.377 M
Since we don't know the equilibrium concentrations of H+ and N3-, we can assume they are x M. Thus, the equilibrium concentrations of H+ and N3- can be written as:
[H+] = [N3-] = x M
Using the equilibrium expression for Ka, we get:
(1.9*10^-5) = (x)(x) / (0.377 - x)
Solving this equation will give us the value of x, which represents the equilibrium concentrations of H+ and N3-.
B) Concentration = 0.107 M
Following the same steps as in part A, we assume the equilibrium concentrations of H+ and N3- as x M. The initial concentration of HN3 at equilibrium is:
[HN3] = 0.107 M
Using the equilibrium expression for Ka, we have:
(1.9*10^-5) = (x)(x) / (0.107 - x)
Solving this equation will give us the value of x.
C) Concentration = 4.16*10^-2 M
Again, following the same steps, we assume the equilibrium concentrations of H+ and N3- as x M. The initial concentration of HN3 at equilibrium is:
[HN3] = 4.16*10^-2 M
Using the equilibrium expression for Ka, we have:
(1.9*10^-5) = (x)(x) / (4.16*10^-2 - x)
Solving this equation will give us the value of x.
Once we determine the value of x, we can calculate the percent ionization using the equation:
Percent ionization = (x/[HN3]) * 100
For each concentration, plug in the value of x obtained from solving the equations and divide by the initial concentration [HN3], then multiply by 100 to convert the fraction to a percentage.