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J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry 4th edition

Problem 15.50

Hydrazoic acid, HN3 (pKa = 4.72), is perhaps best known through its sodium salt, sodium azide, NaN3, the gas forming substance in automobile air-bag systems. What molarity of HN3 is required to produce an aqueous solution with pH = 3.10?






Answer:

Write the balanced equation, write the mass action expression for Ka, find Ka from pKa, set up a table of concentrations, and solve from there.

HN3(aq)
+
H2O(l)
H3O+(aq)
+
N3(aq)
Initial
Cinit
0
0
Change
– x
+x
+x
Equilibrium
Cinit – x
x
x

In this case we do not know the initial concentration so we need to find x from some other information: the pH.

x = [H3O+] = 10–pH = 10–3.10 = 7.9×10–4 M

Now we can plug into the mass action expression, knowing the value of x:

so the initial concentration of HN3 = 0.033 M