Question

4. Ammonia is present in wastewater largely due to human urine, Unionized ammonia (NH) is the conjugate base of the ammonium ion (NH4+) with acid dissociation constant (KA) for NH4 equal to 5.7 x 10-10. Write the acid-base reaction for the deprotonation of the ammonium ion. Assume that a wastewater treatment plant does BOD oxidation only (ie., no ammonia removal). What is the dominant ammonia species in the wastewater at pH 7: unionized ammonia or ammonium ion? Prove your answer with calculations.

Answer 1

The acid - baser reaction for the dissociation of ammonium ion can be written as the following equation

$NH_4^+ _{(aq)} \rightarrow H^+_{(aq)} + NH_3_{(aq)}$

Where NH4+ is the acid and NH3 is the conjugate base.

For a generic reaction $aA \rightarrow bB + cC$ , the equilibrium constant K is written as

$K = \frac{[B]^b[C]^c}{[A]^a}$

Where the concentrations are the equilibrium values.

Hence, for our equation, we can write the expression of Ka for ammonium ion as follows:

$K_a = \frac{[H^+][NH_3]}{[NH_4^+]} = 5.7 \times 10^{-10}$

Now, we have to determine the relative concentrations of NH4+ and NH3 at pH 7 to find which one is the dominant species.

It is given that pH = 7.

We also know that pKa is defined as the negative logarithm of Ka.

Hence, taking the negative logarithm of the Ka expression above

$K_a = \frac{[H^+][NH_3]}{[NH_4^+]} = 5.7 \times 10^{-10} \\ \\ \Rightarrow -\log(K_a) = -\log\left ( \frac{[H^+][NH_3]}{[NH_4^+]} \right ) \\ \\ \Rightarrow -\log(5.7 \times 10^{-10}) = -\log[H^+] -\log(\frac{[NH_3]}{[NH_4^+]}) \\ \\ \Rightarrow 9.24 = pH -\log\left (\frac{[NH_3]}{[NH_4^+]} \right )$

Note that we have replace $pH = -\log[H^+]$ in the equation as it is defined as such.

Now,

$9.24 = pH -\log\left (\frac{[NH_3]}{[NH_4^+]} \right ) \\ \Rightarrow 9.24 = 7 -\log\left (\frac{[NH_3]}{[NH_4^+]} \right ) \\ \\ \Rightarrow \log \left ( \frac{[NH_3]}{[NH_4^+]} \right ) = 7-9.24 \approx -2.24 \\ \\ \Rightarrow \frac{[NH_3]}{[NH_4^+]} = 10^{-2.24} = 0.0057 \\ \\ \Rightarrow [NH_3] = 0.0057 [NH_4^+]$

Hence, clearly, the concentration of NH3 is much smaller than the concentration of NH4+ ion at pH 7. Hence, the dominant species at pH 7 is NH4+ ion.