Question

What is the concentration of Ammonia in the solution?
A solution is prepared by dissolving \[0.20mol\] mol of acetic acid and \[0.20mol\] of ammonium chloride in enough water to make \[1.0L\] of solution. Find the concentration of Ammonia in the solution.

Answer 1

Hint : Ammonia is a nitrogen-hydrogen compound with the formula \[N{H_3}\]. While abundant in nature, both on Earth and the Solar System's outer planets, and widely used, Ammonia is caustic and hazardous in condensed form.

Complete Step By Step Answer:
While both acetic and ammonium chloride are weak acids, ammonium chloride is nearly a million times weaker. As a result, Ammonium Chloride has a "common-ion effect" equilibrium problem.
The \[Ka\] value of acetic acid determines how it dissociates. The \[{H^ + }\] ions in the solution then enter into the Ammonium Chloride equilibrium, and you get a reduced dissociation into Ammonia.
For Acetic Acid:
\[HOAc = {H^ + } + OA{c^ - }\]
Initial concentration,
\[0.2M\]\[0M\]\[0M\]
Let \[x\] mole per litre of each of the product be formed.
At equilibrium:
\[\left( {C - x} \right)M\]\[xM\]\[xM\]
\[\left( {E0.2} \right)M\]\[xM\]\[xM\]
Where \[x\] is the amount of \[{H^ + }\] and \[0A{c^ - }\] at equilibrium.
Hence, equilibrium constant can be written as,
\[Ka = \dfrac{{{x^2}}}{{0.2M}} = 1.8 \times {10^{ - 5}}\]
After solving this, we got \[x = 0.0019M\]
Therefore, \[{H^ + } = 0.0019M\]
Now, consider Ammonium Chloride with \[Ka = 5.6 \times {10^{ - 10}}\]
\[NH_4^ + = N{H_3} + {H^ + }\]
Initial concentration,
\[0.2M\]\[0M\]\[0.0019M\]
Let \[x\] mole per litre of each of the product be formed.
At equilibrium:
\[\left( {C - x} \right)M\]\[xM\]\[xM\]
\[\left( {E0.2 - x} \right)\]\[x0.0019\]\[x\]
Where \[x\] is the amount of \[N{H_3}\] and \[{H^ + }\] at equilibrium.
Hence, equilibrium constant can be written as,
\[Ka = \dfrac{{x\left( {0.0019 + x} \right)}}{{0.2}} = 5.6 \times {10^{ - 10}}\]
That is, \[{x^2} + 0.0019x - 1.12 \times {10^{ - 12}} = 0\]
After solving this, we got \[x = 5.89 \times {10^{ - 10}}M = \left[ {N{H_3}} \right]\]
So, the concentration of Ammonia is \[5.89 \times {10^{ - 10}}M\] .

Additional Information:
The acid dissociation constant, abbreviated as \[Ka\], is the equilibrium constant of an acid's dissociation reaction. This equilibrium constant is a numerical representation of an acid's power in a solution.

Note :
Ammonia is a precursor for amino acid and nucleotide synthesis and is needed for many biological processes. Ammonia is the component of the nitrogen cycle in the ecosystem, and it is formed in soil by bacterial processes. Ammonia is also formed naturally when organic matter, such as plants, livestock, and animal waste, decomposes.