Question

After waste-water treatment in the activated sludge process, nitrogen is mainly in the form of ammonia and ammonium ion. Plot the fraction of nitrogen that is in the ammonia form (and therefore strippable by air purging) as a function of pH (at \(25^{\circ} \mathrm{C}\) ) over the \(\mathrm{pH}\) range from 6 to 10 .

Short answer

The fraction of nitrogen in ammonia form increases with pH, approaching 1 as pH increases.

Step-by-step solution

Understand the Chemical Equilibrium

Ammonia (\(NH_3\)) and ammonium ion (\(NH_4^+\)) exist in equilibrium in water. This equilibrium can be described by the reaction:\[ NH_4^+ \rightleftharpoons NH_3 + H^+ \]The fraction of nitrogen in the ammonia form depends on the pH of the solution.

Write the Equilibrium Equation

The equilibrium constant, \(K_a\), for the dissociation of ammonium ion into ammonia and hydrogen ion is given by:\[K_a = \frac{[NH_3][H^+]}{[NH_4^+]}\]At \(25^{\circ}C\), the value of \(K_a\) is approximately \(5.6 \times 10^{-10}\).

Calculate Ammonia Fraction

To find the fraction of nitrogen as ammonia, use the equation:\[f_{NH_3} = \frac{[NH_3]}{[NH_3] + [NH_4^+]}\]Rearrange the equilibrium expression to substitute \([NH_3]\) in terms of \([H^+]\) and \([NH_4^+]\).

Express in terms of Hydrogen Concentration

Express \([NH_3]\) using the equilibrium constant:\[[NH_3] = \frac{K_a [NH_4^+]}{[H^+]}\]Substitute this into the fraction equation:\[f_{NH_3} = \frac{\frac{K_a [NH_4^+]}{[H^+]}}{\frac{K_a [NH_4^+]}{[H^+]} + [NH_4^+]}\]

Simplify the Expression

Simplify \(f_{NH_3}\):\[f_{NH_3} = \frac{1}{1 + \frac{[H^+]}{K_a}}\]Convert \([H^+]\) using \(pH = -\log[H^+]\), thus \([H^+] = 10^{-pH}\).

Evaluate Fraction Across pH

For pH values from 6 to 10, calculate \(f_{NH_3}\):For example, at pH 6,\[f_{NH_3} = \frac{1}{1 + 10^{6} \times 5.6 \times 10^{-10}} \approx \frac{1}{1 + 5.6 \times 10^{-4}} \approx 0.99944\]Repeat for each pH value to get the fraction of ammonia.

Key concepts

Nitrogen Speciation

In nature and engineered systems such as wastewater treatment, nitrogen can be found in various forms. These forms are collectively known as nitrogen species. Nitrogen speciation is important because different nitrogen compounds have different behaviors and impacts on the environment. For example, ammonia (\(NH_3\)) is toxic to aquatic life, while nitrate (\(NO_3^-\)) can contribute to algae blooms if overabundant in natural waters. In wastewater treatment, controlling the nitrogen forms is crucial for reducing pollution. As wastewater undergoes treatment processes like activated sludge, ammonium ions (\(NH_4^+\)) are present and can convert to ammonia under certain conditions. Understanding nitrogen speciation helps environmental engineers manage these transformations effectively and design treatment facilities that minimize nitrogen-related pollution risks. This is essential for compliance with environmental regulations aimed at protecting water bodies from contamination.

Ammonia and Ammonium Equilibrium

Ammonia (\(NH_3\)) and the ammonium ion (\(NH_4^+\)) exist in a delicate balance within water. This relationship is called ammonia-ammonium equilibrium and is governed by the chemical equation:\[ NH_4^+ \rightleftharpoons NH_3 + H^+ \]The position of this equilibrium depends largely on the pH level of the solution. At a higher pH, more ammonia is present, while at a lower pH, more ammonium ions are present. This is because ammonia is the base form and ammonium is the acidic form of nitrogen in water.A key factor in this equilibrium is the equilibrium constant, known as \(K_a\), which at 25^{\circ}C is approximately \(5.6 \times 10^{-10}\). This constant helps calculate the proportions of ammonia and ammonium ions present at any given pH value. Thus, knowing the pH allows for the calculation of ammonia's fraction and its subsequent removal from water.This equilibrium understanding is particularly critical in wastewater management where ammonia needs to be controlled due to its volatility and toxicity.

pH and Chemical Equilibrium

The pH of a solution is a crucial factor affecting the chemical equilibrium between ammonia and ammonium ions. pH measures the concentration of hydrogen ions (\([H^+]\)) in a solution. Given that the equation for equilibrium includes these ions:\[ K_a = \frac{[NH_3][H^+]}{[NH_4^+]} \]The concentration of hydrogen ions (\([H^+]\)) directly influences this balance. Lower pH (meaning higher \([H^+]\) concentration) shifts the equilibrium towards ammonium (\(NH_4^+\)), while higher pH shifts it towards ammonia (\(NH_3\)).The fraction of nitrogen in the form of ammonia can be expressed as:\[ f_{NH_3} = \frac{1}{1 + \frac{10^{-pH}}{K_a}} \]This equation shows how pH affects the concentration of ammonia relative to ammonium ions in water. Hence, monitoring and adjusting the pH of wastewater is essential for controlling nitrogen in its ammonia form. As the pH increases from 6 to 10, the fraction of ammonia also increases, making it easier to remove by methods such as air stripping during wastewater treatment.