Understanding the pH of a 0.30 M Ammonia Solution with KB8×10-5

Ammonia, a widely used weak base, is known for its distinctive smell and versatile applications. One intriguing aspect of ammonia is its reaction in aqueous solutions. This article delves into the pH calculation of a 0.30 M ammonia solution. By understanding the base dissociation constant (Kb) and the equilibrium process, we can uncover the concentration of hydroxide ions and therefore the pH.

Overview of Ammonia as a Weak Base

Ammonia (NH3) is a weak base that reacts with water (H2O) to form ammonium ions (NH4 ) and hydroxide ions (OH-). This process can be represented by the following equilibrium reaction:

NH3 H2O ? NH4 OH-

Dissociation Equation and Base Dissociation Constant (Kb)

The equilibrium constant for this reaction is known as the base dissociation constant (Kb), which is given as (8 times 10^{-5}).

Using the expression for Kb:

(K_b frac{[NH_4^ ][OH^-]}{[NH_3]})

We can substitute the expressions for the equilibrium concentrations. Let (x) represent the concentration of OH- produced at equilibrium. Initially, the concentration of NH3 is 0.30 M, and at equilibrium, it becomes (0.30 - x). Thus, the equilibrium concentrations can be represented as:

([NH_3] 0.30 - x)

([NH_4^ ] x)

([OH^-] x)

Calculations and Assumptions

Substituting these into the Kb expression, we get:

8 ( times ) 10-5 (frac{x^2}{0.30 - x})

For simplicity, assuming (x) is small compared to 0.30 M (i.e., (0.30 - x approx 0.30)), we can simplify the expression:

8 ( times ) 10-5 ≈ (frac{x^2}{0.30})

Solving for (x): [x^2 8 ( times ) 10-5 ( times ) 0.30] [x sqrt{2.4 ( times ) 10-5} approx 4.89 ( times ) 10-3 M]

This value of (x) represents the concentration of hydroxide ions [OH-].

Calculating pOH and pH

With the concentration of hydroxide ions, we can calculate the pOH using the following expression:

pOH -log[OH-] -log(4.89 ( times ) 10-3) ≈ 2.31

Finally, using the relationship between pH and pOH:

pH pOH 14

pH 14 - pOH 14 - 2.31 ≈ 11.69

Thus, the pH of the 0.30 M ammonia solution is approximately 11.69.

Conclusion

Understanding the pH of a 0.30 M ammonia solution not only enhances our knowledge of chemical equilibrium but also highlights the significance of Kb values in real-life applications. This process demonstrates the importance of equilibrium constants in determining the behavior of weak bases in aqueous solutions.