What Is The Ph At The Equivalence Point For The Titration Of 0.20 M Nitrous Acid By 0.20 M Sodium Hydroxide?
Understanding the pH at the equivalence point of a titration between nitrous acid (HNO₂) and sodium hydroxide (NaOH) is fundamental in analytical chemistry. This specific titration involves a weak acid (nitrous acid) being neutralized by a strong base (sodium hydroxide), resulting in a pH that reflects the properties of the resulting solution. The equivalence point is the moment when the amount of added titrant (NaOH) exactly neutralizes the analyte (HNO₂), leading to a solution primarily composed of the conjugate base (NO₂⁻). Determining the pH at this stage involves understanding the acid-base chemistry, the dissociation constants, and the resulting hydrolysis reactions.
In this comprehensive article, we will explore what the pH at the equivalence point is for this specific titration, delve into the chemical principles involved, and provide step-by-step calculations to arrive at the precise pH value. We will also discuss the significance of this pH in the context of titration curves and analytical chemistry. Whether you're a student preparing for exams or a chemistry enthusiast seeking a deeper understanding, this guide aims to clarify the concepts thoroughly.
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Understanding the Chemistry of Nitrous Acid and Sodium Hydroxide
Properties of Nitrous Acid (HNO₂)
Nitrous acid is a weak, diprotic acid with the chemical formula HNO₂. It exists in solution as an equilibrium between the undissociated acid and its ions:\[ \text{HNO}2 \rightleftharpoons \text{H}^+ + \text{NO}2^- \]
The acid dissociation constant (Ka) for nitrous acid is approximately:
\[ K_a \approx 4.5 \times 10^{-4} \]
This value indicates that nitrous acid is only partially dissociated in aqueous solution, making it a weak acid. Its conjugate base, nitrite ion (NO₂⁻), can undergo hydrolysis, which significantly influences the pH at various stages of titration.
Properties of Sodium Hydroxide (NaOH)
Sodium hydroxide is a strong base that dissociates completely in water:\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Because of its complete dissociation, NaOH readily neutralizes acids, including weak acids like HNO₂, to produce their conjugate bases and water.
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Overview of the Titration Process
Initial Solution: Nitrous Acid
At the start, the solution contains only nitrous acid at a concentration of 0.20 M. Its pH can be calculated based on its dissociation equilibrium:\[ \text{HNO}2 \rightleftharpoons \text{H}^+ + \text{NO}2^- \]
Using the Ka value and initial concentration, we can determine the initial pH.
During Titration: Addition of NaOH
As NaOH is added, it reacts with HNO₂:\[ \text{HNO}2 + \text{OH}^- \rightarrow \text{NO}2^- + \text{H}_2\text{O} \]
This neutralization converts the weak acid into its conjugate base, NO₂⁻. The titration curve will show a typical S-shape, with the pH rising gradually until reaching the equivalence point.
At the Equivalence Point
The equivalence point is reached when all the acid has been neutralized:\[ \text{HNO}2 + \text{NaOH} \rightarrow \text{NaNO}2 + \text{H}_2\text{O} \]
At this stage, the solution contains only the sodium nitrite (NaNO₂), which dissociates into Na⁺ and NO₂⁻ ions.
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Determining the pH at the Equivalence Point
Since the titration involves a weak acid and a strong base, the pH at the equivalence point is not neutral (pH 7). Instead, it is governed by the hydrolysis of the conjugate base (NO₂⁻). This makes the pH basic, as NO₂⁻ acts as a weak base in water.
Step-by-Step Calculation of pH at the Equivalence Point
Step 1: Recognize the Dominant Species at Equivalence Point
At the equivalence point, the solution contains only the conjugate base NO₂⁻, coming from the neutralization of the weak acid. The pH depends on the hydrolysis of NO₂⁻:
\[ \text{NO}2^- + \text{H}2\text{O} \rightleftharpoons \text{HNO}_2 + \text{OH}^- \]
Step 2: Write the Hydrolysis Equilibrium Expression
The equilibrium constant for hydrolysis (Kb) of NO₂⁻ can be derived from the Ka of HNO₂:
\[ Kb = \frac{Kw}{K_a} \]
where \( K_w = 1.0 \times 10^{-14} \) at 25°C.
Calculating \( K_b \):
\[ K_b = \frac{1.0 \times 10^{-14}}{4.5 \times 10^{-4}} \approx 2.22 \times 10^{-11} \]
Step 3: Determine the Concentration of NO₂⁻ at Equivalence Point
Since the initial concentration of HNO₂ was 0.20 M and the titration is 1:1, the concentration of NO₂⁻ at equivalence is also 0.20 M.
Step 4: Set Up the Hydrolysis Equation
Let \( x \) be the concentration of OH⁻ produced by hydrolysis:
\[ \text{NO}2^- + \text{H}2\text{O} \rightleftharpoons \text{HNO}_2 + \text{OH}^- \]
The expression:
\[ Kb = \frac{[\text{OH}^-]^2}{[\text{NO}2^-]} \]
Substituting known values:
\[ 2.22 \times 10^{-11} = \frac{x^2}{0.20} \]
Solve for \( x \):
\[ x^2 = 2.22 \times 10^{-11} \times 0.20 = 4.44 \times 10^{-12} \]
\[ x = \sqrt{4.44 \times 10^{-12}} \approx 6.66 \times 10^{-6} \, \text{M} \]
This is the concentration of OH⁻ ions.
Step 5: Calculate the pOH and then the pH
\[ \text{pOH} = -\log [\text{OH}^-] \]
\[ \text{pOH} = -\log (6.66 \times 10^{-6}) \approx 5.18 \]
Then,
\[ \text{pH} = 14 - \text{pOH} = 14 - 5.18 = 8.82 \]
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Final Result: pH at the Equivalence Point
Based on the calculations, the pH at the equivalence point for the titration of 0.20 M nitrous acid with 0.20 M sodium hydroxide is approximately 8.82.
This basic pH confirms that the conjugate base (NO₂⁻) hydrolyzes to produce hydroxide ions, resulting in a solution that is slightly alkaline at the equivalence point.
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Additional Insights and Practical Significance
Why Is the pH at the Equivalence Point Not Neutral?
In titrations involving a weak acid and a strong base, the resulting solution contains the conjugate base of the weak acid. This conjugate base is weakly basic, which causes the pH at the equivalence point to be greater than 7. Conversely, titrations involving a weak base and a strong acid would produce a pH less than 7 at the equivalence point.Implications for Acid-Base Titration Curves
Understanding the pH at the equivalence point helps in:- Accurately determining the endpoint of a titration using indicators.
- Interpreting titration curves for weak acid-strong base systems.
- Calculating the dissociation constants and properties of weak acids and their conjugates.
Key Points to Remember
- The pH at the equivalence point reflects the hydrolysis of the conjugate base.
- For nitrous acid titration with NaOH, the pH is approximately 8.82.
- The initial concentration and Ka value influence the pH at various stages.
