Problem 57 - Chemistry and Chemical Reactivity

Question

What is the hydronium ion concentration of a \(0.0013 \mathrm{M}\) solution of \(\mathrm{HNO}_{3} ?\) What is its \(\mathrm{pH} ?\)

Step-by-Step Solution

Answer

The hydronium ion concentration is 0.0013 M, and the pH is approximately 2.89.

Step 1: Identify the Nature of the Solution

Nitric acid (\(\mathrm{HNO}_3\)) is a strong acid, which means it completely dissociates in water. Therefore, the concentration of hydronium ions (\(\mathrm{H}^+\)) in the solution is the same as the initial concentration of \(\mathrm{HNO}_3\).

Step 2: Calculate Hydronium Ion Concentration

For a 0.0013 M \(\mathrm{HNO}_3\) solution, the hydronium ion concentration is:\[\left[\mathrm{H}_3\mathrm{O}^+\right] = 0.0013 \, \mathrm{M}\]since the acid dissociates completely releasing one \(\mathrm{H}^+\) ion per molecule of \(\mathrm{HNO}_3\).

Step 3: Calculate the pH of the Solution

The \(\mathrm{pH}\) is calculated using the formula:\[\mathrm{pH} = -\log_{10} \left[\mathrm{H}_3\mathrm{O}^+\right]\]Substitute the hydronium ion concentration:\[\mathrm{pH} = -\log_{10} \left(0.0013\right)\]Using a calculator, this gives:\[\mathrm{pH} \approx 2.89\]

Key Concepts

Understanding Strong Acids

Strong acids like nitric acid (\(\mathrm{HNO}_3\)) play a critical role in chemistry. Unlike weak acids, which partially dissociate in water, strong acids completely dissociate.
This means that all the acid molecules break apart into ions. For \(\mathrm{HNO}_3\), it dissociates to release \(\mathrm{H}^+\) ions in water.

• Complete dissociation leads to a high concentration of \(\mathrm{H}^+\) ions.
• Knowing that an acid is strong helps predict the behavior in solution.
• For calculations, the concentration of the strong acid directly equals the concentration of \(\mathrm{H}^+\) ions.

Having this understanding allows chemists to accurately determine the pH of strong acid solutions.

Calculating Hydronium Ion Concentration

The hydronium ion concentration is a measure of the acidity in a solution. When nitric acid (\(\mathrm{HNO}_3\)) dissolves in water, it boosts the concentration of \(\mathrm{H_3O}^+\) ions, making the solution acidic.
In a 0.0013 M solution of \(\mathrm{HNO}_3\):

• \(\mathrm{HNO}_3\) completely dissociates, producing an equal concentration of \(\mathrm{H}^+\) ions.
• Therefore, \([\mathrm{H}_3\mathrm{O}^+] = 0.0013 \mathrm{M}\).

This is important, as the hydronium ion concentration helps determine pH levels. Understanding the ion concentration is key to understanding the solution's acidic strength.

Role of Acid Dissociation

Acid dissociation is the process by which an acid releases hydrogen ions (\(\mathrm{H}^+\)). For strong acids, this process is complete. This implies that every molecule of the acid dissociates to contribute to acidity.

• Complete dissociation affects pH calculation since all \(\mathrm{H}^+\) ions come from the acid.
• It simplifies calculations for strong acids, as the initial concentration is the concentration of \(\mathrm{H}^+\) ions.
• The understanding of dissociation helps in predicting reaction behaviors in solutions.

These aspects simplify the process of calculating hydronium ion concentrations and ultimately, pH.

Logarithmic Functions in pH Calculation

pH calculation utilizes logarithmic functions to express acidity. The pH is defined as the negative base-10 logarithm of the hydronium ion concentration, \([\mathrm{H}_3\mathrm{O}^+]\). This scale is logarithmic, meaning each pH unit represents a tenfold difference in acidity.
Calculating the pH of a 0.0013 M \(\mathrm{HNO}_3\) solution involves:

• Using the formula \(\text{pH} = -\log_{10}[\mathrm{H}_3\mathrm{O}^+]\).
• Substituting \([\mathrm{H}_3\mathrm{O}^+]\) with 0.0013 leads to the calculation \(\text{pH} \approx 2.89\).

This approach allows for easy interpretation and comparison of acidity levels across different solutions.