Problem 28 - Chemistry The Molecular Science

Question

Calculate the pH of a 0.0013-M solution of \(\mathrm{HNO}_{3} .\) Calculate the pOH of this solution.

Step-by-Step Solution

Answer

The pH is 2.89, and the pOH is 11.11.

Step 1: Recognize HNO3 as a strong acid

Nitric acid ( HNO3) is a strong acid, meaning it completely dissociates in water. Therefore, the concentration of hydrogen ions [H⁺] in the solution is equal to the concentration of HNO₃, which is 0.0013 M.

Step 2: Calculate the pH

The pH of a solution is calculated using the formula: \[ \text{pH} = -\log[\text{H}^+] \]Substitute the concentration of the hydrogen ions (0.0013 M) into the formula.\[ \text{pH} = -\log(0.0013) \]Calculate the logarithm to find the pH.

Step 3: Solve for pH

Calculate the log of 0.0013, which is approximately -2.886. Thus,\[ \text{pH} = -(-2.886) = 2.886 \]The pH of the solution is approximately 2.89.

Step 4: Use the relationship between pH and pOH

The relationship between pH and pOH in water at 25°C (298 K) is given by the equation:\[ \text{pH} + \text{pOH} = 14 \]Since the pH is 2.89, substitute this value into the equation to find pOH:\[ 2.89 + \text{pOH} = 14 \]

Step 5: Calculate pOH

Rearrange the equation to solve for pOH:\[ \text{pOH} = 14 - 2.89 = 11.11 \]The pOH of the solution is approximately 11.11.

Key Concepts

Strong Acid

Nitric Acid (\(\text{HNO}_3\)) is classified as a strong acid. Unlike weak acids, which partially dissociate in water, strong acids fully dissociate. This means all the \(\text{HNO}_3\) molecules in the solution release their hydrogen ions \([\text{H}^+]\). In practical terms, if you have a 0.0013 M solution of \(\text{HNO}_3\), the concentration of \([\text{H}^+]\) is also 0.0013 M.

This characteristic simplifies the process of finding the pH and pOH of the solution because you don't need to consider any undissociated acid molecules. The complete dissociation attribute is what makes the calculations more straightforward compared to dealing with, say, weak acids.

pOH Calculation

The pOH is the counterpart of pH in measuring the alkalinity of a solution. While pH focuses on hydrogen ions, pOH focuses on hydroxide ions \([\text{OH}^-]\).
For any aqueous solution at 25°C, \(\text{pH} + \text{pOH} = 14\). This relationship is crucial. In our example, once the pH of the \(\text{HNO}_3\) solution is calculated (2.89), you can easily find the pOH by rearranging the expression:

• \(\text{pOH} = 14 - \text{pH}\)
• \(\text{pOH} = 14 - 2.89 = 11.11\)

So, the pOH of this \(\text{HNO}_3\) solution is approximately 11.11. It's important to remember that the sum of pH and pOH gives an insight into the balance of acidic and basic components in the solution.

Hydrogen Ion Concentration

The concentration of hydrogen ions \([\text{H}^+]\) in a solution is a primary factor in determining its acidity. With strong acids like \(\text{HNO}_3\), it is straightforward because the hydrogen ion concentration is equal to the molarity of the acid solution itself.

To determine the pH from the hydrogen ion concentration, use the pH formula:

• \( \text{pH} = -\log[\text{H}^+] \)

By inserting our \([\text{H}^+]\) concentration of 0.0013 M into the formula, the logarithmic calculation gives us a pH of 2.89.

The concept of pH is scaled so that every change in one pH unit reflects a tenfold change in \([\text{H}^+]\) concentration, making it easier to handle and compare levels of acidity, even when they vary dramatically.