Problem 54 - Chemistry An Atoms First Approach

Question

The pOH of a sample of baking soda dissolved in water is 5.74 at \(25^{\circ} \mathrm{C}\). Calculate the \(\mathrm{pH},\left[\mathrm{H}^{+}\right],\) and \(\left[\mathrm{OH}^{-}\right]\) for this sample. Is the solution acidic or basic?

Step-by-Step Solution

Answer

The pH of the sample is 8.26, the concentration of \(\mathrm{H}^{+}\) ions is \(5.5 \times 10^{-9}\) M, and the concentration of \(\mathrm{OH}^{-}\) ions is \(1.8 \times 10^{-6}\) M. Since the pH is greater than 7 and the concentration of \(\mathrm{OH}^{-}\) ions is greater than the concentration of \(\mathrm{H}^{+}\) ions, the solution is basic.

Step 1: Calculate the pH

To calculate the pH of the sample, we will use the relationship between pH and pOH: pH = 14 - pOH Given the pOH is 5.74, we can calculate the pH as follows: pH = 14 - 5.74 = 8.26

Step 2: Calculate the concentration of \(\mathrm{H}^{+}\) ions

We will now calculate the concentration of \(\mathrm{H}^{+}\) ions using the relationship between pH and \(\mathrm{H}^{+}\) concentration: pH = -log\(_{10}[\mathrm{H}^{+}]\) We have the pH (8.26), so we can solve for \([\mathrm{H}^{+}]\): \([\mathrm{H}^{+}]\) = 10\(^{-\mathrm{pH}}\) = 10\(^{-8.26}\) = 5.5 x 10\(^{-9}\) M

Step 3: Calculate the concentration of \(\mathrm{OH}^{-}\) ions

To calculate the concentration of \(\mathrm{OH}^{-}\) ions, we will use the relationship between pOH and \(\mathrm{OH}^{-}\) concentration: pOH = -log\(_{10}[\mathrm{OH}^{-}]\) We have the pOH (5.74), so we can solve for \([\mathrm{OH}^{-}]\): \([\mathrm{OH}^{-}]\) = 10\(^{-\mathrm{pOH}}\) = 10\(^{-5.74}\) = 1.8 x 10\(^{-6}\) M

Step 4: Determine whether the solution is acidic or basic

A solution is considered acidic if the concentration of \(\mathrm{H}^{+}\) ions is greater than the concentration of \(\mathrm{OH}^{-}\) ions and pH < 7. A solution is considered basic if the concentration of \(\mathrm{OH}^{-}\) ions is greater than the concentration of \(\mathrm{H}^{+}\) ions and pH > 7. In our case: pH = 8.26 (> 7) \([\mathrm{H}^{+}]\) = 5.5 x 10\(^{-9}\) M \([\mathrm{OH}^{-}]\) = 1.8 x 10\(^{-6}\) M Since the pH is greater than 7 and the concentration of \(\mathrm{OH}^{-}\) ions is greater than the concentration of \(\mathrm{H}^{+}\) ions, the solution is basic.

Key Concepts

pH Calculation

When it comes to understanding pH calculation, it’s all about the balance between hydrogen ions, \( [\mathrm{H}^+] \), and hydroxide ions, \( [\mathrm{OH}^-] \). The pH scale is a way to measure how acidic or basic a solution is. This scale typically ranges from 0 to 14. A pH less than 7 indicates an acidic solution, and a pH greater than 7 indicates a basic solution. If the pH is exactly 7, the solution is neutral, like pure water.

To calculate the pH when you know the pOH, you use the equation:

• \( \mathrm{pH} = 14 - \mathrm{pOH} \)

In our example, the pOH was given as 5.74. Applying the formula:

• \( \mathrm{pH} = 14 - 5.74 = 8.26 \)

This calculation tells us the solution is basic since 8.26 is greater than 7. This basic nature is due to a higher concentration of \( [\mathrm{OH}^{-}] \) ions compared to \( [\mathrm{H}^{+}] \) ions.

pOH Calculation

pOH is similar to pH, but rather than measuring the acidity, it measures how basic a solution is, focusing on the concentration of hydroxide ions, \( [\mathrm{OH}^{-}] \). The pOH scale also ranges from 0 to 14, where a low pOH signifies a highly basic solution.

The formula for finding the pOH from the concentration of hydroxide ions is:

• \( \mathrm{pOH} = -\log_{10}[\mathrm{OH}^{-}] \)

If you have a pOH value, you can easily find the concentration of \( [\mathrm{OH}^{-}] \) ions by rearranging the formula:

• \( [\mathrm{OH}^{-}] = 10^{-\mathrm{pOH}} \)

For example:

• \( [\mathrm{OH}^{-}] = 10^{-5.74} = 1.8 \times 10^{-6} \) M

This indicates the strength of the basicity in our solution.

Concentration of Ions

Understanding the concentration of ions in a solution is crucial in acid-base chemistry. These concentrations are often expressed in molarity (M), which is moles per liter of solution. Both \( [\mathrm{H}^{+}] \) and \( [\mathrm{OH}^{-}] \) concentrations can determine the nature of the solution, whether it's acidic or basic.

For a given pH, the concentration of hydrogen ions, \( [\mathrm{H}^{+}] \), can be calculated using the formula:

• \( [\mathrm{H}^{+}] = 10^{-\mathrm{pH}} \)

In our calculated example:

• \( [\mathrm{H}^{+}] = 10^{-8.26} = 5.5 \times 10^{-9} \) M

Moreover, the concentration of hydroxide ions, \( [\mathrm{OH}^{-}] \), can be derived from the pOH:

• \( [\mathrm{OH}^{-}] = 10^{-5.74} = 1.8 \times 10^{-6} \) M

To decide the nature of a solution – acidic or basic – compare these concentrations. In our case, the hydroxide ions outweigh the hydrogen ions, indicating a basic solution with a pH of 8.26.