Problem 31 - Chemistry Matter and Change

Question

Challenge Calculate the \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in a sample of seawater with a pOH \(=5.60 .\)

Step-by-Step Solution

Answer

\([\mathrm{H}^{+}] \approx 3.98 \times 10^{-9} \text{ M}\) and \([\mathrm{OH}^{-}] \approx 2.51 \times 10^{-6} \text{ M}\).

Step 1: Understanding pOH and its Relation to pH

The pOH of a solution is related to the pH through the equation: \[ \text{pH} + \text{pOH} = 14 \]Given that the pOH is 5.60, we can calculate the pH using this relationship.

Step 2: Calculating the pH

Using the relation from the first step:\[\text{pH} = 14 - \text{pOH} = 14 - 5.60 = 8.40\]So, the pH of the solution is 8.40.

Step 3: Finding \\[\mathrm{H}^{+}\] from pH

To find the \[\mathrm{H}^{+}\] ion concentration, we use the formula:\[\left[ \mathrm{H}^{+} \right] = 10^{-\text{pH}}\]Plugging in the pH value we found:\[\left[ \mathrm{H}^{+} \right] = 10^{-8.40}\]Calculate the value to find \[\mathrm{H}^{+}\].

Step 4: Calculating the \\[\mathrm{H}^{+}\] Concentration

Continuing from the previous step, calculate:\[\left[ \mathrm{H}^{+} \right] \approx 3.98 \times 10^{-9} \text{ M}\]This is the concentration of hydrogen ions in the seawater.

Step 5: Finding \\[\mathrm{OH}^{-}\] from pOH

The \[\mathrm{OH}^{-}\] ion concentration is calculated using the formula:\[\left[ \mathrm{OH}^{-} \right] = 10^{-\text{pOH}}\]Plug in the pOH value:\[\left[ \mathrm{OH}^{-} \right] = 10^{-5.60}\]Calculate the value to find \[\mathrm{OH}^{-}\].

Step 6: Calculating the \\[\mathrm{OH}^{-}\] Concentration

Now, compute the value:\[\left[ \mathrm{OH}^{-} \right] \approx 2.51 \times 10^{-6} \text{ M}\]This is the concentration of hydroxide ions in the seawater.

Key Concepts

pH and pOH calculations

In acid-base chemistry, the concepts of pH and pOH are crucial in understanding the acidity or basicity of a solution. The relation \[ \text{pH} + \text{pOH} = 14 \] is fundamental and provides a convenient way to interconvert between these two variables. In essence, if you know either the pH or the pOH, you can easily find the other by this equation.
For instance, if the pOH of seawater is given as 5.60, the pH can be calculated as: \[ \text{pH} = 14 - \text{pOH} = 14 - 5.60 = 8.40 \] This value indicates a slightly basic solution. Breaking down these calculations helps emphasize the logarithmic scale used in pH and pOH, where each unit represents a tenfold change in ionic concentration. Therefore, understanding this relationship allows us to adjust our approach in various chemical environments efficiently.

Hydrogen Ion Concentration

The concentration of hydrogen ions \( \left[ \text{H}^+ \right] \) plays a central role in determining the acidity of a solution. The pH is a logarithmic measure of this concentration, defined by the formula: \[ \text{pH} = -\log_{10}(\left[ \text{H}^+ \right]) \] To find the \( \left[ \text{H}^+ \right] \) given a pH, reverse this relationship: \[ \left[ \text{H}^+ \right] = 10^{-\text{pH}} \] Continuing with our seawater example where \( \text{pH} = 8.40 \),we compute: \[ \left[ \text{H}^+ \right] = 10^{-8.40} \approx 3.98 \times 10^{-9} \text{ M} \] This result suggests that the seawater is basic, as the concentration of hydrogen ions is low. Understanding these calculations can aid in predicting chemical behavior in different aquatic environments, which is essential in marine chemistry and environmental science.

Hydroxide Ion Concentration

The hydroxide ion concentration \( \left[ \text{OH}^- \right] \) is equally important when discussing basic solutions. The pOH gives us a direct path to find this concentration through the formula: \[ \left[ \text{OH}^- \right] = 10^{-\text{pOH}} \] In our example, where the pOH is 5.60, we calculate: \[ \left[ \text{OH}^- \right] = 10^{-5.60} \approx 2.51 \times 10^{-6} \text{ M} \] This higher concentration of hydroxide ions compared to hydrogen ions reinforces the idea that the solution is basic.
Remember, the presence of hydroxide ions is pivotal in understanding reactions such as neutralization, where acids and bases interact to produce water and salts. These calculations provide clarity on the dynamics of ionic interactions in solutions, facilitating insights into their balancing mechanisms and potential applications.