Question

Calculate the pH corresponding to each of the hydroxide ion concentrations given below, and indicate whether each solution is acidic or basic. a. \(\left[\mathrm{OH}^{-}\right]=4.73 \times 10^{-4} M\) b. \(\left[\mathrm{OH}^{-}\right]=5.99 \times 10^{-1} M\) c. \(\left[\mathrm{OH}^{-}\right]=2.87 \times 10^{-8} M\) d. \(\left[\mathrm{OH}^{-}\right]=6.39 \times 10^{-3} M\)

Short answer

In summary, the calculated pH values and determination of acidity or basicity for each solution are: a. \(pH \approx 10.67\) - Basic b. \(pH \approx 13.78\) - Basic c. \(pH \approx 6.46\) - Acidic d. \(pH \approx 11.81\) - Basic

Step-by-step solution

Find pOH

Using the \(pOH\) formula: \(pOH = -\log\left[\mathrm{OH}^{-}\right]\) We have: \(pOH = -\log(4.73 \times 10^{-4})\) Calculating the pOH value, we get: \(pOH \approx 3.33\)

Find pH

Using the relation between pH and pOH: \(pH = 14.00 - pOH\) \(pH = 14.00 - 3.33\) We get the pH value: \(pH \approx 10.67\)

Determine acidity or basicity

Since, pH > 7, this solution is basic. b. \(\left[\mathrm{OH}^{-}\right]=5.99 \times 10^{-1} M\)

Find pOH

We have: \(pOH = -\log(5.99 \times 10^{-1})\) Calculating the pOH value, we get: \(pOH \approx 0.22\)

Find pH

\(pH = 14.00 - pOH\) \(pH = 14.00 - 0.22\) We get the pH value: \(pH \approx 13.78\)

Determine acidity or basicity

Since, pH > 7, this solution is basic. c. \(\left[\mathrm{OH}^{-}\right]=2.87 \times 10^{-8} M\)

Find pOH

We have: \(pOH = -\log(2.87 \times 10^{-8})\) Calculating the pOH value, we get: \(pOH \approx 7.54\)

Find pH

\(pH = 14.00 - pOH\) \(pH = 14.00 - 7.54\) We get the pH value: \(pH \approx 6.46\)

Determine acidity or basicity

Since, pH < 7, this solution is acidic. d. \(\left[\mathrm{OH}^{-}\right]=6.39 \times 10^{-3} M\)

Find pOH

We have: \(pOH = -\log(6.39 \times 10^{-3})\) Calculating the pOH value, we get: \(pOH \approx 2.19\)

Find pH

\(pH = 14.00 - pOH\) \(pH = 14.00 - 2.19\) We get the pH value: \(pH \approx 11.81\)

Determine acidity or basicity

Since, pH > 7, this solution is basic.

Key concepts

Hydroxide Ion Concentration

Hydroxide ion concentration is a key factor in determining the basicity of a solution.
It indicates the amount of \( \text{OH}^- \) ions present, which are crucial characters in understanding the nature of solutions.
In the context of chemistry, understanding how much \( \text{OH}^- \) ions exist in a solution helps us to deduce not only its major properties but also its reactivity.

• Solutions with high hydroxide ion concentrations are generally basic.
• Conversely, low concentrations often indicate a tendency toward acidity, especially when using pH and pOH relationships.

For example, knowing that a solution has an \( \text{OH}^- \) concentration of \(5.99 \times 10^{-1} M\), as seen in the exercise, directly relates to a high basicity.
The higher \( \text{OH}^- \) concentration results in a lower pOH, subsequently yielding a higher pH.

Acidity and Basicity

Acidity and basicity are concepts that describe the ability of substances to donate or accept protons.
These properties can be quantitatively measured using the pH scale, which ranges typically from 0 to 14.
A neutral solution marks around 7 on this scale.

• A pH less than 7 indicates acidity.
• A pH more than 7 signals basicity.

Understanding which side of neutrality an \( \text{OH}^- \) concentration falls on is pivotal.
For instance, a high pH value, such as 13.78, clearly exemplifies a basic nature, correlating to high hydroxide ion concentration.
Conversely, a pH value like 6.46, which is less than 7, denotes acidity. Thus, monitoring pH changes due to ion concentration informs us about the solution's characteristics and possible reactions.

pOH and pH Relationship

The pOH and pH relationship is foundational in understanding the acidity or basicity of solutions.
It rests upon the equation:\[pH + pOH = 14\]This means that knowing either pH or pOH allows us to calculate the other.
This relationship emphasizes the inverse nature of pH and pOH.

• A high pOH corresponds to low pH, indicating acidity.
• A low pOH corresponds to high pH, signaling basicity.

This relationship was highlighted in the exercise where solutions with lower hydroxide ion concentrations yielded higher pOH values.
Consequently, these resulted in a lower pH, portraying an acidic solution. The interdependence of pH and pOH is vital for understanding chemical balances in many scientific contexts.