Question

What is the \(\mathrm{pH}\) of solutions having the following \(\mathrm{OH}^{-}\) concentrations? Identify each as acidic, basic, or neutral. (a) \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-4} \mathrm{M}\) (b) \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} M\) (c) \(\left[\mathrm{OH}^{-}\right]=8.2 \times 10^{-10} \mathrm{M}\)

Short answer

(a) The solution is basic with a pH of 10. (b) The solution is neutral with a pH of 7. (c) The solution is acidic with a pH of 6.08.

Step-by-step solution

Calculate pOH

Starting with the formula for pOH: \(pOH = -\log {[OH^{-}]}\), for each solution substitute the provided \(OH^{-}\) concentration value into the formula and calculate the pOH.

Calculate pH

Once you have the pOH of each solution, calculate the pH using the equation \(pH = 14 - pOH\). Again, it's crucial to remember that the sum of pH and pOH is always 14 at 25 degrees Celsius.

Identify the Nature of the Solution

Given the calculated pH, identify the nature of the solution where pH < 7 corresponds to an acidic solution, pH = 7 to a neutral solution, and pH > 7 to a basic (or alkaline) solution.

Key concepts

Understanding pOH

To better understand the pH of a solution, we need to first understand pOH. pOH is a measure of the hydroxide ion (\(OH^{-} \)) concentration in a solution. It mirrors the pH scale, but instead of focusing on hydrogen ions (\(H^{+} \)), pOH looks at hydroxide ions. The formula to calculate pOH is:
\[\mathrm{pOH} = -\log [\mathrm{OH}^{-}] \]This equation tells us that the higher the concentration of hydroxide ions, the lower the pOH value. Conversely, lower hydroxide ion concentrations result in higher pOH values.
Understanding pOH helps us figure out whether a solution is more basic or acidic by considering how much a solution is dominated by hydroxide ions.
Once we have the pOH, it becomes easy to determine the pH since the sum of pH and pOH in a solution at 25 °C is always 14:

What Makes a Solution Acidic?

An acidic solution is one where the \( \mathrm{pH} \) level is less than 7. This indicates a higher concentration of hydrogen ions (\(H^{+} \)) compared to hydroxide ions (\(OH^{-} \)). Such an imbalance leads to the sour taste associated with acids.
Reasons for a solution to be acidic include:

• Dissolution of acids in water releasing \(H^{+} \) ions.
• Reaction of certain salts with water to form acids.

Common examples of acidic substances are lemon juice and vinegar, which have a pH typically well below 7.
During pH calculation, if the calculated value is under 7, the solution is confirmed to be acidic.

Defining Basic Solutions

A basic solution has a pH greater than 7, indicating a higher concentration of hydroxide ions (\(OH^{-} \)) than hydrogen ions (\(H^{+} \)). This results in the slippery feel of bases and their ability to neutralize acids.
Factors leading to alkalinity in solutions include:

• Dissolution of bases in water, increasing \(OH^{-} \) concentration.
• Excess reaction of certain chemicals that absorb \(H^{+} \) ions.

Common basic substances include soap and baking soda, both of which naturally have a pH above 7.
In calculations, when you find a pH value more than 7, the solution is identified as basic.

Neutral Solution Characteristics

Neutral solutions have a pH of 7, signifying an equal concentration of hydrogen ions (\(H^{+} \)) and hydroxide ions (\(OH^{-} \)). This balance implies that the solution is neither acidic nor basic.
Water is the classic example of a neutral solution under standard conditions. When \(H^{+} \) and \(OH^{-} \) are in perfect balance, their effects cancel out, meaning they do not alter the nature of the solution.
In practice, solutions classified as neutral are critical, especially in chemical reactions where the pH neutrality can protect reactants or products from damage due to acidity or alkalinity. When performing pH calculations, a result of exactly 7 indicates neutrality. This balanced state is often the goal in numerous industrial and biological processes.