Question

What is the \(\mathrm{pH}\) of solutions having the following \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentrations? Identify each as acidic, basic, or neutral. (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-9} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-14} M\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.2 \times 10^{-3} \mathrm{M}\)

Short answer

The pH values of the solutions are (a) 9 which is basic, (b) 14 which is basic, and (c) 2.14 which is acidic.

Step-by-step solution

Calculate the pH

Use the formula \( \mathrm{pH} = -\log[\mathrm{H}_3\mathrm{O}^+]\) to calculate the pH of each solution. Note that the concentration of the \(\mathrm{H}_3\mathrm{O}^+\) ion is given in moles per liter (M).

Determine the acidity or basicity

After you calculate the pH, determine if the solution is acidic, basic, or neutral. If the pH is less than 7, the solution is acidic. If the pH is greater than 7, it's basic. If the pH is 7, the solution is neutral.

Solution for (a)

First, calculate the pH using the given concentration of the \(\mathrm{H}_3\mathrm{O}^+\) ion which is \(1.0 \times 10^{-9} \mathrm{M}\). The pH is thus equal to \(-\log(1.0 \times 10^{-9}) = 9\). The pH is greater than 7, therefore, the solution is basic.

Solution for (b)

The given \(\mathrm{H}_3\mathrm{O}^+\) concentration is \(1.0 \times 10^{-14} \mathrm{M}\). Using the pH formula gives \(-\log(1.0 \times 10^{-14}) = 14\). As the pH value is greater than 7, the solution is basic.

Solution for (c)

The \(\mathrm{H}_3\mathrm{O}^+\) concentration given is \(7.2 \times 10^{-3} \mathrm{M}\). The pH of the solution is then \(-\log(7.2 \times 10^{-3}) = 2.14 \approx 2.14\). As the pH is less than 7, the solution is acidic.

Key concepts

Acidity

Acidity is a measure of how many hydrogen ions ( H⁺ ) are present in a solution. The more H⁺ ions you have, the more acidic the solution is. The pH scale helps us understand this. It goes from 0 to 14, with 7 being neutral. If a pH is less than 7, the solution is considered acidic.
Examples include:

• Lemon juice
• Vinegar
• Many fruit juices

These substances have a high concentration of hydrogen ions, making them taste sour. In our exercise, a solution with a pH of 2.14 was found. Since the pH is below 7, this solution is acidic. Understanding acidity helps us in everyday life, from cooking to preserving food as acids can help slow bacteria growth.

Basicity

Basicity refers to a solution having fewer H⁺ ions and instead more hydroxide ions ( OH⁻ ). The scale measurement for basicity is again the pH scale. If the pH is above 7, the solution is considered basic or alkaline. These solutions often taste bitter and feel slippery.
Some common basic substances include:

• Soap
• Baking soda solution
• Bleach

The pH value for these solutions is usually above 7. In the exercise, solutions with pH values of 9 and 14 turned out to be basic. Knowing about basicity is important in activities like cleaning, where bases can break down oils and fats.

Neutral Solutions

Neutral solutions have a pH equal to 7. This means that the concentration of H⁺ ions is equal to that of OH⁻ ions. Pure water is the most common example of a neutral solution in everyday life.
Neutral solutions:

• Neither acidic nor basic
• Have balanced H⁺ and OH⁻
• Are usually mild and safe for consumption

Understanding neutral solutions is crucial in fields like agriculture, where the pH of the soil can affect plant growth. If the soil is too acidic or too basic, plants may not be able to absorb nutrients effectively. By keeping solutions neutral or checking their pH levels, we can ensure better outcomes in gardening and agriculture.