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) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-3} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-13} \mathrm{M}\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.4 \times 10^{-10} \mathrm{M}\)

Short answer

The pH of the first solution is 3, making it acidic. The pH of the second solution is 13, making it basic. The pH of the third solution is 9.47, making it basic.

Step-by-step solution

Calculate pH for the first solution

To calculate the pH, use the equation \(\mathrm{pH} = -\log{[\mathrm{H}_{3}\mathrm{O}^{+}]}\). For the first solution, plug \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-3} \mathrm{M}\) into the equation to obtain \(\mathrm{pH} = -\log{(1.0 \times 10^{-3})} = 3\).

Determine whether the first solution is acidic, basic, or neutral

If the pH is less than 7, it is acidic. If the pH is over 7, it is basic. If the pH is 7, it is neutral. The pH of the first solution is 3, so the first solution is acidic.

Repeat steps 1 and 2 for the remaining solutions

For the second solution, plug \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-13} \mathrm{M}\) into the equation to get \(\mathrm{pH} = -\log{(1.0 \times 10^{-13})} = 13\). Since the pH is over 7, this solution is basic. For the third solution, plug \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.4 \times 10^{-10} \mathrm{M}\) into the equation to get \(\mathrm{pH} = -\log{(3.4 \times 10^{-10})} = 9.47\). Since this pH is also over 7, the third solution is basic.

Key concepts

Acidic Solutions

Acidic solutions are those with a pH value less than 7. These solutions have a high concentration of hydronium ions \(\left( \text{H}_3\text{O}^+ \right)\). Let's explore what makes a solution acidic:

• Hydronium ions form when an acid dissolves in water, increasing the \(\text{H}_3\text{O}^+\) concentration.
• The more hydronium ions, the lower the pH.
• A pH of 3, like in our example, indicates a strong acid.

Remember, each unit decrease in pH represents a tenfold increase in hydronium ion concentration. Understanding this can help you identify acidic solutions easily!

Basic Solutions

Basic solutions have a pH greater than 7, indicating a lower concentration of hydronium ions \(\left( \text{H}_3\text{O}^+ \right)\) compared to hydroxide ions \(\left( \text{OH}^- \right)\). Here's what you should know about basic solutions:

• They often result from bases dissolving in water, which decreases the \(\text{H}_3\text{O}^+\) concentration.
• A pH of 13, as we saw in the example, is highly basic.
• pH values from 7 to 14 are characteristic of basic solutions.

Keep in mind that the further the pH is above 7, the stronger the base. Calculating pH from hydronium concentration helps identify the solution's nature.

Hydronium Ion Concentration

The hydronium ion concentration is crucial in determining a solution's pH. Here's how it works:

• The formula \(\text{pH} = -\log{\left[ \text{H}_3\text{O}^+ \right]}\) gives the pH from the hydronium concentration.
• More hydronium ions mean a lower pH, indicating acidity.
• Less hydronium ions result in a higher pH, pointing to basicity.

For instance, if \([\text{H}_3\text{O}^+] = 1.0 \times 10^{-13} \text{ M}\)\, the pH calculated is 13, showing it's a basic solution. Understanding this balance helps you quickly categorize unfamilar solutions as acidic or basic.