Question

What is the \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) for a solution that has a pH of 6.0\(?\)

Short answer

[\text{H}_3\text{O}^+] = 1 \times 10^{-6}\text{ M}.

Step-by-step solution

Understand the relationship between pH and \(\text{[H}_3\text{O}^+\)\text{ concentration}

The pH of a solution is the negative logarithm (base 10) of the hydronium ion concentration. This can be written as: \(\text{pH} = -\text{log}[\text{H}_3\text{O}^+]\).

Rearrange the equation to solve for \(\text{[H}_3\text{O}^+]\)

To find the hydronium ion concentration, rearrange the equation: \([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\).

Substitute the given pH value into the equation

Given that the pH is 6.0, substitute this value into the rearranged equation: \([\text{H}_3\text{O}^+] = 10^{-6.0}\).

Calculate the hydronium ion concentration

Solve the equation: \([\text{H}_3\text{O}^+] = 10^{-6.0} = 1 \times 10^{-6}\text{ M}\).

Key concepts

hydronium ion concentration

In acid-base chemistry, the hydronium ion concentration \(\text{[H}_3\text{O}^+]\) is key. Hydronium ions form when water molecules gain a proton (H\(^+\)). This protonation of water is critical to understanding the acidity of solutions. Acids increase the number of hydronium ions in a solution. This concentration is measured in moles per liter (M), telling us how many hydronium ions exist in a specific volume of solution.
A strong acid will fully dissociate in water, leading to a high \(\text{[H}_3\text{O}^+]\), while weak acids only partially dissociate, resulting in a lower concentration.

pH formula

The pH formula is used to quantify the acidity or basicity of a solution. It is expressed as \(\text{pH} = -\text{log}[\text{H}_3\text{O}^+]\). This logarithmic scale ranges typically from 0 to 14, though values can extend beyond this range in very strong acids or bases. On the pH scale:

• A pH less than 7 indicates an acidic solution.
• A pH of 7 is neutral, akin to pure water.
• A pH greater than 7 indicates a basic or alkaline solution.

The formula shows that a small change in hydronium ion concentration causes a significant change in pH values.

acid-base chemistry

Acid-base chemistry centers on the transfer of protons (H\(^+\)) between substances. Acids are proton donors, releasing H\(^+\) into solutions, thus increasing the \(\text{[H}_3\text{O}^+]\). Bases are proton acceptors, often decreasing \(\text{[H}_3\text{O}^+]\) by forming water when they react with H\(^+\).
Here's a quick overview:

• Strong acids and bases dissociate completely in water, altering \(\text{[H}_3\text{O}^+]\) significantly.
• Weak acids and bases only partially dissociate, barely changing \(\text{[H}_3\text{O}^+]\).

Understanding the pH, hydronium ion concentration, and how acids and bases interact is crucial for mastering chemistry fundamentals.