Question

Saliva has a pH range of \(5.8-7.1\). Approximately what is the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration range of saliva?

Short answer

The \([\mathrm{H}_3\mathrm{O}^+]\) concentration range of saliva is approximately \(1.58 \times 10^{-6}\) M to \(7.94 \times 10^{-8}\) M.

Step-by-step solution

Understand the pH Formula

The pH of a solution is calculated using the formula: \[ \text{pH} = -\log_{10} [\mathrm{H}_3\mathrm{O}^+] \]where \([\mathrm{H}_3\mathrm{O}^+]\) is the concentration of hydronium ions in moles per liter.

Calculate Lower Limit of Hydronium Ion Concentration

For the lower pH limit of 5.8, we use the pH formula: \[ 5.8 = -\log_{10} [\mathrm{H}_3\mathrm{O}^+] \]To find \([\mathrm{H}_3\mathrm{O}^+]\), rewrite it as: \[ [\mathrm{H}_3\mathrm{O}^+] = 10^{-5.8} \]Using a calculator, this gives approximately: \[ [\mathrm{H}_3\mathrm{O}^+] \approx 1.58 \times 10^{-6} \text{ M} \]

Calculate Upper Limit of Hydronium Ion Concentration

For the upper pH limit of 7.1, we use the pH formula: \[ 7.1 = -\log_{10} [\mathrm{H}_3\mathrm{O}^+] \]To solve for \([\mathrm{H}_3\mathrm{O}^+]\), rewrite it as: \[ [\mathrm{H}_3\mathrm{O}^+] = 10^{-7.1} \]Using a calculator, this gives approximately: \[ [\mathrm{H}_3\mathrm{O}^+] \approx 7.94 \times 10^{-8} \text{ M} \]

Combine Results to Find the Range

Now that we have both the lower and the upper limits of the hydronium concentration, the range of \([\mathrm{H}_3\mathrm{O}^+]\) in saliva is approximately from \[1.58 \times 10^{-6} \text{ M} \text{ to } 7.94 \times 10^{-8} \text{ M} \].

Key concepts

Hydronium Ion Concentration

The concentration of hydronium ions \(\mathrm{H}_{3}\mathrm{O}^{+}\) is an important concept in understanding the acidity or basicity of a solution. In the context of saliva, knowing the range of hydronium ion concentration allows us to understand how acidic or neutral it is. \[\mathrm{H}_{3}\mathrm{O}^{+}\] represents the number of moles of hydronium ions present per liter of solution. This is also described in molarity (M), which measures the concentration of a solution. In more acidic solutions, the concentration of hydronium ions is higher—that is, \[\mathrm{H}_{3}\mathrm{O}^{+}\] is large. Conversely, in more basic solutions, this concentration is lower.Let's consider saliva as an example. Saliva typically exhibits a pH range from 5.8 to 7.1:

• At a pH of 5.8, saliva is slightly acidic, and hydronium ions are more concentrated.
• At a pH of 7.1, saliva is moving towards neutral, indicating fewer hydronium ions.

This understanding helps in assessing oral health, since changes in hydronium ion concentration can affect tooth decay and oral bacteria growth.

pH Calculation

pH is a measure of how acidic or basic a solution is, and it’s essential in the study of acid-base chemistry. The pH scale ranges from 0 to 14, where lower values mean more acidity, and higher values mean more alkalinity. Saliva with a pH of 5.8 indicates it's mildly acidic, as opposed to a pH of 7.1, which is closer to neutral. You can calculate pH using the formula: \[ \text{pH} = -\log_{10} [\mathrm{H}_3\mathrm{O}^+] \]Here’s how to use it:

• Take the logarithm (base 10) of the hydronium ion concentration.
• Multiply by -1 to get the pH value.

For a more intuitive example:- If \[ [\mathrm{H}_3\mathrm{O}^+] = 1.58 \times 10^{-6} \text{ M} \], using the formula, the pH would be approximately 5.8.This calculation helps in determining how the concentration of hydronium ions affects the acidity of a solution, and it allows scientists and healthcare professionals to make informed decisions about treatment and diagnosis.

Acid-base Chemistry

Acid-base chemistry is a fundamental area of chemistry that deals with the properties of acids and bases and their reactions. It's closely tied to the concept of pH because acidity and basicity are defined in terms of proton exchange. An acid is a substance that donates protons (\(\mathrm{H}^{+}\ions\)) to solutions, increasing \[\mathrm{H}_3\mathrm{O}^+\] concentration.Bases, on the other hand, accept protons or donate hydroxide (\(\mathrm{OH}^{-}\)) ions, which can decrease \[\mathrm{H}_3\mathrm{O}^+\] concentration:

• An acidic solution has more \[\mathrm{H}_3\mathrm{O}^+\] because acids increase these ions.
• A basic solution has fewer \[\mathrm{H}_3\mathrm{O}^+\] because bases reduce or neutralize these ions.

In the context of saliva, it acts as a buffer, balancing and managing acidity to protect the mouth and teeth from potential harm. An understanding of acid-base chemistry is crucial in the development of dental care products and treatments aimed at maintaining a balanced oral pH and preventing decay.