Question

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pH values. a. $\mathrm{pH}=9.01$ b. $\mathrm{pH}=6.89$ c. $\mathrm{pH}=1.02$ d. $\mathrm{pH}=7.00$

Short answer

The hydrogen ion concentrations for solutions with the given pH values are: a. Approximately $9.77\times {10}^{-10}\mathrm{M}$ b. Approximately $1.29\times {10}^{-7}\mathrm{M}$ c. Approximately $9.54\times {10}^{-2}\mathrm{M}$ d. Approximately $1.00\times {10}^{-7}\mathrm{M}$

Step-by-step solution

Understand the relationship between pH and hydrogen ion concentration

The formula connecting pH and the concentration of hydrogen ions (H+) in a solution is given by: $$\mathrm{pH}=-{\log }_{10}[{\mathrm{H}}^{+}]$$ Here, $\mathrm{pH}$ represents the pH value, and $[{\mathrm{H}}^{+}]$ represents the hydrogen ion concentration in moles per liter (M).

Rearrange the formula to isolate hydrogen ion concentration

To solve for $[{\mathrm{H}}^{+}]$, we need to rearrange the formula and isolate the hydrogen ion concentration term: $$[{\mathrm{H}}^{+}]={10}^{-\mathrm{pH}}$$

Calculate hydrogen ion concentration for each pH value

Below, we calculate the hydrogen ion concentration for each given pH value using the rearranged formula: a. $\mathrm{pH}=9.01$: $$[{\mathrm{H}}^{+}]={10}^{-9.01}\approx 9.77\times {10}^{-10}\mathrm{M}$$ b. $\mathrm{pH}=6.89$: $$[{\mathrm{H}}^{+}]={10}^{-6.89}\approx 1.29\times {10}^{-7}\mathrm{M}$$ c. $\mathrm{pH}=1.02$: $$[{\mathrm{H}}^{+}]={10}^{-1.02}\approx 9.54\times {10}^{-2}\mathrm{M}$$ d. $\mathrm{pH}=7.00$: $$[{\mathrm{H}}^{+}]={10}^{-7}\approx 1.00\times {10}^{-7}\mathrm{M}$$ So, the hydrogen ion concentrations for solutions with the given pH values are: a. Approximately $9.77\times {10}^{-10}\mathrm{M}$ b. Approximately $1.29\times {10}^{-7}\mathrm{M}$ c. Approximately $9.54\times {10}^{-2}\mathrm{M}$ d. Approximately $1.00\times {10}^{-7}\mathrm{M}$

Key concepts

Hydrogen Ion Concentration

The concept of hydrogen ion concentration is integral to understanding solutions in chemistry. It refers to the amount of hydrogen ions (H+) present in a solution, measured in moles per liter (M). The concentration of these ions determines how acidic or basic a solution is. Generally, the more H+ ions a solution has, the more acidic it will be, while fewer H+ ions suggest a basic or alkaline solution.
To calculate the hydrogen ion concentration from a given pH, we use the formula:

• $$[{\text{H}}^{+}]={10}^{-\text{pH}}$$

This equation tells us that to find the concentration of H+ ions, we need to take 10 to the power of the negative pH. Using this simple formula, we can easily convert between pH and hydrogen ion concentration.

Logarithmic Scale

A logarithmic scale is a way of displaying numbers so that they can show large ranges of values in a compact form. This is the type of scale used in measuring pH, which represents the acidity or basicity of a solution. Essentially, on a logarithmic scale, each unit change corresponds to a tenfold change in H+ concentration.
In the pH scale:

• pH is calculated as the negative base-10 logarithm of the hydrogen ion concentration: $$-{\log }_{10}[{\text{H}}^{+}]$$
• This means that a pH change by 1 unit means a tenfold change in hydrogen ion concentration.
• For example, a pH of 5 is ten times more acidic than a pH of 6.

Such scaling allows scientists to handle very large or very small numbers more conveniently. It also reflects how sensitive organisms and reactions can be to changes in acidity or basicity.

Acid-Base Chemistry

Acid-base chemistry is a central theme in many chemical reactions and processes. It revolves around the behavior of acids and bases and their ability to donate or accept protons (H+ ions). An acid is a substance that can release hydrogen ions, while a base can accept them.
Here are some important points about acid-base chemistry:

• Solutions with a pH less than 7 are acidic, indicating a higher concentration of H+ ions.
• Solutions with a pH greater than 7 are basic or alkaline, showing a lower concentration of H+ ions.
• A neutral solution, like pure water, has a pH of exactly 7.

Understanding how acids and bases interact is crucial in fields ranging from medicine to environmental science, as these reactions can dictate conditions of solutions and even entire biological systems.