Question

Calculate the pH corresponding to each of the hydrogen ion concentrations given below, and indicate whether each solution is acidic or basic. a. $\left[{\mathrm{H}}^{+}\right]=4.02\times {10}^{-3}M$ b. $\left[{\mathrm{H}}^{+}\right]=8.99\times {10}^{-7}M$ c. $\left[{\mathrm{H}}^{+}\right]=2.39\times {10}^{-6}M$ d. $\left[{\mathrm{H}}^{+}\right]=1.89\times {10}^{-10}M$

Short answer

a. pH = 2.40, acidic. b. pH = 6.05, acidic. c. pH = 5.62, acidic. d. pH = 9.72, basic.

Step-by-step solution

Calculate the pH using the given hydrogen ion concentrations

Use the formula $pH=-{\log }_{10}[{\mathrm{H}}^{+}]$ to find the pH of each solution. a. $pH=-{\log }_{10}(4.02\times {10}^{-3})$ b. $pH=-{\log }_{10}(8.99\times {10}^{-7})$ c. $pH=-{\log }_{10}(2.39\times {10}^{-6})$ d. $pH=-{\log }_{10}(1.89\times {10}^{-10})$

Perform the logarithmic calculations

Find the pH values. a. $pH=2.40$ b. $pH=6.05$ c. $pH=5.62$ d. $pH=9.72$

Determine if the solutions are acidic or basic

Use the criteria for acidic, basic, and neutral solutions. a. $pH=2.40<7$, so the solution is acidic. b. $pH=6.05<7$, so the solution is acidic. c. $pH=5.62<7$, so the solution is acidic. d. $pH=9.72>7$, so the solution is basic. In conclusion: a. The solution with a hydrogen ion concentration of $\left[{\mathrm{H}}^{+}\right]=4.02\times {10}^{-3}M$ has a pH of 2.40 and is acidic. b. The solution with a hydrogen ion concentration of $\left[{\mathrm{H}}^{+}\right]=8.99\times {10}^{-7}M$ has a pH of 6.05 and is acidic. c. The solution with a hydrogen ion concentration of $\left[{\mathrm{H}}^{+}\right]=2.39\times {10}^{-6}M$ has a pH of 5.62 and is acidic. d. The solution with a hydrogen ion concentration of $\left[{\mathrm{H}}^{+}\right]=1.89\times {10}^{-10}M$ has a pH of 9.72 and is basic.

Key concepts

Hydrogen Ion Concentration

Understanding hydrogen ion concentration is crucial when studying the properties of solutions. In chemistry, the hydrogen ion concentration, often denoted as $\left[{\mathrm{H}}^{+}\right]$, represents the number of hydrogen ions present in a solution, measured in moles per liter (M). These tiny charged particles drastically influence the solution's overall reactivity, corrosiveness, and most notably, acidity or basicity.

When a substance dissolves in water, it either increases the hydrogen ion concentration, making the solution acidic, or it produces hydroxide ions $\left[{\mathrm{OH}}^{-}\right]$, which make the solution basic. A neutral solution, like pure water, has equal concentrations of $\left[{\mathrm{H}}^{+}\right]$) and $\left[{\mathrm{OH}}^{-}\right]$, both at $1\times {10}^{-7}M$. The concept of hydrogen ion concentration is the backbone of understanding the pH scale, as it directly affects the pH value of any solution.

Acidic and Basic Solutions

Solutions can be broadly classified into three categories based on their pH values: acidic, basic (alkaline), or neutral. An acidic solution has a higher concentration of hydrogen ions ($\left[{\mathrm{H}}^{+}\right]$ > $1\times {10}^{-7}M$) and a pH less than 7. Examples include lemon juice and vinegar. Conversely, a basic solution contains more hydroxide ions than hydrogen ions, indicated by $\left[{\mathrm{OH}}^{-}\right]$ > $\left[{\mathrm{H}}^{+}\right]$) and a pH greater than 7; common examples are baking soda and bleach.

A solution is considered neutral when the concentrations of hydrogen and hydroxide ions are equal, typically at $\left[{\mathrm{H}}^{+}\right]$) and $\left[{\mathrm{OH}}^{-}\right]$ = $1\times {10}^{-7}M$, resulting in a pH of 7. This balance is a delicate one, where even small changes in hydrogen ion concentration can lead to significant shifts in pH, thus altering a solution's classification from neutral to either acidic or basic.

pH Scale

The pH scale is a logarithmic measure that quantifies the acidity or basicity of a solution on a scale from 0 to 14. It is an inverse logarithmic representation of hydrogen ion concentration, indicating how acidic or basic a solution is. The scale is centered around the pH value of 7, which is considered neutral, characteristic of pure water at room temperature.

Understanding the Scale

On the pH scale, a lower value represents a higher concentration of hydrogen ions (more acidic), while a higher value indicates a lower concentration of hydrogen ions (more basic). A pH less than 7 signifies acidity, with 0 being the most acidic. A pH greater than 7 indicates basicity, with 14 being the most basic. This scale helps us communicate and compare the acidity and basicity of different solutions in a straightforward manner.

Logarithmic Calculations

Logarithmic calculations are pivotal in pH determination because pH is defined as the negative logarithm (to the base 10) of the hydrogen ion concentration. This relationship transforms the potentially cumbersome numbers representing hydrogen ion concentrations into a more manageable scale - the pH scale.

Calculating pH

To calculate the pH of a solution, use the formula $pH=-{\log }_{10}\left[{\mathrm{H}}^{+}\right]$. This formula translates the concentration of hydrogen ions into a value on the pH scale. It's important to remember that because the pH scale is logarithmic, each whole number change in pH represents a tenfold increase or decrease in hydrogen ion concentration. For instance, a solution with a pH of 4 has ten times more hydrogen ions than a solution with a pH of 5. This logarithmic relationship allows us to work with more convenient numbers when dealing with the extremely tiny or large values often encountered in chemical solutions.