Question

Give the hydronium ion and hydroxide ion concentrations of solutions with the following values of \(\mathrm{pH}\). Which of the solutions is most acidic? Which is most basic? (a) \(\mathrm{pH} 13.0\) (b) \(\mathrm{pH} 3.0\) (c) \(\mathrm{pH} 8.0\)

Short answer

Solution with pH 3.0 is most acidic, and solution with pH 13.0 is most basic.

Step-by-step solution

Understanding pH and its relation to ion concentrations

The pH of a solution is defined as the negative logarithm of the hydronium ion concentration: \( \mathrm{pH} = -\log[\mathrm{H}_3\mathrm{O}^+] \). The hydronium ion concentration \([\mathrm{H}_3\mathrm{O}^+]\) can be found by rearranging the equation to \([\mathrm{H}_3\mathrm{O}^+] = 10^{-\mathrm{pH}}\).

Calculate hydronium ion concentrations

For each given pH value, use the formula \([\mathrm{H}_3\mathrm{O}^+] = 10^{-\mathrm{pH}}\) to find the hydronium ion concentrations:(a) \( \mathrm{pH} = 13.0 \) so \([\mathrm{H}_3\mathrm{O}^+] = 10^{-13.0} = 1 \times 10^{-13} \mathrm{M} \).(b) \( \mathrm{pH} = 3.0 \) so \([\mathrm{H}_3\mathrm{O}^+] = 10^{-3.0} = 1 \times 10^{-3} \mathrm{M} \).(c) \( \mathrm{pH} = 8.0 \) so \([\mathrm{H}_3\mathrm{O}^+] = 10^{-8.0} = 1 \times 10^{-8} \mathrm{M} \).

Calculate hydroxide ion concentrations

The product of the hydronium ion concentration and the hydroxide ion concentration is always \(1.0 \times 10^{-14}\) at 25°C, represented by the expression \([\mathrm{H}_3\mathrm{O}^+][\mathrm{OH}^-] = 1.0 \times 10^{-14}\). Solve for \([\mathrm{OH}^-]\) by rearranging to \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{[\mathrm{H}_3\mathrm{O}^+]}\):(a) \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{1 \times 10^{-13}} = 1.0 \times 10^{-1} \mathrm{M} \).(b) \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{1 \times 10^{-3}} = 1.0 \times 10^{-11} \mathrm{M} \).(c) \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{1 \times 10^{-8}} = 1.0 \times 10^{-6} \mathrm{M} \).

Determine the most acidic and most basic solutions

The lower the pH, the higher the hydronium ion concentration, indicating a more acidic solution. The higher the pH, the higher the hydroxide ion concentration, indicating a more basic solution:(b) \( \mathrm{pH} = 3.0 \) has the highest \([\mathrm{H}_3\mathrm{O}^+]\) and is most acidic.(a) \( \mathrm{pH} = 13.0 \) has the highest \([\mathrm{OH}^-]\) and is most basic.

Key concepts

Hydronium Ion

The hydronium ion, represented as \( \mathrm{H}_3\mathrm{O}^+ \), is a vital player in the chemistry of acids and bases. It's essentially a water molecule with an extra hydrogen ion attached. When acids dissolve in water, they release hydrogen ions \( \mathrm{H}^+ \), which quickly bind with water molecules, forming hydronium ions. This process increases the number of hydronium ions in the solution, which is measurable as pH.
In essence, pH is the negative logarithm of the concentration of hydronium ions in a solution: \[ \mathrm{pH} = -\log[\mathrm{H}_3\mathrm{O}^+] \].
This relationship allows us to determine how acidic a solution is by manipulating this equation to find \([\mathrm{H}_3\mathrm{O}^+] = 10^{-\mathrm{pH}}\).
For example, if you have a solution where the pH is 3.0, you can calculate the hydronium ion concentration to be \( 1 \times 10^{-3} \) M. The higher the concentration of hydronium ions, the more acidic the solution is.

Hydroxide Ion

The hydroxide ion, \( \mathrm{OH}^- \), often acts as the counterpart to the hydronium ion in aqueous solutions. Hydroxide ions are crucial in determining the basicity of a solution. They combine with hydrogen ions to form water molecules, effectively neutralizing acids.
The equation linking the concentrations of hydronium and hydroxide ions is a constant at 25°C:\[ [\mathrm{H}_3\mathrm{O}^+][\mathrm{OH}^-] = 1.0 \times 10^{-14} \].
This expression shows the intrinsic relationship between the two ions: as one increases, the other must decrease to maintain this equilibrium. For a solution with a pH of 13.0, the hydronium ion concentration would be relatively low, \( 1 \times 10^{-13} \) M, while the hydroxide ion concentration would be higher, \( 1.0 \times 10^{-1} \) M. This high concentration of hydroxide ions indicates a strong basic property.

Acidic Solution

An acidic solution is characterized by a higher concentration of hydronium ions than hydroxide ions. In solutions where the pH is less than 7, such as our example at pH 3.0, the number of hydronium ions is significantly higher compared to hydroxide ions. This imbalance tilts the solution towards acidity.
Acidic solutions have several properties due to their hydronium ion content:

• They have a sour taste.
• Can turn blue litmus paper red.
• React with metals to produce hydrogen gas.

Understanding the nature of acidic solutions is essential in many fields, from biology to industrial chemistry. The lower the pH value, the higher the acidity as seen with the pH 3.0 solution having \(1 \times 10^{-3} \) M hydronium ions, making it the most acidic in the provided examples.

Basic Solution

Basic solutions, or alkaline solutions, have a higher concentration of hydroxide ions than hydronium ions. When the pH is greater than 7, the solution leans towards basicity. For instance, with a pH of 13.0, as highlighted in the solution, the concentration of hydroxide ions is higher, at \( 1.0 \times 10^{-1} \) M, signifying strong basic properties.
Some typical properties of basic solutions include:

• They taste bitter.
• Have a soapy feel.
• Turn red litmus paper blue.

In practical applications, bases are used in soap-making and various cleaning agents. A basic solution like the one with pH 13.0 from the example is considered highly basic, particularly because its hydroxide ion concentration is considerably greater compared to its hydronium ion concentration, clearly showcasing its basic nature.