Question

Calculate \(\left[\mathrm{H}^{+}\right]\) in each of the following solutions, and indicate whether the solution is acidic, basic, or neutral. a. \(\left[\mathrm{OH}^{-}\right]=4.22 \times 10^{-3} \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=1.01 \times 10^{-13} \mathrm{M}\) c. \(\left[\mathrm{OH}^{-}\right]=3.05 \times 10^{-7} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=6.02 \times 10^{-6} \mathrm{M}\)

Short answer

a. \(\left[\mathrm{H^+}\right] = 2.37 \times 10^{-12} \mathrm{M}\) - basic b. \(\left[\mathrm{H^+}\right] = 9.90 \times 10^{-2} \mathrm{M}\) - acidic c. \(\left[\mathrm{H^+}\right] = 3.28 \times 10^{-8} \mathrm{M}\) - basic d. \(\left[\mathrm{H^+}\right] = 1.66 \times 10^{-9} \mathrm{M}\) - basic

Step-by-step solution

Given: \(\left[\mathrm{OH}^{-}\right]=4.22 \times 10^{-3} \mathrm{M}\) To find [H⁺], use the ion product constant of water: \[\left[\mathrm{H^+}\right] = \frac{K_w}{\left[\mathrm{OH^-}\right]} = \frac{1.00 \times 10^{-14}}{4.22 \times 10^{-3}} = 2.37 \times 10^{-12} \mathrm{M}\] Since [H⁺] < [OH⁻], the solution is basic. #Case b#: Calculate [H⁺] for the second solution

Given: \(\left[\mathrm{OH}^{-}\right]=1.01 \times 10^{-13} \mathrm{M}\) To find [H⁺], use the ion product constant of water: \[\left[\mathrm{H^+}\right] = \frac{K_w}{\left[\mathrm{OH^-}\right]} = \frac{1.00 \times 10^{-14}}{1.01 \times 10^{-13}} = 9.90 \times 10^{-2} \mathrm{M}\] Since [H⁺] > [OH⁻], the solution is acidic. #Case c#: Calculate [H⁺] for the third solution

Given: \(\left[\mathrm{OH}^{-}\right]=3.05 \times 10^{-7} \mathrm{M}\) To find [H⁺], use the ion product constant of water: \[\left[\mathrm{H^+}\right] = \frac{K_w}{\left[\mathrm{OH^-}\right]} = \frac{1.00 \times 10^{-14}}{3.05 \times 10^{-7}} = 3.28 \times 10^{-8} \mathrm{M}\] Since [H⁺] < [OH⁻], the solution is basic. #Case d#: Calculate [H⁺] for the fourth solution

Given: \(\left[\mathrm{OH}^{-}\right]=6.02 \times 10^{-6} \mathrm{M}\) To find [H⁺], use the ion product constant of water: \[\left[\mathrm{H^+}\right] = \frac{K_w}{\left[\mathrm{OH^-}\right]} = \frac{1.00 \times 10^{-14}}{6.02 \times 10^{-6}} = 1.66 \times 10^{-9} \mathrm{M}\] Since [H⁺] < [OH⁻], the solution is basic.

Key concepts

Acidic and Basic Solutions

In chemistry, solutions can be categorized as acidic, basic, or neutral based on the concentration of hydrogen ions ([H⁺]) and hydroxide ions ([OH⁻]). An acidic solution has a higher concentration of hydrogen ions than hydroxide ions. Conversely, a basic solution has more hydroxide ions than hydrogen ions. A neutral solution has equal concentrations of [H⁺] and [OH⁻], which is typically the case with pure water.
To determine whether a solution is acidic or basic, observe the relative concentrations of these ions:

• If [H⁺] > [OH⁻], the solution is acidic.
• If [H⁺] < [OH⁻], the solution is basic.
• If [H⁺] = [OH⁻], the solution is neutral.

This principle is commonly used in pH calculations, where pH is a logarithmic measure of hydrogen ion concentration. Acidic solutions have a pH less than 7, basic solutions a pH greater than 7, and neutral solutions a pH of exactly 7. Understanding the distinction between acidic and basic solutions is crucial for predicting the behavior of chemical reactions.

Ion Product Constant of Water

The ion product constant of water, denoted as ( K_w ), is a key concept in understanding chemical equilibria in aqueous solutions. At 25°C (298 K), ( K_w ) is equal to ( 1.00 imes 10^{-14} ) M². This constant represents the product of the molar concentrations of hydrogen ions and hydroxide ions in pure water: equation: [ ( [H⁺][OH⁻] = K_w ) ] When water dissociates, it forms equal amounts of ( [H⁺] ) and ( [OH⁻] ), such that their product remains constant. This principle is invaluable for calculating the concentration of one ion, given the concentration of the other.
For example, knowing ( K_w ) allows us to calculate the hydrogen ion concentration in any solution if we know the hydroxide ion concentration: equation: [ ( [H⁺] = rac{K_w}{[OH⁻]} ) ] Understanding ( K_w ) is fundamental for interpreting changes in water chemistry and forms the basis for pH and pOH calculations.

Hydrogen Ion Concentration

Hydrogen ion concentration, represented by ( [H⁺] ), is a crucial parameter in characterizing the acidity of a solution. Higher hydrogen concentrations imply greater acidity. Calculating ( [H⁺] ) in solutions allows chemists to identify how acidic or basic a solution is and is fundamental to pH determination.
When hydroxide ion concentration ( [OH⁻] ) is known, ( [H⁺] ) can be found using the ion product constant of water: equation: [ ( [H⁺] = rac{K_w}{[OH⁻]} ) ]

This calculation helps predict the pH and the overall behavior of the solution in chemical processes. For a given ( [OH⁻] ), a lower calculated ( [H⁺] ) indicates a basic solution, whereas a higher ( [H⁺] ) suggests an acidic environment.
The relationship between hydrogen ion concentration and solution behavior is essential in disciplines like analytical chemistry and environmental science, offering insights into reactive potential and biological compatibility. For quick reference, remember that ( [H⁺] ) and pH are inversely related: higher ( [H⁺] ) values lead to lower pH.