Question

Calculate \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in each of the following solutions. \(\begin{array}{ll}{\text { a. Milk, } p H=6.50 .} & {\text { c. Milk of magnesia, } p H=10.50} \\ {\text { b. Lemon juice, pH }=2.37} & {\text { d. Household ammonia, } p H=11.90}\end{array}\)

Short answer

a. Milk: \( [\mathrm{H}^{+}] = 3.16 \times 10^{-7} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 3.16 \times 10^{-8} \, \mathrm{M} \) b. Lemon juice: \( [\mathrm{H}^{+}] = 4.27 \times 10^{-3} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 2.34 \times 10^{-12} \, \mathrm{M} \) c. Milk of magnesia: \( [\mathrm{H}^{+}] = 3.16 \times 10^{-11} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 3.16 \times 10^{-4} \, \mathrm{M} \) d. Household ammonia: \( [\mathrm{H}^{+}] = 1.26 \times 10^{-12} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 7.94 \times 10^{-3} \, \mathrm{M} \)

Step-by-step solution

Calculate the concentration of hydrogen ions (H+) in each solution

First, we need to find the H+ ion concentration for each solution using the pH value and the equation: \( pH=-\log[\mathrm{H}^{+}] \) For each solution, we'll find [H+]: a. Milk: \( pH = 6.50 \) b. Lemon juice: \( pH = 2.37 \) c. Milk of magnesia: \( pH = 10.50 \) d. Household ammonia: \( pH = 11.90 \)

Calculate the concentration of hydroxide ions (OH-) in each solution

Next, we'll find the pOH value for each solution using the equation: \( pH + pOH = 14 \) For each solution, we'll find pOH: a. Milk: \( pOH = 14 - 6.50 \) b. Lemon juice: \( pOH = 14 - 2.37 \) c. Milk of magnesia: \( pOH = 14 - 10.50 \) d. Household ammonia: \( pOH = 14 - 11.90 \) Finally, we'll find the concentration of hydroxide ions (OH-) in each solution using the equation: \( pOH=-\log[\mathrm{OH}^{-}] \) For each solution, we'll find [OH-]: a. Milk b. Lemon juice c. Milk of magnesia d. Household ammonia

Final results

After performing the calculations, we find the concentrations of H+ and OH- ions in each solution: a. Milk: \( [\mathrm{H}^{+}] = 3.16 \times 10^{-7} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 3.16 \times 10^{-8} \, \mathrm{M} \) b. Lemon juice: \( [\mathrm{H}^{+}] = 4.27 \times 10^{-3} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 2.34 \times 10^{-12} \, \mathrm{M} \) c. Milk of magnesia: \( [\mathrm{H}^{+}] = 3.16 \times 10^{-11} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 3.16 \times 10^{-4} \, \mathrm{M} \) d. Household ammonia: \( [\mathrm{H}^{+}] = 1.26 \times 10^{-12} \, \mathrm{M} \) \( [\mathrm{OH}^{-}] = 7.94 \times 10^{-3} \, \mathrm{M} \)

Key concepts

Hydrogen Ion Concentration

The hydrogen ion concentration in a solution is a fundamental measure when it comes to understanding the solution's acidity. It is typically expressed in moles per liter (\textbf{M}), where 1 mole of a substance is composed of 6.022 x 10^23 particles. The concentration of hydrogen ions, noted as \( [\mathrm{H}^{+}] \) in solutions, provides an insight into how acidic a substance is. The smaller the \( [\mathrm{H}^{+}] \), the less acidic the solution, and vice versa.

For example, lemon juice, with a \( pH = 2.37 \), has a high hydrogen ion concentration, making it highly acidic. In contrast, household ammonia, with a \( pH = 11.90 \), has a much lower hydrogen ion concentration, indicating it is very basic. Calculating \( [\mathrm{H}^{+}] \) entails using the expression \( pH = -\log[\mathrm{H}^{+}] \), a logarithmic function that inversely correlates the \( pH \)-values and \( [\mathrm{H}^{+}] \) of a solution.

Hydroxide Ion Concentration

Complementary to hydrogen ions, the hydroxide ion concentration, represented as \( [\mathrm{OH}^{-}] \), tells us about the basicity of a solution. Similar to \( [\mathrm{H}^{+}] \), it is expressed in molarity (\textbf{M}). In a neutral solution, the concentrations of \( [\mathrm{H}^{+}] \) and \( [\mathrm{OH}^{-}] \) are equal, because water dissociates equally into \( [\mathrm{H}^{+}] \) and \( [\mathrm{OH}^{-}] \) ions.

For acidic solutions, \( [\mathrm{OH}^{-}] \) will be lower compared to \( [\mathrm{H}^{+}] \) and for basic solutions, it will be higher. To calculate the hydroxide ion concentration, we first find the pOH using \( pOH = 14 - pH \) and then use the equation \( pOH = -\log[\mathrm{OH}^{-}] \). This process allows us to understand how the concentration of these ions affects a solution's overall acidity or basicity.

Acid and Base Solutions

Acids and bases are fundamental chemical solutions characterized by their pH levels. Acids have a pH less than 7, where they release hydrogen ions \( ([\mathrm{H}^{+}]) \) into the solution, thus increasing its concentration. Examples of acidic solutions are lemon juice and gastric acid.

Bases, on the other hand, have a pH greater than 7, and they accept hydrogen ions, creating more hydroxide ions \( ([\mathrm{OH}^{-}]) \) and thereby reducing the concentration of hydrogen ions. Milk of magnesia and household ammonia are basic solutions. An acid-base reaction typically involves the transfer of hydrogen ions from the acid to the base, often resulting in the production of water and a salt.

pH Scale

The pH scale is a dimensional, logarithmic scale used to specify the acidity or basicity of an aqueous solution. pH is defined as the negative logarithm of the hydrogen ion concentration: \( pH = -\log[\mathrm{H}^{+}] \). The pH scale ranges from 0 to 14, with 7 being neutral.

Each unit change on the pH scale corresponds to a tenfold change in hydrogen ion concentration. Therefore, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4. This scale helps chemists, biologists, and students to quickly and easily understand the relative acidity or basicity of various substances—this is vital for many chemical processes and is especially important in biological systems where specific pH levels are crucial for proper function.