Problem 73 - Chemistry The Molecular Nature of Matter

Question

Rhododendrons are shrubs that produce beautiful flowers in the springtime. They only grow well in soil that has a \(\mathrm{pH}\) that is 5.5 or slightly lower. What is the hydrogen ion concentration in the soil moisture if the \(\mathrm{pH}\) is 5.5 ?

Step-by-Step Solution

Answer

The hydrogen ion concentration in the soil moisture is \( 3.16 \times 10^{-6} \) M.

Step 1: Understanding pH

The pH of a solution is a measure of its acidity or alkalinity, defined by the negative logarithm (base 10) of the hydrogen ion concentration. The formula is \(\mathrm{pH} = -\log[H^+]\), where \(\mathrm{pH}\) is the pH level and \(\left[H^+\right]\) is the hydrogen ion concentration in moles per liter.

Step 2: Converting pH to Hydrogen Ion Concentration

To find the hydrogen ion concentration, we need to apply the inverse of the logarithmic function used to define pH. This means we will raise 10 to the power of the negative pH value. The formula to calculate the hydrogen ion concentration is \( [H^+] = 10^{-\mathrm{pH}} \) where \(\mathrm{pH} = 5.5\).

Step 3: Calculating the Hydrogen Ion Concentration

Substitute \(\mathrm{pH} = 5.5\) into the formula to get \( [H^+] = 10^{-5.5} \.\) Use a calculator to find the value of \( 10^{-5.5} \) which gives the hydrogen ion concentration.

Key Concepts

Hydrogen Ion Concentration

Understanding the hydrogen ion concentration in a solution is pivotal in various scientific fields, including botany, as seen in the rhododendron's soil pH requirements. Hydrogen ions, denoted as \(H^+\), influence the soil's acidity and essentially determine how well certain plants will thrive.

To calculate this concentration from the known pH, one uses the equation \( [H^+] = 10^{-\mathrm{pH}} \). When the pH is given, as in our rhododendron example with a pH of 5.5, simply input that value into the equation to determine the concentration. What this reveals is that a pH of 5.5 correlates to a hydrogen ion concentration of \(10^{-5.5}\) moles per liter, which requires a calculator for precise computation. It's important to note that a small change in pH corresponds to a significant change in ion concentration due to the logarithmic scale on which pH is based.

Acidity and Alkalinity

The terms 'acidity' and 'alkalinity' refer to the chemical characteristics of a substance that dictate its pH level. Acidity is associated with higher concentrations of hydrogen ions (\(H^+\)), whereas alkalinity is associated with lower concentrations or higher concentrations of hydroxide ions (\(OH^-\)).

In the context of natural environments like soil, these properties can be critical. For rhododendrons, which prefer acidic conditions, the soil needs a pH lower than 7, which is considered neutral. The pH scale ranges from 0 to 14, with values less than 7 indicating acidity and greater than 7 signifying alkalinity. The ideal pH of 5.5 for rhododendrons suggests the soil is acidic enough to maintain the necessary balance of nutrients and minerals for their growth.

Negative Logarithm

A logarithm is a mathematical operation that tells us how many times we need to multiply a number (called the base) to get another number. When the base is 10, any negative logarithm of a number gives us the pH. To be precise, pH is the negative base-10 logarithm of the hydrogen ion concentration in the solution.

The negative sign is used because as the hydrogen ion concentration increases (meaning more acidity), the pH value decreases. Thus, for a lower pH, the concentration is higher. The logarithmic relationship means that each integer pH value change represents a tenfold increase or decrease in the hydrogen ion concentration, which explains why pH differences can indicate dramatic shifts in soil chemistry, as is crucial for plant life like rhododendrons.