Problem 40 - Chemistry Matter and Change

Question

Calculate The pH of a tomato is approximately \(4.50 .\) What are \(\left[H^{+}\right]\) and \(\left[0 \mathrm{H}^{-}\right]\) in a tomato?

Step-by-Step Solution

Answer

[H^{+}]=3.16\times 10^{-5} M; [OH^{-}]=3.16\times 10^{-10} M.

Step 1: Understand pH Definition

The pH of a solution is a measure of how acidic or basic it is. It is determined by the concentration of hydrogen ions ( H^{+} ). The pH scale ranges from 0 to 14. A pH of 7 is neutral, below 7 is acidic, and above 7 is basic.

Step 2: Find H^{+} Concentration

The formula to find the hydrogen ion concentration from pH is: \[ \left[H^{+}\right] = 10^{-pH} \] In this case, the pH of the tomato is given as 4.50, so: \[ \left[H^{+}\right] = 10^{-4.50} \] Calculate this value to find the resulting concentration of hydrogen ions.

Step 3: Calculate H^{+} Concentration

Compute 10^{-4.50} using a calculator to find the concentration of hydrogen ions: \[ \left[H^{+}\right] = 3.16 \times 10^{-5} \text{ M} \] This indicates the molarity (M) which is moles per liter of H^{+} ions in the tomato.

Step 4: Use Water Ion Product

The ion product of water at 25°C (K_w) is: \[ K_w = \left[H^{+}\right] \times \left[OH^{-}\right] = 1.0 \times 10^{-14} \] Use this relationship to determine the OH^{-} concentration.

Step 5: Calculate OH^{-} Concentration

Rearrange the water ion product to solve for OH^{-} concentration: \[ \left[OH^{-}\right] = \frac{K_w}{\left[H^{+}\right]} = \frac{1.0 \times 10^{-14}}{3.16 \times 10^{-5}} \] Perform the division to find OH^{-} concentration.

Step 6: Final Calculation of OH^{-}

Calculate the value obtained in the previous step: \[ \left[OH^{-}\right] \approx 3.16 \times 10^{-10} \text{ M} \] This result is the molarity of hydroxide ions in the tomato.

Key Concepts

Acid-Base Chemistry

Acid-base chemistry is a fundamental area of chemistry that focuses on the properties of acids and bases, and the reactions between them. In simple terms, acids are substances that donate hydrogen ions (\(H^{+}\)) when dissolved in water, while bases accept hydrogen ions. Understanding this concept helps us explain things like why a lemon tastes sour or why soap is slippery.
The pH scale is an easy way to measure how acidic or basic a solution is.

• If a substance has a pH less than 7, it is considered acidic.
• A pH of exactly 7 is neutral, like pure water.
• Substances with a pH greater than 7 are basic or alkaline.

In this exercise, the pH of tomato juice is given as 4.50, indicating that it is mildly acidic.

Hydrogen Ion Concentration

The concentration of hydrogen ions in a solution is crucial in determining its pH.

To find the hydrogen ion concentration (\([H^{+}]\)) from pH, you use the formula: \([H^{+}] = 10^{-pH}\).

For example, with the tomato's pH of 4.50, the hydrogen ion concentration can be calculated as follows:

• Substitute 4.50 into the formula: \([H^{+}] = 10^{-4.50}\).
• Use a calculator to find \([H^{+}] = 3.16 \times 10^{-5} \text{ M}\), indicating the amount of hydrogen ions per liter.

A higher concentration of \(H^{+}\) ions means a solution is more acidic, while a lower concentration indicates a more basic solution.

Water Ion Product

The concept of the water ion product, \(K_w\), is essential to understanding the relationship between \(H^{+}\) and \(OH^{-}\) concentrations. At 25°C, \(K_w\) is always \(1.0 \times 10^{-14}\).It is expressed by the formula:

• \(K_w = [H^{+}] \times [OH^{-}]\)

This equilibrium constant reflects the natural state of water, where both hydrogen and hydroxide ions are present. If the concentration of one ion increases, the other must decrease to maintain this constant product. Thus, knowing the \(H^{+}\) concentration lets us calculate the \(OH^{-}\) concentration, and vice versa.

Hydroxide Ion Concentration

To determine the concentration of hydroxide ions (\(OH^{-}\)), you rearrange the ion product of water formula:

• \([OH^{-}] = \frac{K_w}{[H^{+}]}\)

Given \([H^{+}] = 3.16 \times 10^{-5} \text{ M}\) in tomato juice, we can calculate \([OH^{-}]\): \([OH^{-}] = \frac{1.0 \times 10^{-14}}{3.16 \times 10^{-5}} \approx 3.16 \times 10^{-10} \text{ M}\).This calculation shows the basicity level in comparison to the acidity, inverting the hydrogen ion concentration to hydroxide concentration. Hydroxide ions are present in much lower concentrations in acidic solutions, such as tomatoes. Understanding \([OH^{-}]\) aids in assessing the basic characteristics of a solution.