Question

The \(\mathrm{pH}\) of lemon juice is about \(2.0,\) whereas tom ato juice's \(\mathrm{pH}\) is about 4 . Therefore, the concentration of hy drogen ions in the tomato juice is ______ times _______ than the lemon juice. a. \(2 ;\) greater b. 2; less c. 100 ; less d. 100 ; greater

Short answer

Answer: The concentration ratio of hydrogen ions between tomato juice and lemon juice is 1:100, and the tomato juice has a lesser concentration of hydrogen ions.

Step-by-step solution

Write down the pH values

Lemon juice has a pH of \(2.0\) and tomato juice has a pH of \(4\).

Use the pH formula to find the H+ concentration

Using the formula \(\mathrm{pH} = -\log_{10}\left([\mathrm{H^{+}}]\right)\), we can express the concentration of hydrogen ions as \([\mathrm{H^+}] = 10^{-\mathrm{pH}}\).

Calculate the H+ concentrations for both juices

For the lemon juice, the concentration of hydrogen ions is: \([\mathrm{H^{+}}]_{\mathrm{lemon}} = 10^{-2.0} = 0.01\) For the tomato juice, the concentration of hydrogen ions is: \([\mathrm{H^{+}}]_{\mathrm{tomato}} = 10^{-4} = 0.0001\)

Find the ratio of the H+ concentrations

To find the ratio, divide the concentration of hydrogen ions in the tomato juice by the concentration of hydrogen ions in the lemon juice: \(Ratio = \frac{[\mathrm{H^{+}}]_{\mathrm{tomato}}}{[\mathrm{H^{+}}]_{\mathrm{lemon}}} = \frac{0.0001}{0.01} = \frac{1}{100} = 0.01\)

Interpret the ratio

The ratio of hydrogen ions in tomato juice compared to lemon juice is \(0.01\). Since this is a ratio less than one, the tomato juice has a lower concentration of hydrogen ions. Therefore, there are 100 times less hydrogen ions in the tomato juice as compared to lemon juice. So, the correct answer is: c. 100; less

Key concepts

pH scale

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with 7 being neutral. A pH value less than 7 denotes an acidic solution, while a value greater than 7 indicates a basic (alkaline) solution. The pH scale is logarithmic, meaning that each unit change represents a tenfold difference in acidity or basicity. For example, a solution with a pH of 4 is ten times more acidic than one with a pH of 5 and a hundred times more acidic than one with a pH of 6.

This is crucial to understand when comparing substances like lemon and tomato juices; lemon juice with a pH of 2.0 is significantly more acidic than tomato juice with a pH of 4.0. To get a grasp on just how much more acidic, one can calculate the hydrogen ion concentration, which reveals that the lemon juice is 100 times more acidic than the tomato juice.

Calculating H+ concentration

Hydrogen ion concentration, often represented as \( [H^+] \), determines a solution's acidity and directly relates to pH value. The mathematical relationship to calculate this concentration from pH is given by the formula \( [H^+] = 10^{-\text{pH}} \). The formula indicates that the hydrogen ion concentration is equal to ten raised to the power of the negative pH value.

Applying this formula allows us to convert a pH value into a measurable concentration. For instance, lemon juice with a pH of 2.0 will have a hydrogen ion concentration of \( [H^+] = 10^{-2} = 0.01 \) M (molar), while tomato juice with a pH of 4.0 will have a concentration of \( [H^+] = 10^{-4} = 0.0001 \) M. Understanding how to conduct these calculations is essential for chemistry and biology students, as it helps to quantify the acidity of various environments.

Logarithmic relationships in pH

The pH scale's logarithmic nature is not just a quirky detail—it's a fundamental aspect that describes how we perceive changes in acidity. A logarithmic relationship means that with every increase of one pH unit, the hydrogen ion concentration decreases by a factor of ten. Conversely, a decrease by one pH unit increases the hydrogen ion concentration by a factor of ten.

To comprehend this better, consider our lemon and tomato juice comparison again. While the difference in pH is 2 units (from pH 4 to pH 2), the hydrogen ion concentration changes by a factor of \(10^2\text{ or }100\). This demonstrates the dramatic effect that even small changes in pH can have on the chemical nature of a solution. Exploring logarithms in the context of pH not only improves understanding of acid-base chemistry but also reinforces math skills related to exponential changes and inverse logarithmic functions.