Question

The pH of lemon juice is about \(2.0,\) whereas tomato juice's \(\mathrm{pH}\) is about \(4.0 .\) Approximately how much of an increase in hydrogen ion concentration is there between tomato juice and lemon juice? a. 2 times b. 10 times c. 100 times d. 1000 times

Short answer

c. 100 times

Step-by-step solution

Understand pH Scale

Understand that the pH scale is logarithmic. Each decrease of 1 on the pH scale corresponds to a tenfold increase in acidity or hydrogen (H+) ion concentration.

Calculate Change in pH

Find the change in the pH scale between the tomato juice and the lemon juice. In this case, the change is \(4.0 - 2.0 = 2\) units.

Translate Change in pH to Change in H+ Concentration

Translate this change in pH to a change in hydrogen ion concentration. Since each decrease of 1 on the pH scale multiplies the acidity by 10, a decrease of 2 units multiplies the acidity by \(10^2\) or 100.

Key concepts

Logarithmic pH Scale

Understanding the pH scale is crucial for studying chemistry, especially when dealing with acids and bases. The pH scale measures the acidity or alkalinity of a solution. It is a logarithmic scale, meaning each whole number on the scale represents a tenfold increase or decrease in the hydrogen ion (H+) concentration.

For example, a solution with a pH of 3 is ten times more acidic than one with a pH of 4 and one hundred times more acidic than a pH of 5. This allows us to compare the acidity of substances easily, even when the actual concentration of hydrogen ions varies widely. It's also important to note that the pH scale generally runs from 0 to 14, with 7 being neutral, below 7 being acidic, and above 7 being alkaline or basic.

Hydrogen Ion Concentration

The hydrogen ion concentration in a solution is what dictates its pH value. In scientific terms, we describe this concentration with the notation \[\left[ H^+ \right]\], and it is measured in moles per liter (M). High concentrations of hydrogen ions (low pH values) correspond to acidic solutions, while low concentrations (high pH values) indicate basic solutions.

The relationship between pH and hydrogen ion concentration is given by the formula \( pH = -\log_{10}\left[ H^+ \right] \). Therefore, if we know the pH, we can calculate the hydrogen ion concentration and vice versa. It's essential to realize that a small change in pH represents a significant change in \[\left[ H^+ \right]\] due to the logarithmic nature of the pH scale.

Acidity Calculation

When comparing the acidity of two solutions, as in the exercise with lemon and tomato juice, the calculation involves determining the difference in pH. Once the change in pH is established, we translate this into the factor of change in hydrogen ion concentration.

For a decrease of 1 on the pH scale, there's a tenfold increase in acidity; for a decrease of 2, it's a hundredfold increase (\(10^2\)), as seen in the step-by-step solution. Thus, moving from pH 4.0 to pH 2.0, the acidity increases by 100 times, answering the exercise with choice (c). This concept is vital for chemists when adjusting the pH of solutions and for understanding natural processes like soil acidity affecting plant growth.