Question

Most cola soft drinks have a pH of 3.1. Green tea has a \(\mathrm{pH}\) of 5.8 (a) Calculate \(\left[\mathrm{H}^{+}\right]\) for the cola soft drink and green tea. (b) How much more acidic is a cola soft drink than green tea? Express your answer as a ratio of \(\left[\mathrm{H}^{+}\right]\) (cola) to \(\left[\mathrm{H}^{+}\right]\) (green tea).

Short answer

Answer: A cola soft drink is \(10^{2.7}\) times more acidic than green tea.

Step-by-step solution

Find the H+ concentration for cola soft drink

We are given the pH of cola soft drink, which is 3.1. We can use the pH formula to find the \(\mathrm{H}^+\) concentration: \(pH = -\log_{10}[\mathrm{H}^+]\) \(3.1 = -\log_{10}[\mathrm{H}^+_{cola}]\) Now, solve for the \(\mathrm{H}^+_{cola}\) concentration: \([\mathrm{H}^+_{cola}] = 10^{-3.1}\)

Find the H+ concentration for green tea

The pH of green tea is given as 5.8. Using the pH formula: \(5.8 = -\log_{10}[\mathrm{H}^+_{tea}]\) Now, solve for the \(\mathrm{H}^+_{tea}\) concentration: \([\mathrm{H}^+_{tea}] = 10^{-5.8}\)

Calculate the ratio of H+ concentrations

To find how much more acidic the cola soft drink is than green tea, we need to find the ratio of their H+ concentrations: \(\frac{[\mathrm{H}^+_{cola}]}{[\mathrm{H}^+_{tea}]} = \frac{10^{-3.1}}{10^{-5.8}}\) Simplify the ratio: \(\frac{[\mathrm{H}^+_{cola}]}{[\mathrm{H}^+_{tea}]} = 10^{(-3.1)-(-5.8)} = 10^{2.7}\) Therefore, a cola soft drink is \(10^{2.7}\) times more acidic than green tea.

Key concepts

pH and Acidity

Understanding pH and acidity is crucial for comprehending the chemical nature of many substances, including everyday items like cola soft drinks and green tea. The pH scale is a measure of how acidic or basic a solution is, ranging from 0 to 14. A pH lower than 7 indicates acidity, while a pH higher than 7 indicates alkalinity. A pH of 7 is considered neutral, which is the pH of pure water.

The acidity of a substance is directly linked to the concentration of hydrogen ions, denoted as \[\mathrm{H}^+\], in the solution. The more hydrogen ions present, the higher the acidity and, therefore, the lower the pH value. For instance, most cola soft drinks have a pH of 3.1, making them acidic, while green tea, with a pH of 5.8, is less acidic. Understanding this concept allows us to compare the acidity of different substances and calculate how much more acidic one substance is compared to another.

Hydrogen Ion Concentration

The concentration of hydrogen ions in a solution, represented by \[\mathrm{H}^+\], is a cornerstone concept in chemistry, particularly when discussing pH and acidity. In quantitative terms, pH is the negative logarithm (base 10) of the hydrogen ion concentration:
\(pH = -\log_{10}[\mathrm{H}^+]\).

If we have the pH of a solution, we can determine the hydrogen ion concentration. For example, the pH for cola soft drinks and green tea are given as 3.1 and 5.8, respectively. To find the hydrogen ion concentrations, we input these pH values into the pH formula to get:\[\mathrm{H}^+_{cola} = 10^{-3.1}\] and \[\mathrm{H}^+_{tea} = 10^{-5.8}\]. These calculations show that \[\mathrm{H}^+\] concentration in the cola is higher than in the green tea, indicating greater acidity.

Chemical Ratio Comparison

To compare the acidity of two substances, such as cola and green tea, we can use a chemical ratio comparison of their hydrogen ion concentrations. By calculating this ratio, we can express how many times more acidic one substance is compared to another. The calculation is straightforward once you have both hydrogen ion concentrations:
\(\frac{[\mathrm{H}^+_{cola}]}{[\mathrm{H}^+_{tea}]} = \frac{10^{-3.1}}{10^{-5.8}}\).

By simplifying, you can see that the cola is significantly more acidic: \(10^{2.7}\) times more acidic than green tea to be exact. Such comparisons are valuable in chemistry and can be applied across many disciplines, including food science, environmental science, and medicine.