Question

Calculate the \(\mathrm{pH}\) of each of the following given the molar hydrogen ion concentration: (a) carrots, \(\left[\mathrm{H}^{+}\right]=0.0000079 \mathrm{M}\) (b) peas, \(\left[\mathrm{H}^{+}\right]=0.00000039 \mathrm{M}\)

Short answer

The pH of carrots is approximately 5.1, and the pH of peas is approximately 6.4.

Step-by-step solution

Understanding 6H^+7 and pH

The pH of a solution is calculated using the formula: \[ \text{pH} = -\log_{10} [\mathrm{H}^+] \] where \([\mathrm{H}^+]\) is the hydrogen ion concentration.

Calculate the pH for Carrots

For carrots, the hydrogen ion concentration is \([\mathrm{H}^+] = 0.0000079\, \text{M}\). Use the formula \( \text{pH} = -\log_{10} [\mathrm{H}^+] \), substituting the given value:\[ \text{pH} = -\log_{10} (0.0000079) \]Calculate using a calculator or logarithm table to find:\[ \text{pH} \approx 5.1 \].

Calculate the pH for Peas

For peas, the hydrogen ion concentration is \([\mathrm{H}^+] = 0.00000039\, \text{M}\). Using the same formula:\[ \text{pH} = -\log_{10} (0.00000039) \]Compute the logarithm to find the pH:\[ \text{pH} \approx 6.4 \].

Key concepts

Hydrogen Ion Concentration

In chemistry, the hydrogen ion concentration is a measure of the number of hydrogen ions present in a solution. It is represented as \( [\mathrm{H}^+] \). Hydrogen ions are crucial because they determine the acidity or basicity of a solution. The concentration is typically measured in moles per liter (M), which is known as molarity. High hydrogen ion concentration indicates a more acidic solution, while a lower concentration points to a more basic or neutral solution. To easily compare acidity levels, chemists use the pH scale, which translates concentrations into a more user-friendly number. The pH is a logarithmic scale ranging from 0 to 14, with 7 being neutral. Values below 7 indicate acidic solutions, while numbers above 7 signify basic solutions.

Logarithms in Chemistry

Logarithms are mathematical operations that are used extensively in chemistry to simplify calculations involving very small or large numbers, such as hydrogen ion concentrations. When we talk about the pH scale, we're actually referring to a logarithmic scale. The pH is calculated using the formula:

• \( \text{pH} = -\log_{10} [\mathrm{H}^+] \).

This formula transforms the molarity of hydrogen ions into a more comprehensible number, making it easier to determine a solution's acidity.Logarithms make it easier to understand changes in concentration. For example, a change in 1 pH unit corresponds to a tenfold change in hydrogen ion concentration. This means that a solution with a pH of 5 is ten times more acidic than one with a pH of 6.

Acid-Base Chemistry

Acid-base chemistry is the study of acids, bases, and their reactions. It is a fundamental concept in chemistry that helps understand reactions in water, known as aqueous reactions. Acids are substances that increase the hydrogen ion concentration in a solution, whereas bases reduce it. This dynamic often involves the transfer of hydrogen ions between substances. Understanding pH, which measures how acidic or basic a solution is, is crucial to predicting the outcomes of acid-base reactions. Various indicators and measurement tools are used in conjunction with the pH concept to monitor these reactions in labs or industrial processes. For instance, determining the pH of soil can aid in providing the right conditions for plant growth, explaining why substances like carrots and peas have different pH values.