Question

Challenge Calculate the pH of a solution having \([0 \mathrm{H}-]=8.2 \times 10^{-6} \mathrm{M} .\)

Short answer

The pH of the solution can be calculated using the formula \(pH = -\log_{10} [0 \mathrm{H}-]\). Given the hydrogen ion concentration \([0 \mathrm{H}-] = 8.2 \times 10^{-6} \mathrm{M}\), we can substitute the value into the formula: \(pH = -\log_{10} (8.2 \times 10^{-6}) \approx 5.09\). Since the pH is approximately 5.09 and less than 7, the solution is acidic.

Step-by-step solution

Write the pH definition

Recall the definition of pH: \(pH = -\log_{10} [0 \mathrm{H}-]\) Where \(pH\) - the acidity or basicity of a solution \([0 \mathrm{H}-]\) - the hydrogen ion concentration in moles per liter (M)

Plug in the given hydrogen ion concentration

Substitute the given hydrogen ion concentration value \([0 \mathrm{H}-] = 8.2 \times 10^{-6} \mathrm{M}\) into the pH equation: \(pH = -\log_{10} (8.2 \times 10^{-6})\)

Calculate the pH

Using a calculator, find the value of the negative logarithm of the hydrogen ion concentration: \(pH = -\log_{10} (8.2 \times 10^{-6}) \approx 5.09\)

Interpret the result

The pH of the solution is approximately 5.09. Since the pH is less than 7, it indicates that the solution is acidic.

Key concepts

pH Definition

Understanding the pH level of a solution is crucial when studying chemistry, especially when it comes to analyzing the solution's acidic or basic nature. The term 'pH' refers to the 'potential of Hydrogen' or 'power of Hydrogen' and provides a measure on a logarithmic scale of how acidic or basic a water-based solution is. The pH scale typically runs from 0 to 14, with 7 being neutral. A pH less than 7 indicates acidity, whereas a value greater than 7 indicates basicity (or alkalinity).

The pH value is calculated using the formula: \[ pH = -\log_{10} [H^+] \]Where \( [H^+] \) stands for the hydrogen ion concentration in the solution expressed in moles per liter (M). This calculated value tells us how reactive the hydrogen ions are within the solution, which directly affects the solution's acidic or basic characteristics.

Hydrogen Ion Concentration

Hydrogen ion concentration is a pivotal aspect when it comes to chemical reactions in aqueous solutions. It is denoted as \([H^+]\) and measures the moles of hydrogen ions per liter of solution. The more hydrogen ions present, the more acidic the solution is. Conversely, fewer hydrogen ions correspond to a basic or alkaline solution. This concept is at the core of acid-base chemistry.

It's essential to note that slight changes in hydrogen ion concentration can lead to significant shifts in pH due to the logarithmic nature of the pH scale. For example, a concentration of \(8.2 \times 10^{-6} M\) of hydrogen ions, once plugged into the pH formula mentioned earlier, results in a pH of approximately 5.09, indicating an acidic solution.

Acidity and Basicity of Solutions

The concepts of acidity and basicity describe the reactive nature of solutions with respect to hydrogen ions. Acidity refers to the presence of excess hydrogen ions (\([H^+]>10^{-7} M\)), resulting in a pH lower than 7, while basicity indicates a deficiency of hydrogen ions (\([H^+] < 10^{-7} M\)), resulting in a pH greater than 7.

Solutions with higher acidity typically taste sour and can be corrosive, whereas solutions with higher basicity are bitter and feel slippery to the touch. Understanding the pH level helps us predict the behavior of substances in different chemical reactions, biological systems, and even in our daily lives, such as in cooking or medicine.

Furthermore, the pH value can influence the solubility of compounds, the availability of nutrients, and the toxicity of pollutants. This makes the control and measurement of pH in industrial processes, environmental monitoring, and clinical diagnostics extremely important.