Problem 56 - Chemistry The Molecular Nature of Matter

Question

A soft drink was put on the market with \(\left[\mathrm{H}^{+}\right]=1.4 \times\) \(10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}\). What is its \(\mathrm{pH}\) ?

Step-by-Step Solution

Answer

The pH of the soft drink is approximately 4.85.

Step 1: Recall the definition of pH

The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration. It is given by the formula: \(pH = -\text{log}_{10}[\text{H}^+]\).

Step 2: Insert the given hydrogen ion concentration

Substitute the given hydrogen ion concentration \([\text{H}^+]=1.4\times 10^{-5}\text{ mol L}^{-1}\) into the pH formula.

Step 3: Calculate the pH

Compute the pH using the provided concentration: \(pH = -\text{log}_{10}(1.4\times 10^{-5})\). Use a calculator to find the approximate numerical value.

Key Concepts

Hydrogen Ion Concentration

Understanding the hydrogen ion concentration in a solution is crucial for studying chemical properties, especially acidity. In chemistry, the concentration of hydrogen ions \( \left[\mathrm{H}^{+}\right] \) refers to the number of moles of hydrogen ions (\( \mathrm{H}^{+} \) ions) present in one liter of a solution. This measurement is fundamental because it helps determine how acidic or basic a solution is.

In the context of the exercise, the soft drink has a hydrogen ion concentration of \( 1.4 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \). This means that in every liter of the soft drink, there are \( 1.4 \times 10^{-5} \) moles of \( \mathrm{H}^{+} \) ions. A higher concentration of hydrogen ions indicates a more acidic solution, while a lower concentration suggests a less acidic or more basic solution. To fully understand the acidity of the soft drink, we need to calculate its pH, which is a more convenient scale for expressing acidity level.

Logarithmic Scale

The concept of a logarithmic scale is an essential mathematical tool that helps us deal with a wide range of quantities. In pH calculations, we use a logarithmic scale because the hydrogen ion concentrations can vary over many orders of magnitude. A logarithmic scale transforms the potentially huge range of \( \left[\mathrm{H}^{+}\right] \) values into a more manageable, compact scale.

The pH scale is logarithmic and inverse; it is defined as the negative base 10 logarithm of the hydrogen ion concentration: \( pH = -\text{log}_{10}\left[\text{H}^+\right] \). By using this scale, a decrease in pH by one unit represents a tenfold increase in acidity, which means the solution is ten times more acidic. This inverted relationship helps distinguish the acidity levels of different substances in a clear, concise manner. Small changes in pH indicate significant changes in hydrogen ion concentration, which can drastically alter a substance's properties.

Acidic Solutions Chemistry

In the realm of acidic solutions chemistry, acids are substances that release hydrogen ions (\( \mathrm{H}^{+} \) ions) when dissolved in water. The greater the concentration of \( \mathrm{H}^{+} \) ions, the more acidic the solution is. The pH scale is a measure used to quantify the acidity or basicity of a solution. On this scale, a pH less than 7 is acidic, 7 is neutral, and greater than 7 is basic.

Substances with a low pH, such as the soft drink in the original exercise, have high hydrogen ion concentrations and therefore are more acidic. The chemistry of these acidic solutions is significant for many processes, including metabolism in living organisms, industrial chemical reactions, and the preservation and flavor of foods and beverages like the soft drink mentioned. By calculating the pH, we gain insight into the chemical behavior and potential reactivity of these solutions.