Question

What is the \(\mathrm{pH}\) of a solution whose hydronium ion concentration is \(0.0010 \mathrm{M?}\) Is the solution acidic or basic?

Short answer

The pH of the solution can be found by using the formula \(pH = -\log_{10} [\mathrm{H^{+}}]\). With the given hydronium ion concentration of \(0.0010 \mathrm{M}\), we can calculate the pH as \(pH = -\log_{10} (0.0010) = 3\). Since the pH is less than 7, the solution is acidic.

Step-by-step solution

Write the formula to calculate pH

The formula to calculate pH is: \(pH = -\log_{10} [\mathrm{H^{+}}]\) where \( [\mathrm{H^{+}}] \) is the hydronium ion (H+) concentration. Here, the given hydronium ion concentration is \(0.0010 \mathrm{M}\).

Calculate the pH

Next, we will substitute the given H+ concentration into the pH formula: \(pH = -\log_{10} (0.0010)\). Using a calculator, we get: \(pH = 3\)

Determine whether the solution is acidic, basic, or neutral

A solution is considered acidic if its pH value is less than 7, neutral if the pH value is exactly 7, and basic if its pH is greater than 7. In this case, the pH value of the solution is 3, which is less than 7. So, the solution is acidic.

Key concepts

Hydronium Ion Concentration

Understanding hydronium ion concentration is essential when examining the acidity or basicity of a solution. In chemical terms, hydronium ions are denoted as H3O+, and they are formed when an acid dissolves in water and donates a hydrogen ion (H+) to a water molecule. This concentration is typically measured in moles per liter (Molarity, M).

For the provided exercise, the concentration of hydronium ions is 0.0010 M. It is this specific concentration that directly influences the pH level of a solution. To calculate the pH from this information, you would use the formula:

pH = -log_{10} [H3O^+]

This equation is a logarithmic function that provides the acidity level on a scale that's easier for humans to comprehend, as the actual concentrations can be either very small or very large numbers.

Acidic and Basic Solutions

The terms acidic and basic (or alkaline) refer to the pH level of a solution. As we've seen, the pH level is determined by the concentration of hydronium ions. Solutions with high concentrations of hydronium ions, greater than pure water, are acidic, while those with lower concentrations are basic.

An important point to highlight is that water self-ionizes to a very small extent, producing equal concentrations of hydronium and hydroxide ions. Pure water has a hydronium ion concentration of 1 x 10^-7 M, making its pH neutral at 7. So, a solution with a hydronium ion concentration of 0.0010 M, like in our exercise, will have a pH lower than 7 indicating that the solution is acidic. Conversely, a solution with a hydronium ion concentration less than 1 x 10^-7 M would be basic, having a pH higher than 7.

pH Scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It typically ranges from 0 to 14, with 7 being neutral. Values lower than 7 represent an acidic solution, while values above 7 indicate a basic or alkaline solution.

The scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 3 is ten times more acidic than one with a pH of 4 and a hundred times more acidic than one with a pH of 5. This is a crucial piece of information, as the pH of a solution can drastically affect chemical reactions and biological processes.

In the context of our exercise, a pH of 3 means the solution is quite acidic and significantly different from a neutral pH of 7. When explaining pH, it's helpful to provide real-world examples, such as how a pH of 2 is comparable to lemon juice, and a pH of 3 to vinegar, which underscores the acidic nature of the solution in question.