Question

For each pair of concentrations, tell which represents the more acidic solution. a. \(\left[\mathrm{H}^{+}\right]=1.2 \times 10^{-3} M\) or \(\left[\mathrm{H}^{+}\right]=4.5 \times 10^{-4} M\) b. \(\left[\mathrm{H}^{+}\right]=2.6 \times 10^{-6} M\) or \(\left[\mathrm{H}^{+}\right]=4.3 \times 10^{-8} M\) c. \(\left[\mathrm{H}^{+}\right]=0.000010 \mathrm{M}\) or \(\left[\mathrm{H}^{+}\right]=0.0000010 \mathrm{M}\)

Short answer

a. The first solution, \(\left[\mathrm{H}^{+}\right]=1.2 \times 10^{-3} M\), is more acidic. b. The first solution, \(\left[\mathrm{H}^{+}\right]=2.6 \times 10^{-6} M\), is more acidic. c. The first solution, \(\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-5} M\), is more acidic.

Step-by-step solution

In this step, we will compare the \(\left[\mathrm{H}^{+}\right]\) concentrations for each pair of solutions. #Step 2: Determine which solution has a higher hydrogen ion concentration for a#

The two given concentrations for part a are: 1. \(\left[\mathrm{H}^{+}\right]=1.2 \times 10^{-3} M\) 2. \(\left[\mathrm{H}^{+}\right]=4.5 \times 10^{-4} M\) Comparing these values, \(1.2 \times 10^{-3} M > 4.5 \times 10^{-4} M\), therefore the first solution is more acidic. #Step 3: Determine which solution has a higher hydrogen ion concentration for b#

The two given concentrations for part b are: 1. \(\left[\mathrm{H}^{+}\right]=2.6 \times 10^{-6} M\) 2. \(\left[\mathrm{H}^{+}\right]=4.3 \times 10^{-8} M\) Comparing these values, \(2.6 \times 10^{-6} M > 4.3 \times 10^{-8} M\), therefore the first solution is more acidic. #Step 4: Determine which solution has a higher hydrogen ion concentration for c#

The two given concentrations for part c are: 1. \(\left[\mathrm{H}^{+}\right]=0.000010 \mathrm{M}=1.0 \times 10^{-5} M\) 2. \(\left[\mathrm{H}^{+}\right]=0.0000010 \mathrm{M}=1.0 \times 10^{-6} M\) Comparing these values, \(1.0 \times 10^{-5} M > 1.0 \times 10^{-6} M\), therefore the first solution is more acidic.

Key concepts

Hydrogen Ion Concentration

Understanding the hydrogen ion concentration in a solution is key to determining its acidity. The concentration is commonly represented with the notation \( \left[\mathrm{H}^{+}\right] \) and is measured in moles per liter (M). A mole is a unit that represents a specific number of molecules or ions—in this case, hydrogen ions. The higher the concentration of hydrogen ions, the more acidic the solution is.

For example, in comparing \( \left[\mathrm{H}^{+}\right]=1.2 \times 10^{-3} M \) and \( \left[\mathrm{H}^{+}\right]=4.5 \times 10^{-4} M \) we can see that the first solution has more hydrogen ions per liter. In the context of acidity, more hydrogen ions mean the solution is more capable of donating protons, which is a characteristic of acids.

When we encounter solutions with different hydrogen ion concentrations, we effectively compare the number of hydrogen ions present. The solution with the higher concentration of \( \mathrm{H}^{+} \) ions will always be the more acidic one. Remember, when dealing with scientific notation, a lower exponent indicates fewer ions, and therefore less acidity.

pH Level

The pH level is an abbreviation for 'power of hydrogen' or 'potential of hydrogen' and it's a scale used to specify how acidic or basic (alkaline) a water-based solution is. The pH scale normally ranges from 0 to 14. A pH of 7 is considered neutral, which is the pH of pure water. Numbers less than 7 on the pH scale represent acidity, with 0 being the most acidic. Numbers greater than 7 indicate alkalinity (basicity), with 14 being the most alkaline.

The pH level is inversely related to hydrogen ion concentration. This means that as the concentration of hydrogen ions in a solution increases, the pH level decreases. So, a low pH indicates a high concentration of hydrogen ions and therefore, a more acidic solution. Calculating pH from hydrogen ion concentration involves negative logarithms, specifically \( \text{pH} = -\log(\left[\mathrm{H}^{+}\right]) \). Conversely, you can calculate hydrogen ion concentration if you know the pH by using the reverse process, \( \left[\mathrm{H}^{+}\right] = 10^{-\text{pH}} \).

This logarithmic relationship means that each step on the pH scale represents a tenfold change in hydrogen ion concentration. For instance, a solution with a pH of 3 has ten times more hydrogen ions than one with a pH of 4, making it significantly more acidic.

Acidity in Chemistry

In chemistry, acidity is not just a vague concept but a well-defined characteristic related to the presence of hydrogen ions or protons (\(H^+\)). Substances that release more hydrogen ions when dissolved in water are considered to be strong acids, while those that release fewer ions are weak acids.

It is crucial to distinguish between concentration and strength when discussing acids. Concentration refers to the amount of acid in a given quantity of solution, typically defined by the molarity (M). Strength, however, is an inherent property of the acid molecule and depends on its ability to dissociate in water. In other words, a strong acid like hydrochloric acid (HCl) dissociates completely in water to give a high concentration of hydrogen ions, while a weak acid like acetic acid (CH3COOH) only partially dissociates.

For meaningful comparisons between the acidity of different solutions, both the concentration and the strength of the acids need to be taken into account. In practical applications, using pH as a measure is commonly preferred because it considers both these aspects and provides a clear and quick way to assess acidity.