Question

If you were given a solution that has a pH of 8.5 what would be its concentration of protons? What is the difference in proton concentration between this solution and one that has a pH of \(7 ?\)

Short answer

The proton concentration of the solution with a pH of 8.5 is approximately \(3.16 \times 10^{-9}\,M\). The proton concentration of the solution with a pH of 7 is \(1 \times 10^{-7}\,M\). The difference in proton concentration between these two solutions is approximately \(9.68 \times 10^{-8}\,M\).

Step-by-step solution

Calculate the proton concentration of the solution with a pH of 8.5.

To find the concentration of protons in the solution with pH 8.5, we will use the pH formula and solve for the proton concentration. We can rearrange the formula as follows: \([H^+] = 10^{-pH}\) Now substitute the given pH value into the equation: \([H^+]_{8.5} = 10^{-8.5}\) Calculate the proton concentration: \([H^+]_{8.5} \approx 3.16 \times 10^{-9}\,M\)

Calculate the proton concentration of the solution with a pH of 7.

Similarly, we can find the proton concentration for the solution with a pH of 7 as: \([H^+]_{7} = 10^{-7}\) Calculate the proton concentration: \([H^+]_{7} = 1 \times 10^{-7}\,M\)

Find the difference in proton concentrations between both solutions.

Now that we have the proton concentration of both solutions, we can find the difference between them as: Difference = \([H^+]_{7} - [H^+]_{8.5}\) Substitute the proton concentration values: Difference = \( (1 \times 10^{-7}) \, M - (3.16 \times 10^{-9}) \, M\) Calculate the difference in proton concentrations: Difference ≈ \(9.68 \times 10^{-8}\,M\) So, the difference in proton concentration between a solution with a pH of 8.5 and one with a pH of 7 is approximately \(9.68 \times 10^{-8}\,M\).

Key concepts

Proton Concentration

Understanding proton concentration is crucial when studying acidity and basicity in chemistry. It refers to the number of hydrogen ions, denoted as H+, present in a solution. These ions are key players in the pH level of a solution.

When a substance dissolves in water, it may release hydrogen ions into the solution, increasing the solution's proton concentration. The more protons present, the more acidic the solution becomes. This is why proton concentration is a determining factor in the acidity of solutions.

For instance, in our original exercise, calculating the concentration involves using the negative power of 10. The pH of a solution specifies the negative base-10 logarithm of the hydrogen ion concentration. So, for a pH of 8.5, you would have a concentration of \( [H+]_{8.5} = 10^{-8.5} \) or approximately \( 3.16 \times 10^{-9} \) M (molar). This conversion from pH to proton concentration allows scientists to quantify and compare the acidity of various solutions.

pH Scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 considered neutral, values less than 7 acidic, and values greater than 7 basic (or alkaline).

The pH scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. For example, a pH of 3 is ten times more acidic than a pH of 4. This logarithmic nature allows the scale to cover a wide range of hydrogen ion concentrations in a compact format.

It is important for students to understand that the pH is the negative logarithm of the hydrogen ion concentration, given by the formula \( pH = - \log[H+] \). So, a lower pH means a higher concentration of hydrogen ions. For practical pH calculations, remembering that a change in one pH unit represents a tenfold change in hydrogen ion concentration can be immensely helpful.

Hydrogen Ion Concentration

The hydrogen ion concentration is a precise way of expressing the acidity of a solution. It's quantitatively represented by the concentration of hydrogen ions in moles per liter (M).

In our original problem, understanding this concept allows us to find that a solution with a pH of 7 has a hydrogen ion concentration of \( [H+]_{7} = 10^{-7} \) M. Comparing it to a solution with a pH of 8.5, which has a lower hydrogen ion concentration of \( 3.16 \times 10^{-9} \) M, illustrates how pH and hydrogen ion concentration are inversely related.

Furthermore, calculating the difference in concentration between two solutions involves subtracting their hydrogen ion concentrations. Hence, the difference in concentration between our two solutions is \( 9.68 \times 10^{-8} \) M. This clearly shows that even a small difference in pH can signify a considerable change in hydrogen ion concentration, underscoring the sensitivity of the pH scale.