Problem 38 - Chemistry The Science in Context

Question

Calculate the pH of a \(6.9 \times 10^{-8} M\) solution of HBr.

Step-by-Step Solution

Answer

Answer: The pH of the HBr solution is approximately 7.16.

Step 1: Calculate the concentration of \(H^+\) ions

Since HBr is a strong acid and fully dissociates in water, the concentration of \(H^+\) ions will be equal to the concentration of HBr in the solution. In this case, the concentration of HBr is \(6.9 \times 10^{-8} M\), so the concentration of \(H^+\) ions will also be \(6.9 \times 10^{-8} M\).

Step 2: Calculate the pH of the solution

Now, we can use the formula for pH to find the pH of the solution. Plug the concentration of \(H^+\) ions into the pH formula: $$ pH = -\log_{10}(6.9 \times 10^{-8}) $$ Calculate the value of the logarithm: $$ pH \approx -(-7.16) = 7.16 $$ So, the pH of the \(6.9 \times 10^{-8} M\) HBr solution is approximately 7.16.

Key Concepts

Solution Concentration

The term "solution concentration" refers to how much solute (in this case, HBr) is present in a given amount of solvent (usually water). It's often expressed in terms of molarity (M), which is the number of moles of solute per liter of solution.

In this exercise, the solution concentration is given as \(6.9 \times 10^{-8} M\), meaning there are \(6.9 \times 10^{-8}\) moles of HBr in one liter of the solution. This very low concentration indicates that the solution is quite dilute.

• Molarity (M) is central to determining the concentrations in reactions.
• It helps in understanding how much of a compound is interacting with the solvent.
• This understanding is crucial for continuous calculations like pH.

With this information, you can calculate the concentration of ions or molecules resulting from the dissociation of acids or bases.

Strong Acid Dissociation

Strong acids, like HBr, dissociate completely in water. This means that every molecule of HBr breaks apart to form the maximum number of hydrogen ions (\(H^+\)) and bromide ions (\(Br^-\)).

Because of this complete disassociation, the concentration of \(H^+\) ions in the solution is exactly the same as the initial concentration of the acid. Therefore, for the HBr solution:

• If you have \(6.9 \times 10^{-8} M\) HBr, you'll have \(6.9 \times 10^{-8} M\) \(H^+\) ions.
• This principle applies to all strong acids, making calculations more straightforward.
• Knowing the concentration of \(H^+\) ions directly from dissolution helps in easily calculating the pH.

This concept highlights the predictability and simplicity when dealing with strong acids as opposed to weak ones, which do not fully dissociate.

Hydrogen Ion Concentration

The hydrogen ion concentration is crucial in determining the acidity or basicity of a solution, which we express as pH. The pH calculation involves the negative logarithm of the hydrogen ion concentration:
\[ pH = -\log_{10}(\text{[H}^+\text{]}) \]
For our solution, using the concentration \(6.9 \times 10^{-8} M\), the formula gives us:

• Plugging in the value: \[ pH = -\log_{10}(6.9 \times 10^{-8}) \]
• The resulting pH is approximately 7.16.
• A pH of around 7 is considered neutral, but due to how close this value is to diluted water's effect, the neutral result is due to the extreme dilution rather than true neutrality.

This demonstrates how a very low concentration of a strong acid can reflect a pH close to neutrality in practical conditions.