- Understand that the hydrogen ion concentration is calculated as \([H^{+}] = 10^{-pH}\).
- Calculate \([H^{+}]_1 = 10^{-4.5} \approx 3.16 \times 10^{-5}\).
- Calculate \([H^{+}]_2 = 10^{-5.0} = 1.0 \times 10^{-5}\).
- Subtract to find the difference: \(3.16 \times 10^{-5} - 1.0 \times 10^{-5} = 2.16 \times 10^{-5}\), which is approximately \(\boxed{2.2 \times 10^{-5}}\).
Explanation
- Understanding the pH Formula and Concentrations
The problem asks us to find the difference in hydrogen ion concentration, \([H^{+}]\), between two brands of vinegar with given pH values. The pH of a substance is related to its hydrogen ion concentration by the formula:
\[pH = -\log_{10}[H^{+}]\]
We are given two brands:
- Brand 1: \(pH_1 = 4.5\)
- Brand 2: \(pH_2 = 5.0\)
To find the hydrogen ion concentration for each, we rearrange the formula to:
\[[H^{+}] = 10^{-pH}\]
- Calculating Hydrogen Ion Concentrations
Using the formula \([H^{+}] = 10^{-pH}\), we calculate the concentration for each brand:
- For Brand 1: \([H^{+}]_1 = 10^{-4.5} \approx 3.162 \times 10^{-5} \, \text{mol/L}\)
- For Brand 2: \([H^{+}]_2 = 10^{-5.0} = 1.0 \times 10^{-5} \, \text{mol/L}\)
- Calculating the Difference and Concluding
To find the difference between the two concentrations, we subtract the concentration of Brand 2 from Brand 1:
\[\text{Difference} = [H^{+}]_1 - [H^{+}]_2\]
\[\text{Difference} = 10^{-4.5} - 10^{-5.0}\]
\[\text{Difference} \approx 3.162 \times 10^{-5} - 1.0 \times 10^{-5}\]
\[\text{Difference} \approx 2.162 \times 10^{-5} \, \text{mol/L}\]
Rounding this to one decimal place gives approximately \(2.2 \times 10^{-5} \, \text{mol/L}\). Comparing this to the given options, we find it corresponds to the first choice.
Examples
Understanding pH is crucial in many everyday tasks, such as in chemistry, gardening, and cooking. For example, knowing the concentration of hydrogen ions allows you to maintain the right soil acidity for different plants or ensure that a pool or a food product is at a safe and desired pH level. By converting pH values into actual ion concentrations, we can accurately measure and adjust chemical balances in various practical scenarios.