Problem

e. In two consecutive years, scientists measured the $\mathrm{pH}$ in a pond as 6.8 and 6.4 , respectively. Find the percent change of the hydrogen ion concentration in the pond between the two years.

Solution

Step 1 :The pH of a solution is a measure of the concentration of hydrogen ions in the solution. The pH scale is logarithmic, meaning that each unit represents a tenfold difference in hydrogen ion concentration. Therefore, to find the percent change in hydrogen ion concentration, we first need to convert the pH values to hydrogen ion concentrations, then calculate the percent change.

Step 2 :The formula to convert pH to hydrogen ion concentration is: \([H^+] = 10^{-\text{pH}}\) where [H+] is the hydrogen ion concentration.

Step 3 :Using the formula, the hydrogen ion concentration for the first year is calculated as \(1.584893192461114 \times 10^{-7}\) and for the second year as \(3.981071705534969 \times 10^{-7}\).

Step 4 :The formula for percent change is: \(\text{Percent Change} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%\)

Step 5 :Substituting the values into the formula, the percent change in hydrogen ion concentration is calculated as approximately 151.19%.

Step 6 :Final Answer: The percent change of the hydrogen ion concentration in the pond between the two years is approximately \(\boxed{151.19\%}\).

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Source: https://solvelyapp.com/problems/17634/

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