Problem 102 - Chemistry The Molecular Science

Question

From the mid-1800s to the present, the average acidity of the oceans' surface water has increased \(30 \%\) to its current \(\mathrm{pH}\) of \(8.1 .\) Calculate what the \(\mathrm{pH}\) was in the mid-1800s.

Step-by-Step Solution

Answer

The pH in the mid-1800s was approximately 8.21.

Step 1: Understanding the Relationship

The pH scale is logarithmic, meaning that a decrease in pH by 1 unit represents a tenfold increase in acidity. Since the average acidity increased by 30% from the mid-1800s to the present, we need to determine the original pH using this information.

Step 2: Calculate the Current Acidity Ratio

Given the current pH of 8.1, convert this to hydrogen ion concentration using the formula: \[ [H^+] = 10^{-pH} \]So, \[ [H^+]_{current} = 10^{-8.1} \]

Step 3: Determine the Previous Acidity

To find the previous hydrogen ion concentration before the 30% increase, divide the current concentration by 1.30. So,\[ [H^+]_{previous} = \frac{[H^+]_{current}}{1.30} \]

Step 4: Calculate the Previous pH

Convert the previous hydrogen ion concentration back to pH using the formula:\[ pH_{previous} = -\log_{10}([H^+]_{previous}) \]

Step 5: Final Calculation

Substitute and calculate:1. Calculate \[ [H^+]_{current} = 10^{-8.1} \approx 7.94 \times 10^{-9} \]2. Find \[ [H^+]_{previous} = \frac{7.94 \times 10^{-9}}{1.30} \approx 6.11 \times 10^{-9} \]3. Find \[ pH_{previous} = -\log_{10}(6.11 \times 10^{-9}) \approx 8.21 \]

Step 6: Conclusion

The pH in the mid-1800s was approximately 8.21.

Key Concepts

pH Scale

The pH scale is a tool used to measure how acidic or basic a substance is. It ranges from 0 to 14.
A lower pH value (closer to 0) means higher acidity, while a higher pH value (closer to 14) indicates more basicity.

• A pH of 7 is considered neutral, like pure water.
• If a solution's pH lowers by 1 unit, it means the acidity has increased tenfold.
• This logarithmic nature is crucial for understanding changes in acidity.

The pH of ocean water generally remains on the slightly basic side.
However, even small changes in the pH scale can have significant effects on marine life and ecosystems.

Acidity

Acidity refers to the concentration of hydrogen ions \([H^+]\) in a solution.
The more hydrogen ions present, the more acidic the solution is.

• An increase in acidity implies more hydrogen ions are present.
• The term 'acidity' often highlights how reactive or corrosive a solution can be.

When we say that ocean acidity has increased by 30%, we're talking about the increase in hydrogen ions.
Even a small percentage change can have a big impact due to the logarithmic nature of the pH scale.

Hydrogen Ion Concentration

Hydrogen ion concentration \([H^+]\) is key to understanding a solution's acidity.
It's represented in scientific notation, reflecting the number of hydrogen ions per liter.

• A pH of 8.1 means the hydrogen ion concentration is \(10^{-8.1}\).
• It's important to see how concentrations change under different pH conditions.

When calculating changes, dividing or multiplying the current concentration by a factor gives us insight into past or future states.
This is how we discover the previous pH of ocean water, using the formula \( [H^+] = 10^{-pH} \), and adapting it for percentage changes.