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If the pH of an acid rain storm is approximately 3.0, how many times greater is the [H ] in the rain than in a cup of coffee having a pH of 5.0

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CintiaSalazar

Taking into account the definition of pH, the [H⁺] in the rain is 100 times greater than in a cup of coffee.

Definition of pH

pH is the Hydrogen Potential. It is a measure of acidity or alkalinity that indicates the amount of hydrogen ions present in a solution or substance.

Mathematically, pH is calculated as the negative base 10 logarithm of the activity of hydrogen ions:

pH= - log [H⁺]

The numerical scale that measures the pH of substances includes the numbers from 0 to 14. The pH value 7 corresponds to neutral substances. Acidic substances are those with a pH lower than 7, while basic substances have a pH higher than 7.

Comparison of [H⁺]

In this case, you know:

  • pH= 3
  • pH= 5

You can replace this values in the definition of pH:

  • 3= -log [H⁺]  →  [H⁺]=1×10⁻³ M
  • 5= -log [H⁺]  →  [H⁺]=1×10⁻⁵ M

Solving:

  • [H⁺]=1×10⁻³ M
  • [H⁺]=1×10⁻⁵ M

Comparing [H⁺], you get:

[tex]\frac{1x10^{-3} }{1x10^{-5} } =100[/tex]

Finally, the [H⁺] in the rain is 100 times greater than in a cup of coffee.

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