Video: Calculating pH from the Concentration of Hydrogen Ions

What is the pH value when the concentration of hydrogen ions [H⁺] = 1.0 M? [A] Zero [B] Between 0 and 7 [C] 7 [D] Between 7 and 10 [E] Greater than 10

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Video Transcript

What is the pH value when the concentration of hydrogen ions H+ equals 1.0 molar? A) Zero. B) Between zero and seven. C) Seven. D) Between seven and 10. Or E) Greater than 10.

PH is defined as the negative log of the concentration of hydrogen ions in a solution. So to find the pH, we simply need to plug in the concentration of hydrogen ions given in the problem. If the base of a log is unspecified, you can assume that it’s log base 10. Since logs effectively undo exponents, this means that our log base 10 will undo anything that’s raised to the power of 10.

Our concentration, which is one, is not something raised to the power of 10. But anything raised to the power of zero equals one. So we could rewrite our expression for pH to have log of 10 to the power of zero instead of the log of one. Since logs undo exponents, we just get zero for the log of 10 to the power of zero. So we get zero for the pH. This matches answer choice A. So the pH of a solution with a concentration of hydrogen ions equal to one molar is zero.

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