Video: Calculating the Concentration of Hydrogen Ions from pH

A solution of a base that has a pH of 8.0 has a hydrogen ion concentration of _. [A] 1 × 10⁻⁹ molar [B] 1 × 10⁻⁸ molar [C] 1 × 10⁻⁶ molar [D] 1 × 10⁻⁵ molar [E] 1 × 10⁻⁴ molar

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Video Transcript

A solution of a base that has a pH of 8.0 has a hydrogen ion concentration of A) one times 10 to the minus nine molar, B) one times 10 to the minus eight molar, C) one times 10 to the minus six molar, D) one times 10 to the minus five molar, or E) one times 10 to the minus four molar.

The pH is defined as the negative log of the concentration of hydrogen ions in your solution. But in this problem, we’re given the pH. And we want to know the hydrogen ion concentration. We’ll be able to use log rules to solve for the concentration of hydrogen ions in our solution. Logs and exponents kind of undo each other. Any log that doesn’t have a base specified you can assume is log base 10. So the pH is in log base 10.

Let’s create an expression for the concentration of hydrogen ions, using what we know about log rules. First, I’ll divide by negative one to move the negative over to the left-hand side of the equation. Since exponents cancel logs and our log is a log base 10, we can raise both sides to the power of 10 to get rid of the log. So the concentration of H⁺ is equal to 10 to the negative pH. Now, we can plug in the pH of our solution, which was eight. So the concentration of hydrogen ions in our solution is 10 to the minus eight. This matches answer choice B, one times 10 to the minus eight molar.

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