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Math  /  Algebra

QuestionThe pH scale for acidity is defined by pH=−log⁡10[H+]\mathrm{pH}=-\log _{10}\left[\mathrm{H}^{+}\right]where [H+]\left[\mathrm{H}^{+}\right]is the concentration of hydrogen ions measured in moles per liter (M). A solution has a pH of 12.65. Calculate the concentration of hydrogen ions in moles per liter (M).
The concentration of hydrogen ions is □\square moles per liter.
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Studdy Solution

STEP 1

1. The pH scale is defined by the equation pH=−log⁡10[H+]\mathrm{pH} = -\log_{10}[\mathrm{H}^+].
2. We are given the pH value and need to find the concentration of hydrogen ions [H+][\mathrm{H}^+].
3. The concentration [H+][\mathrm{H}^+] is expressed in moles per liter (M).

STEP 2

1. Set up the equation using the given pH value.
2. Solve for the hydrogen ion concentration [H+][\mathrm{H}^+].

STEP 3

Start by setting up the equation using the given pH value:
Given pH=12.65\mathrm{pH} = 12.65, substitute into the pH formula:
12.65=−log⁡10[H+]12.65 = -\log_{10}[\mathrm{H}^+]

STEP 4

To solve for [H+][\mathrm{H}^+], we need to remove the logarithm. We do this by rewriting the equation in exponential form:
−log⁡10[H+]=12.65-\log_{10}[\mathrm{H}^+] = 12.65
Multiply both sides by −1-1:
log⁡10[H+]=−12.65\log_{10}[\mathrm{H}^+] = -12.65
Convert the logarithmic equation to its exponential form:
[H+]=10−12.65[\mathrm{H}^+] = 10^{-12.65}
The concentration of hydrogen ions is:
[H+]=10−12.65≈2.24×10−13 moles per liter[\mathrm{H}^+] = 10^{-12.65} \approx 2.24 \times 10^{-13} \, \text{moles per liter}
The concentration of hydrogen ions is 2.24×10−13\boxed{2.24 \times 10^{-13}} moles per liter.

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