Math  /  Algebra

QuestionThe pH scale for acidity is defined by pH=log10[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
To solve for [H+][\mathrm{H}^+], we need to remove the logarithm. We do this by rewriting the equation in exponential form:
log10[H+]=12.65-\log_{10}[\mathrm{H}^+] = 12.65
Multiply both sides by 1-1:
log10[H+]=12.65\log_{10}[\mathrm{H}^+] = -12.65
Convert the logarithmic equation to its exponential form:
[H+]=1012.65[\mathrm{H}^+] = 10^{-12.65}
The concentration of hydrogen ions is:
[H+]=1012.652.24×1013moles per liter[\mathrm{H}^+] = 10^{-12.65} \approx 2.24 \times 10^{-13} \, \text{moles per liter}
The concentration of hydrogen ions is 2.24×1013\boxed{2.24 \times 10^{-13}} moles per liter.

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