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How to calculate the \(pH\) of a solution?
The \(pH\) is the negative logarithm of the hydrogen ion concentration.
i.e, \(pH= -log_{10}[H^+]\)
Example:
Calculate the \(pH\) of \(0.01\) \(M\) \(HNO_3\).
Solution:
\([H^+] = 0.01\)
\(pH = -log_{10}\) \([H^+]\)
\(pH = -log_{10}\) \([0.01]\)
\(pH = -log_{10}\) \([1\times10^{-2}]\)
\(pH = -(log_{10}·1 - 2\, log_{10}10)\)
\(pH = 0 + 2\times\,log_{10}\,10\)
\(pH = 0 + 2\times1 = 2\)
\(pH = 2\)
pOH
The \(pH\) is related to the \(pOH\) of an aqueous solution.
The \(pOH\) is the negative logarithm of the hydroxyl ion concentration.
\(pOH= -log_{10}[OH^-]\)
Example:
The hydroxyl ion concentration of a solution is \(1\times10^{-9}\) \(M\). What is the \(pOH\) of the
solution?
Solution:
\(pOH = -log_{10}[OH^-]\)
\(pOH = -log_{10}[1\times10^{-9}]\)
\(pOH = -(log_{10}\times1.0 + log_{10}\times10^{-9})\)
\(pOH = -(0 - 9\,log_{10}\,10)\)
\(pOH = -(0 - 9)\)
\(pOH = 9\)
Relationship between \(pH\) and \(pOH\):
At \(25°C\), the \(pH\) and \(pOH\) of a water solution are related by the following equation:
\(pH + pOH = 14\)
It is possible to calculate the other value if the \(pH\) or \(pOH\) of a solution is known.
Example:
\(pOH\) of a solution is \(11.76\). What is the \(pH\) of this solution?
\(pH = 14 - pOH\)
\(pH = 14 – 11.76 = 2.24\)
\(pH\) indicates acidity or hydrogen ion concentration, whereas \(pOH\) indicates alkalinity or hydroxide ion concentration.
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