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Example 13.4: Calculation of pH from [H3O+]

What is the pH of stomach acid, a solution of \(\ce{HCl}\) with a hydronium ion concentration of \(1.2\times 10^{-3 }\)M?

Solution

\(c_{\mathrm{\ce{H3O+}}}\) \(= 1.2\times 10^{-3}\ \mathrm{M}\)


\(\mathrm{pH}\) = ?


The pH is defined as


Before we can take the logaritm, we have to divide \(c_{\mathrm{\ce{H3O+}}}\) by the standard concentration, 1M, to get the pure number [H3O+]

\([\ce{H3O+}]\) \(= \dfrac{c_{\mathrm{\ce{H3O+}}}}{1\ \mathrm{M}}\)

\(\ \ \ =\dfrac{1.2\times 10^{-3}\ \mathrm{M}}{1\ \mathrm{M}}\)

\(\ \ \ =1.2\times 10^{-3}\)


\(\mathrm{pH}\) \(= -\mathrm{log}([\ce{H3O+}])\)

\(\ \ \ =-\mathrm{log}(1.2\times 10^{-3})\)

\(\ \ \ =2.92\)


(The use of logarithms is explained in Appendix B. Recall that, as we have done here, when taking the log of a value, keep as many decimal places in the result as there are significant figures in the value.)