Question A.SE.2: (a) What is the pH of a solution whose hydrogen ion concentr...
(a) What is the pH of a solution whose hydrogen ion concentration is 0.015 M ? (b) If the pH of a solution is 3.80, what is its hydrogen ion concentration?
(1) We are given the value of [H^+]. We use the LOG key of our calculator to calculate the value of log[H^+]. The pH is obtained by changing the sign of the value obtained. (Be sure to change the sign after taking the logarithm.)
\begin{aligned}{\left[ H ^{+}\right]}&=0.015 \\\log \left[ H ^{+}\right] &=-1.82 \quad(2 \,\,\text{significant figures}) \\pH &=-(-1.82)=1.82\end{aligned}
(2) To obtain the hydrogen ion concentration when given the pH, we must take the antilog of -pH.
\begin{aligned}pH &=-\log \left[ H ^{+}\right]=3.80 \\\log \left[ H ^{+}\right] &=-3.80 \\{\left[ H ^{+}\right]}&=\operatorname{antilog}(-3.80)=10^{-3.80}=1.6 \times 10^{-4}\,M\end{aligned}