The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ ,where $\left[ \mathrm { H } ^ { + } \right]$ is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.4,how many times higher is its $\left[ \mathrm { H } ^ { + } \right]$ than pure water's,which has a pH of 7?
A) $4.0 \times 10 ^ { 3 }$
B) $2.5 \times 10 ^ { 4 }$
C)7
D) $2.5 \times 10 ^ { 3 }$
E) $4.0 \times 10 ^ { 4 }$

Question

Quizplus · Accepted Answer

The difference in pH between the rain sample and pure water is $7 - 3.4 = 3.6$. Since pH is a logarithmic scale, a difference of 1 unit means the concentration changes by a factor of 10. Therefore, a difference of 3.6 means the concentration changes by a factor of $10^{3.6}$, which is approximately $4.0 \times 10^3$.

The Chemical Acidity of a Solution Is Measured in Units pH=−log⁡[H+]\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]pH=−log[H+]

The Chemical Acidity of a Solution Is Measured in Units $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$