The pH of a solution is a measure of its acidity or basicity. In fact, pH is related to the molar concentration (in moles per liter) of hydrogen ions in the substance. In particular, if $C$ is the molar concentration of hydrogen ions in a solution, then the approximate pH of that solution is given by: $$pH = -\log(C).$$

a) If a certain type of vinegar has a molar concentration of hydrogen ions of approximately $10^{-6}$ moles per liter, what is the approximate pH of the vinegar?

b) Pure water has a pH of 7 and marks the neutral point between acids and bases, with acidic solutions having a lower pH value, and basic solutions having a higher pH value. What is the molar concentration of hydrogen ions in pure water?

c) Over what interval of molar concentrations of hydrogen ions will the solution be an acid? (Hint: is vinegar an acid or a base? Is its molar concentration smaller or larger than that of pure water?)

A. $(10^{-5}, \infty)$
B. $(10^{-5}, 1)$
C. $(0, 10^{-7})$
D. $(10^{-7}, \infty)$

d) How many times more concentrated are hydrogen ions in the vinegar than in pure water?

Hint: