Exercise 2 solution

Rule (PH article): a difference of one pH unit is a tenfold difference in hydrogen ion concentration.
The lower pH has the higher concentration.

(a) pH 1 versus pH 4: difference = 3 units, so the factor is 10^3 = 1000.
    The pH 1 sample has 1000 times the hydrogen-ion concentration.
    Check with concentrations: pH 1 is 1 x 10^-1 mol/L, pH 4 is 1 x 10^-4 mol/L;
    10^-1 / 10^-4 = 1000.

(b) pH 3 versus pH 5: difference = 2 units, so the factor is 10^2 = 100.
    The pH 3 sample (the vinegar value in the data given) has 100 times the hydrogen-ion
    concentration of the pH 5 sample (the black coffee value).

(c) pH 3 to pH 6 is 3 units, so the concentration changes by a factor of 1000 (10^-3 mol/L
    falls to 10^-6 mol/L). It does not "halve": the pH scale is logarithmic, so equal steps
    of pH are equal factors, not equal amounts.

Note: the arithmetic was run in Python (check, my own calculation).