When the hydrogen ion concentration [H⁺] changes by a factor of 1000, the value of pH of the solution __________

Solution

Chemistry ma’am · 3 steps

pH is a log scale, so a factor of 1000 in [H⁺] means log 1000 = 3 units of pH.

1. Definition. pH = -log[H⁺]. Every factor of 10 in [H⁺] moves the pH by exactly 1 unit. The minus sign means more H⁺ gives a lower pH.
2. Read the change. Here [H⁺] grows 1000 times, so the new value is 1000[H⁺]. A rise in [H⁺] is the reading that matches the options. A fall would raise the pH by 3, and no option says that.

   pH_(new) = -log(1000[H⁺]) = -log 1000 - log[H⁺] = pH - 3

3. So. Since 1000 = 10³, the pH decreases by 3 units, which is option (c).

The idea to keep. Count the powers of 10. If [H⁺] goes up 10ⁿ times, pH goes down by n. If [H⁺] goes down 10ⁿ times, pH goes up by n.

Answer from the NTA final answer key. Solution by PrepWiser.