1. Use the definition of pH

   $\text{pH} = -\log_{10}[H^+]$

2. Let the initial hydrogen ion concentration be

   $[H^+] = x$

   Then initial pH is

   $\text{pH}_1 = -\log x$

3. If $[H^+]$ changes by a factor of 1000

   Since pH is inversely related to $[H^+]$, take the common interpretation that hydrogen ion concentration increases by a factor of $1000 = 10^3$.

   So new concentration is

   $[H^+]_2 = 1000x = 10^3x$

4. Find the new pH

   $\text{pH}_2 = -\log(10^3x)$

   $\text{pH}_2 = -\left(\log x + 3\right)$

   $\text{pH}_2 = -\log x - 3$

   $\text{pH}_2 = \text{pH}_1 - 3$

5. Interpret the result

   The pH becomes smaller by 3 units.

   So, the pH decreases by 3 units.

6. Check options

   • A: decreases by 2 units — incorrect
   • B: increases by 2 units — incorrect
   • C: decreases by 3 units — correct
   • D: increases by 1000 units — incorrect

Final Answer: Option C.