Question

What is the pH of a 0.01 M solution of hydrochloric acid (HCl)?

• A. 12
• B. 2
• C. 7
• D. 1

Hint:

Remember the relation pH plus pOH equals 14 at room temperature, connected through the ion product of water, Kw. For a strong acid like HCl, the hydrogen ion concentration is equal to the acid concentration itself.

Answer 1

The Correct Option is B

Hydrochloric acid (HCl) is a strong acid, meaning it dissociates completely in water. The concentration of \( \text{H}^+ \) ions is the same as the concentration of the acid, which is 0.01 M. The pH is calculated using the formula: \[ \text{pH} = -\log [\text{H}^+] \] Substitute \( [\text{H}^+] = 0.01 \) M: \[ \text{pH} = -\log (0.01) = 2 \] Thus, the pH of the solution is 2, corresponding to option (2).

Answer 2

Concept:

• Water has a constant ion product, $K_w = [H^+][OH^-] = 10^{-14}$ at room temperature, which links the hydrogen ion and hydroxide ion concentrations in any aqueous solution.
• Finding pOH first through $K_w$ and then converting it to pH using $pH + pOH = 14$ gives an independent cross-check on the pH value, starting from a completely different quantity.

Step 1: Find the hydrogen ion concentration.
HCl is a strong acid and dissociates completely, so $[H^+] = 0.01\,M = 10^{-2}\,M$

Step 2: Find the hydroxide ion concentration using $K_w$.
$[OH^-] = \dfrac{K_w}{[H^+]} = \dfrac{10^{-14}}{10^{-2}} = 10^{-12}\,M$

Step 3: Find pOH and then pH.
$pOH = -\log(10^{-12}) = 12$
$pH = 14 - pOH = 14 - 12 = 2$

Final Answer: The pH of the solution is 2.