Question

An aqueous solution of which of the following has the highest pH value

• A. 0.10 M HCl
• B. 0.50 M H\(_2\)SO\(_4\)
• C. 0.10 M NaOH
• D. 0.5 M HCl
• E. 0.01 M NaOH

Hint:

A higher concentration of a strong base gives a higher pH (more basic).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The pH scale measures the acidity or alkalinity of a solution. A high pH value (pH>7) indicates a basic or alkaline solution, while a low pH value (pH<7) indicates an acidic solution. The highest pH will correspond to the strongest and most concentrated basic solution among the choices.
Step 2: Key Formula or Approach:
For strong acids: pH = -log[H\(^+\)].
For strong bases: pOH = -log[OH\(^-\)], and pH = 14 - pOH.
Step 3: Detailed Explanation:
Let's calculate the approximate pH for each solution:

(A) 0.10 M HCl: HCl is a strong acid, so it dissociates completely. [H\(^+\)] = 0.10 M = 10\(^{-1}\) M.
pH = -log(10\(^{-1}\)) = 1.

(B) 0.50 M H\(_2\)SO\(_4\): H\(_2\)SO\(_4\) is a strong acid. For the first dissociation, it is complete. Assuming complete dissociation for both protons for a quick comparison: [H\(^+\)] \(\approx\) 2 \(\times\) 0.50 M = 1.0 M.
pH = -log(1.0) = 0. (This is a very acidic solution).

(C) 0.10 M NaOH: NaOH is a strong base, so it dissociates completely. [OH\(^-\)] = 0.10 M = 10\(^{-1}\) M.
pOH = -log(10\(^{-1}\)) = 1.
pH = 14 - pOH = 14 - 1 = 13.

(D) 0.5 M HCl: HCl is a strong acid. [H\(^+\)] = 0.5 M.
pH = -log(0.5) = -log(5 \(\times\) 10\(^{-1}\)) = -(log 5 + log 10\(^{-1}\)) = - (0.7 - 1) = 0.3.

(E) 0.01 M NaOH: NaOH is a strong base. [OH\(^-\)] = 0.01 M = 10\(^{-2}\) M.
pOH = -log(10\(^{-2}\)) = 2.
pH = 14 - pOH = 14 - 2 = 12.

Comparing the calculated pH values: 1, 0, 13, 0.3, and 12. The highest value is 13.
Step 4: Final Answer:
The 0.10 M NaOH solution has the highest pH value of 13. This corresponds to option (C).