Question

Calculate the \([\text{H}_3\text{O}^+]\) if pH of the solution is \(4.25\)

• A. \(6.123\times 10^{-5}\) M
• B. \(5.623\times 10^{-5}\) M
• C. \(4.508\times 10^{-5}\) M
• D. \(4.085\times 10^{-5}\) M

Hint:

Use [H3O+] = 10^(-pH).

Answer 1

The Correct Option is B

Step 1: Understand the concept
pH is defined as \(\text{pH} = -\log[\text{H}_3\text{O}^+]\). Reversing this gives \([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\).

Step 2: Substitute
\[ [\text{H}_3\text{O}^+] = 10^{-4.25} = 10^{-5} \times 10^{0.75} \]

Step 3: Evaluate
\(10^{0.75} = 5.623\) (since \(\log 5.623 = 0.75\)). So
\[ [\text{H}_3\text{O}^+] = 5.623 \times 10^{-5}\ \text{M} \]

Step 4: Check the other options
Option (A) 6.123e-5 has pH = 4.21, option (C) 4.508e-5 has pH = 4.35 and option (D) 4.085e-5 has pH = 4.39. None of them equals 4.25. Only 5.623e-5 gives \(-\log(5.623 \times 10^{-5}) = 4.25\).

Final Answer:
The hydronium ion concentration is 5.623 x 10^-5 M. This is option (B). \[ \boxed{\text{(B) }5.623 \times 10^{-5}\ \text{M}} \]