To determine the pH of a solution, you need to use the formula for pH, which is given by:
[tex]\[ \text{pH} = -\log[H_3O^+] \][/tex]
Where [tex]\([H_3O^+]\)[/tex] represents the concentration of hydronium ions in moles per liter (M). In this problem, the concentration of [tex]\([H_3O^+]\)[/tex] is given as [tex]\(4.2 \times 10^{-5} \, M\)[/tex].
Here are the steps to calculate the pH:
1. Identify the concentration of [tex]\(H_3O^+\)[/tex] ions:
[tex]\[ [H_3O^+] = 4.2 \times 10^{-5} \, M \][/tex]
2. Apply the pH formula:
[tex]\[ \text{pH} = -\log(4.2 \times 10^{-5}) \][/tex]
3. Using logarithmic properties and a calculator, find the value of the logarithm:
[tex]\[ \log(4.2 \times 10^{-5}) \approx -4.376750709602099 \][/tex]
Since [tex]\(\log(4.2 \times 10^{-5})\)[/tex] gives a negative value due to the exponent being negative, taking the negative of this result will provide a positive value for the pH:
[tex]\[ \text{pH} = -(-4.376750709602099) = 4.376750709602099 \][/tex]
4. Round the pH to the nearest hundredths place for simplicity:
[tex]\[ \text{pH} \approx 4.38 \][/tex]
Based on this calculation, the correct answer is:
[tex]\[ \boxed{4.38} \][/tex]
