Let's analyze the given question step-by-step to understand the conditions for an acidic solution.
1. Definition of an Acidic Solution:
- An acidic solution has a pH less than 7.
2. Relationship between pH and \([H_3O^+]\):
- The pH of a solution is given by the formula:
[tex]\[
\text{pH} = -\log[H_3O^+]
\][/tex]
- In an acidic solution, since the pH is less than 7, the concentration of hydronium ions \([H_3O^+]\) must be greater than \(1 \times 10^{-7} \, M\).
Given these facts, let's match each option to these criteria:
A. \( \text{pH} < 7, [H_3O^+]<1 \times 10^{-7} \, M \):
- This option is incorrect because for a solution to be acidic (\( \text{pH} < 7 \)), \([H_3O^+]\) should actually be greater than \(1 \times 10^{-7} \, M\).
B. \( \text{pH} < 7, [H_3O^+]>1 \times 10^{-7} \, M \):
- This option is correct as it accurately represents the conditions of an acidic solution.
C. \( \text{pH} = 7, [H_3O^+] = 1 \times 10^{-7} \, M \):
- This option describes a neutral solution, not an acidic one.
D. \( \text{pH} > 7, [H_3O^+] < 1 \times 10^{-7} \, M \):
- This option describes a basic solution, not an acidic one.
Hence, the correct option that fits the criteria for an acidic solution is:
B. [tex]\( \text{pH} < 7, [H_3O^+] > 1 \times 10^{-7} \, M \)[/tex]
