Question

Problem 1. If solution A has a pH of 5 and solution B has 10,000 times more the hydrogen ion concentration of solution A, what is the pH of solution B?

Answer 1

To find the pH of solution B, we start with the pH of solution A, which is given as 5. The pH is defined as:

\[
\text{pH} = -\log[\text{H}^+]
\]

From this definition, we can determine the hydrogen ion concentration (\([\text{H}^+]\)) of solution A:

\[
[\text{H}^+]_A = 10^{-\text{pH}} = 10^{-5} \, \text{M}
\]

Now, it is given that solution B has 10,000 times more hydrogen ion concentration than solution A. Therefore, we calculate the hydrogen ion concentration of solution B as follows:

\[
[\text{H}^+]_B = 10,000 \times [\text{H}^+]_A = 10,000 \times 10^{-5} \, \text{M}
\]

Calculating this gives:

\[
[\text{H}^+]_B = 10^{4} \times 10^{-5} = 10^{-1} \, \text{M}
\]

Now we can find the pH of solution B:

\[
\text{pH}_B = -\log[\text{H}^+]_B = -\log(10^{-1}) = 1
\]

Thus, the pH of solution B is:

\[
\boxed{1}
\]