To determine the pH of a substance where the concentration of hydrogen ions [tex]\( H \)[/tex] is given as 0.00032, we can follow the detailed steps below. The formula for calculating pH is:
[tex]\[ pH = -\log H \][/tex]
Given [tex]\( H = 0.00032 \)[/tex], we can rewrite this concentration in scientific notation to facilitate the logarithmic calculations. This means:
[tex]\[ H = 3.2 \times 10^{-4} \][/tex]
Now, substituting [tex]\( H = 3.2 \times 10^{-4} \)[/tex] into the pH formula, we perform the following steps:
1. Calculate the logarithm of [tex]\( H \)[/tex]:
[tex]\[ \log (3.2 \times 10^{-4}) \][/tex]
Using the properties of logarithms:
[tex]\[ \log (3.2 \times 10^{-4}) = \log 3.2 + \log 10^{-4} \][/tex]
2. Evaluate each part separately:
- [tex]\(\log 3.2\)[/tex]
- [tex]\(\log 10^{-4} = -4\)[/tex]
3. Sum the results of the two individual logarithms:
[tex]\[ \log 3.2 - 4 \][/tex]
4. Multiply that result by -1 (as per the pH formula):
[tex]\[ pH = - (\log 3.2 - 4) \][/tex]
This process leads to a calculated pH value.
From the steps mentioned above, the correct and valid step in calculating the pH of the substance is:
[tex]\[ -\log (3.2 \times 10^{-4}) = pH \][/tex]
Here is the valid step in the process:
[tex]\[ -\log (3.2 \times 10^{-4}) = pH \][/tex]
Therefore, the correct answer is:
[tex]\[
-\log (3.2 \cdot 10^{-4}) = pH
\][/tex]
