Question: User: Q. Which formula is a valid rearrangement to make the hydrogen ion concentration the subject?
a. [H⁺] = 10^-pH
b. [H⁺] = log(10 + pH)
c. [H⁺] = 10^pH
d. [H⁺] = 10 - pH
Q. Use the pH equation and its rearranged form to find the [H⁺] concentration of known pH solutions, and the pH of known [H⁺] concentrations.
pH Hydrogen ion concentration
1 1.00 × 10^-7
2 1.41 × 10^-4
8.00
6.72
Q. Answer this question by filling in the blanks in the following paragraph:
top-right: Multiple-choice math text with formulas; a valid rearrangement is shown as [H⁺] = 10^-pH in option a. center: A table labeled pH and Hydrogen ion concentration with entries 1.00 × 10^-7, 1.41 × 10^-4, pH 8.00, and pH 6.72. bottom-left: Prompt text for a paragraph fill-in question.
1. **State the problem:** We need to identify the correct formula to express hydrogen ion concentration $[H^+]$ as the subject in terms of pH, and then use this formula to calculate missing values in a table of pH and $[H^+]$ concentrations.
2. **Recall the pH definition:** The pH is defined as
$$\text{pH} = -\log_{10} [H^+]$$
This means the hydrogen ion concentration can be found by rearranging this formula:
$$[H^+] = 10^{-\text{pH}}$$
3. **Check the options:**
- a. $[H^+] = 10^{-\text{pH}}$ is the correct rearrangement.
- b. $[H^+] = \log(10 + \text{pH})$ is incorrect because pH is inside a log added to 10, which is not related.
- c. $[H^+] = 10^{\text{pH}}$ is incorrect because the exponent should be negative.
- d. $[H^+] = 10 - \text{pH}$ is incorrect because pH is not subtracted from 10.
4. **Use the formula to find missing values:**
- For pH = 1, calculate $[H^+]$:
$$[H^+] = 10^{-1} = 0.1$$
Given is $1.00 \times 10^{-7}$, which seems inconsistent; likely a typo in the table.
- For pH = 2, calculate $[H^+]$:
$$[H^+] = 10^{-2} = 0.01$$
Given is $1.41 \times 10^{-4}$, also inconsistent; possibly a typo.
- For $[H^+] = 1.00 \times 10^{-7}$, calculate pH:
$$\text{pH} = -\log_{10}(1.00 \times 10^{-7}) = 7$$
- For $[H^+] = 1.41 \times 10^{-4}$, calculate pH:
$$\text{pH} = -\log_{10}(1.41 \times 10^{-4}) \approx 3.85$$
- For pH = 8.00, calculate $[H^+]$:
$$[H^+] = 10^{-8.00} = 1.00 \times 10^{-8}$$
- For pH = 6.72, calculate $[H^+]$:
$$[H^+] = 10^{-6.72} \approx 1.91 \times 10^{-7}$$
5. **Summary:**
- The valid rearrangement is option a: $[H^+] = 10^{-\text{pH}}$.
- Use this formula to convert between pH and hydrogen ion concentration.