To determine the pH of a solution given the hydrogen ion concentration [tex]\([H^+]\)[/tex], we can use the formula for pH, which is defined as:
[tex]\[ \text{pH} = -\log[H^+] \][/tex]
Here's a step-by-step solution to calculate the pH:
1. Identify the given hydrogen ion concentration:
[tex]\[
[H^+] = 4.0 \times 10^{-8} \, \text{M}
\][/tex]
2. Substitute the hydrogen ion concentration into the pH formula:
[tex]\[
\text{pH} = -\log [4.0 \times 10^{-8}]
\][/tex]
3. Use the properties of logarithms to simplify:
[tex]\[
\log [4.0 \times 10^{-8}] = \log 4.0 + \log 10^{-8}
\][/tex]
4. Calculate each part separately:
- The logarithm of 4.0 can be approximated or calculated using a calculator:
[tex]\[
\log 4.0 \approx 0.6
\][/tex]
- The logarithm of [tex]\(10^{-8}\)[/tex] is straightforward:
[tex]\[
\log 10^{-8} = -8
\][/tex]
5. Combine the results:
[tex]\[
\log [4.0 \times 10^{-8}] \approx 0.6 - 8 = -7.4
\][/tex]
6. Apply the negative sign to get the pH:
[tex]\[
\text{pH} = -(-7.4) = 7.4
\][/tex]
After performing these steps, we find that the pH of blood with a hydrogen ion concentration of [tex]\(4.0 \times 10^{-8}\)[/tex] M is approximately 7.4.
Therefore, the correct answer is:
- c. 7.4
