To find the pH of a solution, we use the formula:
[tex]\[ pH = -\log_{10} [H^+] \][/tex]
where [tex]\([H^+]\)[/tex] is the molar concentration of hydrogen ions in the solution.
### For Oven Cleaner:
Given: [tex]\[H^+] = 10^{-13}
1. Substitute the concentration into the pH formula:
\[ pH = -\log_{10}(10^{-13}) \][/tex]
2. Recall that [tex]\(\log_{10}(10^{-x}) = -x\)[/tex]:
[tex]\[ pH = -(-13) \][/tex]
3. Simplify the expression:
[tex]\[ pH = 13 \][/tex]
Thus, the pH of the oven cleaner is 13.0.
### For Water:
Given: [tex]\[H^+] = 0.0000007\][/tex]
1. Substitute the concentration into the pH formula:
[tex]\[ pH = -\log_{10}(0.0000007) \][/tex]
2. Calculate the logarithm:
[tex]\[ \log_{10}(0.0000007) \approx -6.155 \][/tex]
3. Apply the negative sign:
[tex]\[ pH = -(-6.155) \][/tex]
[tex]\[ pH = 6.155 \][/tex]
4. Round to the nearest tenth:
[tex]\[ pH \approx 6.2 \][/tex]
Thus, the pH of water is 6.2.
### For Blood:
Given: [tex]\[H^+] = 0.00000004\][/tex]
1. Substitute the concentration into the pH formula:
[tex]\[ pH = -\log_{10}(0.00000004) \][/tex]
2. Calculate the logarithm:
[tex]\[ \log_{10}(0.00000004) \approx -7.398 \][/tex]
3. Apply the negative sign:
[tex]\[ pH = -(-7.398) \][/tex]
[tex]\[ pH = 7.398 \][/tex]
4. Round to the nearest tenth:
[tex]\[ pH \approx 7.4 \][/tex]
Thus, the pH of blood is 7.4.
### For Vinegar:
Given: [tex]\[H^+] = 0.0063\][/tex]
1. Substitute the concentration into the pH formula:
[tex]\[ pH = -\log_{10}(0.0063) \][/tex]
2. Calculate the logarithm:
[tex]\[ \log_{10}(0.0063) \approx -2.201 \][/tex]
3. Apply the negative sign:
[tex]\[ pH = -(-2.201) \][/tex]
[tex]\[ pH = 2.201 \][/tex]
4. Round to the nearest tenth:
[tex]\[ pH \approx 2.2 \][/tex]
Thus, the pH of vinegar is 2.2.
The pH values are:
Oven cleaner: 13.0
Water: 6.2
Blood: 7.4
Vinegar: 2.2
