Answer :
To calculate the pH for each of the given substances, we will use the formula for pH, which is:
[tex]\[ \text{pH} = -\log_{10} [H^+] \][/tex]
Here’s the detailed step-by-step solution for each substance:
### Oven Cleaner
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for the oven cleaner is [tex]\(10^{-13}\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(10^{-13}) \][/tex]
3. Using properties of logarithms:
[tex]\[ -\log_{10}(10^{-13}) = 13 \][/tex]
4. The pH of the oven cleaner is:
[tex]\[ \text{pH} = 13.0 \][/tex]
### Water
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for water is [tex]\(0.0000007\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(0.0000007) \][/tex]
3. Using a calculator:
[tex]\[ -\log_{10}(0.0000007) \approx 6.2 \][/tex]
4. The pH of water is:
[tex]\[ \text{pH} = 6.2 \][/tex]
### Blood
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for blood is [tex]\(0.00000004\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(0.00000004) \][/tex]
3. Using a calculator:
[tex]\[ -\log_{10}(0.00000004) \approx 7.4 \][/tex]
4. The pH of blood is:
[tex]\[ \text{pH} = 7.4 \][/tex]
### Vinegar
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for vinegar is [tex]\(0.0063\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(0.0063) \][/tex]
3. Using a calculator:
[tex]\[ -\log_{10}(0.0063) \approx 2.2 \][/tex]
4. The pH of vinegar is:
[tex]\[ \text{pH} = 2.2 \][/tex]
In summary, the approximate pH values rounded to the nearest tenth are:
- Oven cleaner: [tex]\( pH = 13.0 \)[/tex]
- Water: [tex]\( pH = 6.2 \)[/tex]
- Blood: [tex]\( pH = 7.4 \)[/tex]
- Vinegar: [tex]\( pH = 2.2 \)[/tex]
[tex]\[ \text{pH} = -\log_{10} [H^+] \][/tex]
Here’s the detailed step-by-step solution for each substance:
### Oven Cleaner
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for the oven cleaner is [tex]\(10^{-13}\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(10^{-13}) \][/tex]
3. Using properties of logarithms:
[tex]\[ -\log_{10}(10^{-13}) = 13 \][/tex]
4. The pH of the oven cleaner is:
[tex]\[ \text{pH} = 13.0 \][/tex]
### Water
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for water is [tex]\(0.0000007\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(0.0000007) \][/tex]
3. Using a calculator:
[tex]\[ -\log_{10}(0.0000007) \approx 6.2 \][/tex]
4. The pH of water is:
[tex]\[ \text{pH} = 6.2 \][/tex]
### Blood
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for blood is [tex]\(0.00000004\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(0.00000004) \][/tex]
3. Using a calculator:
[tex]\[ -\log_{10}(0.00000004) \approx 7.4 \][/tex]
4. The pH of blood is:
[tex]\[ \text{pH} = 7.4 \][/tex]
### Vinegar
1. The hydrogen ion concentration [tex]\([H^+]\)[/tex] for vinegar is [tex]\(0.0063\)[/tex].
2. Substitute [tex]\([H^+]\)[/tex] into the pH formula:
[tex]\[ \text{pH} = -\log_{10}(0.0063) \][/tex]
3. Using a calculator:
[tex]\[ -\log_{10}(0.0063) \approx 2.2 \][/tex]
4. The pH of vinegar is:
[tex]\[ \text{pH} = 2.2 \][/tex]
In summary, the approximate pH values rounded to the nearest tenth are:
- Oven cleaner: [tex]\( pH = 13.0 \)[/tex]
- Water: [tex]\( pH = 6.2 \)[/tex]
- Blood: [tex]\( pH = 7.4 \)[/tex]
- Vinegar: [tex]\( pH = 2.2 \)[/tex]
