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Sagot :
Let's work through the given problem step-by-step to convert the percent transmittance values to absorbance values. The blank current is 100%, so we'll use this as our reference.
The formula to calculate absorbance ([tex]\(A\)[/tex]) from percent transmittance ([tex]\(T\)[/tex]) is:
[tex]\[ A = -\log_{10}\left(\frac{T}{100}\right) \][/tex]
Here's the detailed calculation for each concentration:
### 1. For [tex]\(4.0 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 17.9%
[tex]\[ A = -\log_{10}\left(\frac{17.9}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.179) \][/tex]
[tex]\[ A \approx 0.747 \][/tex]
The absorbance is approximately 0.747.
### 2. For [tex]\(3.2 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 25.0%
[tex]\[ A = -\log_{10}\left(\frac{25.0}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.25) \][/tex]
[tex]\[ A \approx 0.602 \][/tex]
The absorbance is approximately 0.602.
### 3. For [tex]\(2.4 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 35.7%
[tex]\[ A = -\log_{10}\left(\frac{35.7}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.357) \][/tex]
[tex]\[ A \approx 0.447 \][/tex]
The absorbance is approximately 0.447.
### 4. For [tex]\(1.6 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 50.2%
[tex]\[ A = -\log_{10}\left(\frac{50.2}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.502) \][/tex]
[tex]\[ A \approx 0.299 \][/tex]
The absorbance is approximately 0.299.
### 5. For [tex]\(8.0 \times 10^{-5} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 70.8%
[tex]\[ A = -\log_{10}\left(\frac{70.8}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.708) \][/tex]
[tex]\[ A \approx 0.150 \][/tex]
The absorbance is approximately 0.150.
### Summary of Results
| [tex]\( FeCl_3 \)[/tex] Concentration (M) | \% Transmittance | Absorbance |
|-------------------------------|-------------------|-------------|
| [tex]\( 4.0 \times 10^{-4} \)[/tex] | 17.9 | 0.747 |
| [tex]\( 3.2 \times 10^{-4} \)[/tex] | 25.0 | 0.602 |
| [tex]\( 2.4 \times 10^{-4} \)[/tex] | 35.7 | 0.447 |
| [tex]\( 1.6 \times 10^{-4} \)[/tex] | 50.2 | 0.299 |
| [tex]\( 8.0 \times 10^{-5} \)[/tex] | 70.8 | 0.150 |
These are the calculated absorbance values for the given solutions.
The formula to calculate absorbance ([tex]\(A\)[/tex]) from percent transmittance ([tex]\(T\)[/tex]) is:
[tex]\[ A = -\log_{10}\left(\frac{T}{100}\right) \][/tex]
Here's the detailed calculation for each concentration:
### 1. For [tex]\(4.0 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 17.9%
[tex]\[ A = -\log_{10}\left(\frac{17.9}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.179) \][/tex]
[tex]\[ A \approx 0.747 \][/tex]
The absorbance is approximately 0.747.
### 2. For [tex]\(3.2 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 25.0%
[tex]\[ A = -\log_{10}\left(\frac{25.0}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.25) \][/tex]
[tex]\[ A \approx 0.602 \][/tex]
The absorbance is approximately 0.602.
### 3. For [tex]\(2.4 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 35.7%
[tex]\[ A = -\log_{10}\left(\frac{35.7}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.357) \][/tex]
[tex]\[ A \approx 0.447 \][/tex]
The absorbance is approximately 0.447.
### 4. For [tex]\(1.6 \times 10^{-4} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 50.2%
[tex]\[ A = -\log_{10}\left(\frac{50.2}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.502) \][/tex]
[tex]\[ A \approx 0.299 \][/tex]
The absorbance is approximately 0.299.
### 5. For [tex]\(8.0 \times 10^{-5} M\)[/tex]
Given:
- Percent transmittance ([tex]\(T\)[/tex]) = 70.8%
[tex]\[ A = -\log_{10}\left(\frac{70.8}{100}\right) \][/tex]
[tex]\[ A = -\log_{10}(0.708) \][/tex]
[tex]\[ A \approx 0.150 \][/tex]
The absorbance is approximately 0.150.
### Summary of Results
| [tex]\( FeCl_3 \)[/tex] Concentration (M) | \% Transmittance | Absorbance |
|-------------------------------|-------------------|-------------|
| [tex]\( 4.0 \times 10^{-4} \)[/tex] | 17.9 | 0.747 |
| [tex]\( 3.2 \times 10^{-4} \)[/tex] | 25.0 | 0.602 |
| [tex]\( 2.4 \times 10^{-4} \)[/tex] | 35.7 | 0.447 |
| [tex]\( 1.6 \times 10^{-4} \)[/tex] | 50.2 | 0.299 |
| [tex]\( 8.0 \times 10^{-5} \)[/tex] | 70.8 | 0.150 |
These are the calculated absorbance values for the given solutions.
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