Questions: Determine the absorbance if the percent transmission is 68.6%.

Transcript text: 4. Determine the absorbance if the percent transmission is $68.6 \%$.

Solution

Step 1: Understanding the Relationship Between Absorbance and Percent Transmission

Absorbance ($A$) and percent transmission ($T$) are related by the formula: \[ A = -\log_{10}\left(\frac{T}{100}\right) \]

Step 2: Converting Percent Transmission to a Decimal

Given the percent transmission $T = 68.6\%$, we first convert it to a decimal: \[ \frac{T}{100} = \frac{68.6}{100} = 0.686 \]

Step 3: Calculating the Absorbance

Using the formula from Step 1, we substitute $T = 0.686$: \[ A = -\log_{10}(0.686) \]

Step 4: Computing the Logarithm

Calculate the logarithm: \[ \log_{10}(0.686) \approx -0.1635 \]

Step 5: Determining the Absorbance

Finally, we find the absorbance: \[ A = -(-0.1635) = 0.1635 \]

$\boxed{A = 0.1635}$

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