A 2.78 x 10-4 M solution of a compound has an absorbance of 0.469 at 520 nm in a 1.00 cm cell. The solvent's absorbance under the same conditions is 0.024. (a) What is the molar absorptivity of the unknown compound? 4.0 1687 XM-1cm-1
A 2.78 x 10-4 M solution of a compound has an absorbance of 0.469 at 520 nm in a 1.00 cm cell. The solvent's absorbance under the same conditions is 0.024. (a) What is the molar absorptivity of the unknown compound? 4.0 1687 XM-1cm-1
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![**Absorbance and Molar Absorptivity Calculation**
A \(2.78 \times 10^{-4} \, M\) solution of a compound has an absorbance of **0.469** at 520 nm in a 1.00 cm cell. The solvent's absorbance under the same conditions is **0.024**.
**(a) What is the molar absorptivity of the unknown compound?**
The calculated molar absorptivity is **1687 \, M^{-1} \text{cm}^{-1}**.
---
**Explanation of Concepts:**
- **Absorbance (\(A\))**: A measure of the amount of light absorbed by a solution.
- **Molar Absorptivity (\(\varepsilon\))**: A constant that indicates how strongly a substance absorbs light at a particular wavelength, expressed in \(M^{-1} \text{cm}^{-1}\).
- **Beer's Law**: Relates absorbance to molar absorptivity, concentration (\(C\)), and path length (\(l\)):
\[
A = \varepsilon \times C \times l
\]
In this problem, we calculate the molar absorptivity (\(\varepsilon\)) by adjusting the observed absorbance to account for the solvent absorbance and rearranging Beer's Law:
\[
\varepsilon = \frac{(A - A_{\text{solvent}})}{C \times l}
\]
Where:
- \(A\) is the observed absorbance (0.469).
- \(A_{\text{solvent}}\) is the solvent's absorbance (0.024).
- \(C\) is the concentration of the solution (\(2.78 \times 10^{-4}\) M).
- \(l\) is the path length (1.00 cm).
**Solution:**
1. Subtract the solvent's absorbance from the total absorbance:
\[
A_{\text{compound}} = A - A_{\text{solvent}} = 0.469 - 0.024 = 0.445
\]
2. Apply Beer's Law to find the molar absorptivity:
\[
\varepsilon = \frac{0.445}{2.78 \times 10^{-4} \times 1.00} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2F8129e2fb-6072-4f18-b95a-24b57c083f32%2Fmamil24_processed.png&w=3840&q=75)
Transcribed Image Text:**Absorbance and Molar Absorptivity Calculation**
A \(2.78 \times 10^{-4} \, M\) solution of a compound has an absorbance of **0.469** at 520 nm in a 1.00 cm cell. The solvent's absorbance under the same conditions is **0.024**.
**(a) What is the molar absorptivity of the unknown compound?**
The calculated molar absorptivity is **1687 \, M^{-1} \text{cm}^{-1}**.
---
**Explanation of Concepts:**
- **Absorbance (\(A\))**: A measure of the amount of light absorbed by a solution.
- **Molar Absorptivity (\(\varepsilon\))**: A constant that indicates how strongly a substance absorbs light at a particular wavelength, expressed in \(M^{-1} \text{cm}^{-1}\).
- **Beer's Law**: Relates absorbance to molar absorptivity, concentration (\(C\)), and path length (\(l\)):
\[
A = \varepsilon \times C \times l
\]
In this problem, we calculate the molar absorptivity (\(\varepsilon\)) by adjusting the observed absorbance to account for the solvent absorbance and rearranging Beer's Law:
\[
\varepsilon = \frac{(A - A_{\text{solvent}})}{C \times l}
\]
Where:
- \(A\) is the observed absorbance (0.469).
- \(A_{\text{solvent}}\) is the solvent's absorbance (0.024).
- \(C\) is the concentration of the solution (\(2.78 \times 10^{-4}\) M).
- \(l\) is the path length (1.00 cm).
**Solution:**
1. Subtract the solvent's absorbance from the total absorbance:
\[
A_{\text{compound}} = A - A_{\text{solvent}} = 0.469 - 0.024 = 0.445
\]
2. Apply Beer's Law to find the molar absorptivity:
\[
\varepsilon = \frac{0.445}{2.78 \times 10^{-4} \times 1.00} =
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