Compound X Absorbance Calculation

This solution details the calculation of the absorbance for compound X using the Beer-Lambert Law, based on given transmittance and concentration data.

Beer-Lambert Law Explained

The Beer-Lambert Law relates absorbance to concentration and path length. The formula is:

$A = \epsilon \times b \times c$

Where:

• $A$ is absorbance (unitless)
• $\epsilon$ is molar absorptivity (M^-1cm^-1)
• $b$ is path length (cm)
• $c$ is concentration (M)

Absorbance can also be calculated from transmittance (T) using:

$A = -\log_{10}(T)$

Calculate Initial Absorbance (A1)

First, calculate the absorbance (A1) for the initial solution:

• Transmittance (T) = 80% = 0.8
• Path length (b) = 1.0 cm
• Concentration (c1) = 0.005 M

Using the transmittance formula:

$A1 = -\log_{10}(0.8)$

$A1 \approx 0.09691$

Determine Molar Absorptivity ($\epsilon$)

Use the calculated A1 and the given conditions (c1, b) to find the molar absorptivity ($\epsilon$):

$\epsilon = \frac{A1}{b \times c1}$

Substitute the values:

$\epsilon = \frac{0.09691}{1.0 \text{ cm} \times 0.005 \text{ M}}$

$\epsilon \approx 19.382 \text{ M}^{-1}\text{cm}^{-1}$

Calculate Absorbance for 0.01 M Solution (A2)

Now, calculate the absorbance (A2) for the new concentration (c2 = 0.01 M) using the determined molar absorptivity and the same path length:

• Molar absorptivity ($\epsilon$) $\approx 19.382 \text{ M}^{-1}\text{cm}^{-1}$
• Path length (b) = 1.0 cm
• Concentration (c2) = 0.01 M

Using the Beer-Lambert Law formula:

$A2 = \epsilon \times b \times c2$

$A2 = 19.382 \text{ M}^{-1}\text{cm}^{-1} \times 1.0 \text{ cm} \times 0.01 \text{ M}$

$A2 \approx 0.19382$

Final Rounded Absorbance

Rounding the calculated absorbance (A2) to three decimal places gives:

$A2 \approx 0.194$

This value is consistent with the provided range (0.193 to 0.195).