Measuring Absorbance: Videos & Practice Problems

In UV-Vis spectroscopy, absorbance and percent transmittance are inversely related. The formula for percent transmittance (T) is given by ${10}^{-A}$, where A is absorbance. For an absorbance of 0.419, percent transmittance calculates to 38.1%. Conversely, if percent transmittance is 39.1%, absorbance can be determined using the same relationship. Understanding this relationship is crucial for analyzing sample concentration and light absorption properties.

Measuring Absorbance Calculations 1

In UV-Vis Spectroscopy, understanding the relationship between absorbance and percent transmittance is crucial. Absorbance (A) quantifies the amount of light absorbed by a sample, while percent transmittance (T) indicates the fraction of light that successfully passes through the sample. These two measurements are inversely related; when a sample absorbs 100% of light, it transmits 0%, and vice versa.

The formula to calculate percent transmittance from absorbance is given by:

\[T = 10^{-A} \times 100\]

For example, if the absorbance of a substance is measured at 0.419, we can calculate the percent transmittance as follows:

\[T = 10^{-0.419} \times 100\]

This calculation yields:

\[T = 10^{-0.419} \approx 0.381 \times 100 = 38.1\%\]

This result indicates that 38.1% of light passes through the sample, meaning the remaining 61.9% is absorbed. It is essential to remember that as the concentration of a sample increases, its ability to transmit light decreases, leading to higher absorbance values.

Conversely, if you know the percent transmittance and want to find the absorbance, you can rearrange the formula. For a percent transmittance of 39.1%, the absorbance can be calculated using:

\[A = -\log_{10}\left(\frac{T}{100}\right)\]

By substituting the value of T, you can determine the absorbance, reinforcing the concept that absorbance and transmittance are two sides of the same coin in spectroscopic analysis.

Measuring Absorbance Calculations 1

To determine absorbance from percent transmittance, we start with the relationship defined by the equation:

$$\text{Percent Transmittance} = 10^{2 - A}$$

To manipulate this equation for absorbance (A), we take the logarithm of both sides. This leads to:

$$\log(\text{Percent Transmittance}) = 2 - A$$

By rearranging the equation, we subtract 2 from both sides:

$$\log(\text{Percent Transmittance}) - 2 = -A$$

Next, we multiply through by -1 to isolate A:

$$A = -\log(\text{Percent Transmittance}) + 2$$

When you substitute the value of percent transmittance into this equation, you can calculate the absorbance. For example, if the percent transmittance is given, plugging it into the equation yields:

$$A = -\log(T) + 2$$

In a specific case, if the calculation results in an absorbance value of 0.408, this indicates the relationship between absorbance and percent transmittance is crucial for understanding how light interacts with substances.

Additionally, when identifying the colors of a compound based on the colors it absorbs, the color wheel can be a helpful tool. The color wheel illustrates complementary colors, which can guide you in determining the color that is not absorbed by the compound. For instance, if a compound absorbs blue light, it will appear orange, as orange is the complementary color to blue on the color wheel.

Identify the colors of a compound that absorbs green light, yellow-green light and blue light.

• A. green, yellow-green, blue
• B. violet-red, violet-red, blue-violet
• C. red, violet-red, orange
• D. red, violet, orange-yellow
• E. red, violet-red, orange, yellow

Answer: (C)

Here’s what students ask on this topic:

What is the relationship between absorbance and percent transmittance in UV-Vis spectroscopy?

In UV-Vis spectroscopy, absorbance (A) and percent transmittance (%T) are inversely related. The relationship is given by the formula:

${10}^{-A}$

where A is the absorbance. For example, if the absorbance is 0.419, the percent transmittance can be calculated as:

${10}^{-0.419}=\; 38.1\%$

This means that 38.1% of the light passes through the sample, while the rest is absorbed. Conversely, if the percent transmittance is known, the absorbance can be calculated using the same relationship.

How do you calculate percent transmittance from absorbance?

To calculate percent transmittance (%T) from absorbance (A), you use the formula:

${10}^{-A}$

For example, if the absorbance is 0.419, the percent transmittance is calculated as:

${10}^{-0.419}=\; 38.1\%$

This means that 38.1% of the light passes through the sample, while the remaining 61.9% is absorbed by the sample.

How do you determine absorbance if percent transmittance is given?

To determine absorbance (A) from percent transmittance (%T), you use the inverse of the transmittance formula. The relationship is given by:

$A=\; -{10}^{log\left(\mathrm{\%T}\right)}$

For example, if the percent transmittance is 39.1%, the absorbance is calculated as:

$A=\; -{10}^{log\left(0.391\right)}=\; 0.408$

This means that the sample has an absorbance of 0.408.

Why is understanding the relationship between absorbance and percent transmittance important in UV-Vis spectroscopy?

Understanding the relationship between absorbance and percent transmittance is crucial in UV-Vis spectroscopy because it allows for the accurate analysis of sample concentration and light absorption properties. Absorbance is directly related to the concentration of the absorbing species in the sample, according to Beer-Lambert Law. By measuring the percent transmittance, one can calculate the absorbance and thus determine the concentration of the sample. This relationship is essential for various applications, including chemical analysis, quality control, and research in fields such as chemistry, biology, and environmental science.

What is the formula for calculating absorbance from percent transmittance?

The formula for calculating absorbance (A) from percent transmittance (%T) is:

$A=\; -{10}^{log\left(\mathrm{\%T}\right)}$

For example, if the percent transmittance is 39.1%, the absorbance is calculated as:

$A=\; -{10}^{log\left(0.391\right)}=\; 0.408$

This formula is essential for converting transmittance data into absorbance values, which are more directly related to the concentration of the sample.