A solution has a percentage transmittance of 80%

A solution has a percentage transmittance of 80%. Calculate its absorbance

The correct answer and explanation is:

To calculate the absorbance (A) of a solution from its percentage transmittance (%T), we use the following formula: A=−log⁡10(%T100)A = -\log_{10}\left(\frac{\%T}{100}\right)

Given:

• %T = 80%

Step-by-step calculation:

A=−log⁡10(80100)A = -\log_{10}\left(\frac{80}{100}\right) A=−log⁡10(0.80)A = -\log_{10}(0.80) A≈−(−0.09691)A \approx -(-0.09691) A≈0.097A \approx 0.097

✅ Final Answer:

0.097\boxed{0.097}

Explanation (Approx. 300 words):

Absorbance is a measure of how much light is absorbed by a solution as light passes through it. It’s widely used in spectrophotometry to determine the concentration of solutes in a solution, based on Beer-Lambert’s Law. The higher the absorbance, the less light passes through the solution, which typically indicates a higher concentration of the absorbing species.

The percentage transmittance (%T) is the ratio of the intensity of transmitted light to the intensity of incident light, multiplied by 100. If 100% of light passes through a solution, its absorbance is zero, meaning the solution doesn’t absorb any light. Conversely, as transmittance decreases, absorbance increases.

The relationship between absorbance (A) and transmittance is logarithmic: A=−log⁡10(%T100)A = -\log_{10} \left(\frac{\%T}{100}\right)

This equation reflects the logarithmic scale used in spectroscopy, similar to how sound levels are measured in decibels. This allows for small differences in transmittance to result in easily distinguishable absorbance values, which is useful in analytical chemistry.

In this case, the solution transmits 80% of the incident light. That means only 20% is being absorbed. Plugging 80% into the formula gives an absorbance of approximately 0.097, a relatively low value, which implies that the solution is fairly transparent and only absorbs a small amount of light.

This relationship is fundamental in laboratory analysis, especially in determining concentrations using spectrophotometers, as absorbance is directly proportional to concentration under constant path length and wavelength.