The Beer-Lambert Law - Online Tutor, Practice Problems & Exam Prep

The Beer-Lambert law describes the linear relationship between a solution's concentration and its light absorbance. The absorbance (A) is calculated using the equation: A=log(I₀), where I₀ is the initial light intensity and I is the transmitted intensity. This relationship also incorporates molar absorptivity (ε), concentration (c), and path length (l): A=ε·c·l. Understanding this law is crucial for quantitative analysis in absorption spectroscopy.

The Beer-Lambert Law Concept 1

Hey, everyone. So here we're going to do a quick breakdown of the Beer-Lambert law. Now here we're going to say that the Beer-Lambert law itself is a linear relationship between the concentration of a sample and how strongly it absorbs light. Now you're going to say it's used to measure concentration, which uses the variable c here of a solution, its absorbance, which uses capital A, or its molar absorptivity, which uses ε here. Now when the sample solution absorbs light, we're going to say that I is going to be smaller than I₀.

If we take a look here, we have our light source. This light source is going to pass through what we call a monochrome monitor, and we're going to say that it basically focuses that light. That light passes through our solution. Now before it enters the solution, we have I₀. And as it passes outside of the solution, we have I then.

It then goes through our detector. And from the detector, we're able to construct our chart here, which has absorbance on our y-axis and then concentration on our x-axis. Here, we would say that, as we're graphing and charting this out, we would create what's called a lambda max wave. That's going to be the peak of this chart. And we're going to say here that as the light passes through our solution, if the solution is not very concentrated, we can still see that the solution does absorb some.

So the intent we're going to say I, again, is smaller than I₀. And then here, if we're saying that it's a concentrated solution, the same effect, the light still passes through. But, again, I will be even lower because more of the solution absorbs this light, giving us an even smaller I. So the concentration of the solution can also affect the size of I in comparison to I₀. A diluted solution can't absorb the light as easily, so we're going to see that our I is a little bit more concentrated, much larger.

But then if we're dealing with a more concentrated solution, it absorbs the light more readily, so I becomes even smaller. Right. So here, this is just the basic premise when we're talking about the Beer-Lambert law. Click on the next video, and let's take a look at the equation associated with the Beer-Lambert law.

The Beer-Lambert Law Concept 2

Hey, everyone. Now that we understand the basics of the Beer-Lambert law, let's take a look at the equation itself. Here we're going to say that \( a \) represents the absorbance of our sample. It's equal to the log of, so here we're gonna say, \( I_0 \) divided by \( I \), where \( I_0 \) equals the intensity of light, and then \( I \) in italicized is just the intensity of light through the sample. This also equals our molar absorptivity times our concentration times our path length.

Now our molar absorptivity, this is in units of liters times molarities inverse times centimeters inverse. Here, \( c \) equals our sample concentration. Concentration is a term we've learned throughout chemistry. We know that it is molarity. So here, this would just be capital \( M \).

And then here, \( L \), it's the path length of light. If we look at the molar absorptivity, we see that centimeters inverse are involved. That's because the path length is in centimeters. Right. So just remember, when we're dealing with the Beer-Lambert law in terms of calculations, this is what we can utilize.

We can say, \( a \), our absorbance is equal to log of \( I_0 \) divided by \( I \), which is also equal to our molar absorptivity times our concentration times our path length. So just remember the two interpretations of this formula to help you with any calculations dealing with the Beer-Lambert Law.

The Beer-Lambert Law Example 1

Hey, everyone. So in this example question, it says, a sample solution was found to have an absorbance of 0.602. Calculate the I₀ divided by I ratio. Alright. So here we're talking about absorbance, and we're talking about this ratio.

That means the formula we need to utilize is that absorbance equals log of this ratio. Now we need to determine what the ratio is, so we're going to plug in the information that we know. The absorbance is 0.602, which is equal to log of our ratio. Now we don't want the log of our ratio; we just want our ratio.

So you're going to take the inverse log of both sides. So that's going to become 100.602 equals taking the inverse log of the right side drops the log, and so it now just equals our ratio. When you punch this into your calculator, you'll get 3.999, which is basically 4, equals our ratio. But remember, when we're saying the term ratio, this 4 for 4 would actually mean 4 over 1. So that means our ratio would be a 4 to 1 ratio.

4 for I₀ and then one just for I itself. Alright. So this will be our final answer. It's a 4 to 1 ratio.

A 1.6 x 10^-3 g sample of compound (MM = 136 g/mol) was dissolved in 15 mL of methanol. Maximum absorption at λ _max (258 nm) represents absorbance of 0.73. Determine the molar absorptivity of the sample if the light travels through a 1.6 cm UV cell.

• A. 581718 M^-1 cm^-1 
• B. 58.0 M^-1 cm^-1 
• C. 2.06 x 10⁵ M^-1 cm^-1  
• D. 580 M^-1 cm^-1

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What is the Beer-Lambert Law and how is it used in chemistry?

The Beer-Lambert Law describes the linear relationship between the concentration of a solution and its absorbance of light. It is used in chemistry to determine the concentration of a solute in a solution by measuring the absorbance of light at a specific wavelength. The law is expressed by the equation:

$A=\epsilon \cdot c\cdot l$

where $A$ is the absorbance, $\epsilon$ is the molar absorptivity, $c$ is the concentration, and $l$ is the path length. This law is crucial for quantitative analysis in absorption spectroscopy.

How do you calculate absorbance using the Beer-Lambert Law?

To calculate absorbance using the Beer-Lambert Law, you use the equation:

$A=\epsilon \cdot c\cdot l$

where $A$ is the absorbance, $\epsilon$ is the molar absorptivity (in L·mol^-1·cm^-1), $c$ is the concentration of the solution (in mol/L), and $l$ is the path length of the light through the solution (in cm). By knowing the values of $\epsilon$, $c$, and $l$, you can calculate the absorbance $A$.

What factors affect the absorbance in the Beer-Lambert Law?

The absorbance in the Beer-Lambert Law is affected by three main factors:

1. Concentration (c): Higher concentration of the absorbing species increases absorbance.
2. Path Length (l): Longer path length through which light travels increases absorbance.
3. Molar Absorptivity (ε): This is a constant that depends on the nature of the absorbing species and the wavelength of light used. Higher molar absorptivity means higher absorbance for a given concentration and path length.

These factors are incorporated into the Beer-Lambert Law equation:

$A=\epsilon \cdot c\cdot l$

What is molar absorptivity and how is it determined?

Molar absorptivity, denoted as $\epsilon$, is a measure of how strongly a chemical species absorbs light at a given wavelength. It is determined experimentally by measuring the absorbance of a series of known concentrations of the species and plotting absorbance (A) against concentration (c). The slope of the resulting linear plot, when the path length (l) is known, gives the molar absorptivity:

$\epsilon =\frac{A}{c\cdot l}$

Molar absorptivity has units of L·mol^-1·cm^-1 and is specific to the substance and the wavelength of light used.

How does the Beer-Lambert Law apply to real-world applications?

The Beer-Lambert Law is widely used in various real-world applications, particularly in analytical chemistry and biochemistry. It is used to determine the concentration of substances in solutions, such as measuring the concentration of pollutants in water, determining the concentration of DNA or proteins in biological samples, and monitoring the progress of chemical reactions. By measuring the absorbance of light at specific wavelengths, scientists can quantify the amount of a substance present in a sample, making it a crucial tool for quality control, environmental monitoring, and research.