Spectrophotometry - Online Tutor, Practice Problems & Exam Prep

Spectrophotometry quantifies proteins by measuring light absorbance, following Beer's Law, which relates absorbance (A) to the concentration (c), path length (l), and extinction coefficient (ε). The extinction coefficient indicates how strongly a solute absorbs light at a specific wavelength (λ). Proteins typically absorb light at 280 nm due to tryptophan and tyrosine. Understanding these principles is crucial for accurate protein quantification and requires attention to unit consistency in calculations.

Spectrophotometry

In this video, we're going to talk about spectrophotometry. So as you guys probably recall from your previous courses, the light absorbance of a molecule can determine the amount of that molecule. And so, proteins can actually be quantified by measuring their light absorbance. Biochemists use specific instruments that are called spectrophotometers in order to acquire these light absorbance values. Then, biochemists can use the light absorbance values to determine the concentration of the absorbing solute or the concentration of the protein. Down below, you can see that the relationship between the light absorbance and the absorbing solute concentration is expressed by the Lambert Beer law, which is also commonly known as just Beer's law. Now, in our example image on the right-hand side, you can see Beer's Law with all of its different variables. First, what we're going to do up above is define each of these variables as we refresh our memories on how a typical spectrophotometer works, and then afterwards, I'll let you guys know how you should expect to use Beer's law moving forward in this course.

We know that spectrophotometers are used to acquire the light-absorbing values. The first variable here in Beer's law, the a, is really just referring to the absorbance of the solute, or the absorbance of the protein. With a typical spectrophotometer, there's going to be a light source; down below in our image, this white light is coming from the light source. The white light can be directed towards a diffractor, which is this triangular prism here. The diffractor acts as a wavelength selector. So when the white light is directed towards the diffractor, it will split the light into all of its wavelengths, and then one particular wavelength can be selected to move forward in the process. Before this wavelength of light that is selected actually hits the protein sample, it's referred to as the incident light. The incident light can be abbreviated with the symbol I0, where the 0 here means initial or incident, at the beginning.

Now, observe the presence of this incident light variable in our Beer's Law. Up above, we determined that I0 is really just referring to the initial intensity of light or the incident light. Now, note that when this incident light actually hits the protein sample, some of our proteins are going to absorb some of that light, but not all of the light is absorbed. Some of the light passes through the sample. Some of the light is transmitted through the sample. The transmitted light here is less intense than the incident light because some of the light was absorbed by the protein sample. This transmitted light is referred to as the transmitted light, and it can be abbreviated with the symbol I. In our Beer's Law equation, we also have this variable I. Up above, we determined that this variable is the transmitted intensity of light after the incident light passes through the sample. The transmitted light can hit a detector, and the detector can measure the amount of transmitted light.

Next, consider the protein sample. What factors can actually influence the amount of light that's absorbed by the protein sample? One factor is the concentration of the protein. The concentration can be abbreviated with the symbol c, and in our Beer's law equation, we have this variable c representing the amount of proteins. The greater the concentration of proteins, the cloudier the substance is going to be, and the more light it will absorb. The concentration is an important variable we want to consider.

Another factor is the length of the container, which will determine how much light is absorbed by extending the light path the light needs to travel through the sample. The length here is a factor and can be abbreviated with the symbol l, typically measured in centimeters. In our Beer's law on the right, there is this variable l referring to the length of the light path.

Our last variable is the trickiest as it's not as easily represented. This variable is the Greek symbol epsilon, referring to the extinction coefficient or the absorptivity of a molecule. This property controls how much light is absorbed and is specific to each molecule. For now, know that epsilon represents the extinction coefficient, a crucial factor in the Beer's law equation. You'll see that the epsilon here is the molar extinction coefficient.

Beer's Law is divided into three parts by two equal signs: 1) absorbance, 2) the log of the incident light over transmitted light, and 3) the extinction coefficient times the concentration times the length of the light path. Depending on the information provided in practice problems, we may focus on specific parts of Beer's Law. This concludes our lesson on spectrophotometry and Beer's law. In our next lesson video, we'll delve deeper into the extinction coefficient. Until then, let's practice. See you in that video.

What is the relationship between light absorbance (A) & the amount of light transmitted through a sample?

• A. Increased transmitted light results in increased A.
• B. Decreased transmitted light results in decreased A.
• C. Decreased transmitted light results in increased A.
• D. Transmitted light & A should always remain equal.

Spectrophotometry

So now that we've refreshed our memories on spectrophotometry and we've covered Beer's law, in this video, we're going to focus on the extinction coefficient, which we know is also sometimes called the absorptivity and is symbolized with the Greek symbol epsilon. The extinction coefficient is really just a specific property of a chemical that measures how strongly that chemical absorbs light at a particular wavelength of light. The wavelength of light can be symbolized with the Greek symbol, lambda shown here. The greater the molar extinction coefficient is, the greater the absorbance is going to be. The molar extinction coefficient will actually vary with different wavelengths of light. This means that the wavelength of light is going to be very critical to pay attention to moving forward as we use Beer's law. The molar extinction coefficient has units of inverse molarity and inverse centimeters. This is also important to take note of because, in our practice problems using Beer's law, we're going to need to make sure that all of the units appropriately match. If not, we need to do some unit conversion.

Now, down below in our image, we have a graph being shown, and on the y-axis, we have the extinction coefficient in units of inverse molarity inverse centimeters, and on the x-axis, we have the wavelength in units of nanometers. What you'll notice is we're measuring the extinction coefficient of a specific molecule at multiple different wavelengths. The wavelength actually changes the molar extinction coefficient. Again, because the extinction coefficient is involved in Beer's law, the extinction coefficient has an effect on the absorbance. Since the extinction coefficient varies with different wavelengths of light, that means that the absorbance also varies with different wavelengths of light. Because the wavelength here is so critical to the extinction coefficient and to the absorbance, that means that we're going to need to pay attention closely to what wavelength of light we're using. In our next lesson video, we're going to talk about exactly what wavelength of light is typically used to analyze proteins. Before we actually get to that lesson video, we'll get a little bit of practice with these concepts here in our next video. So, I'll see you guys there.

Which of the following options is false for Beer's Law?

• A. Absorbance increases as concentration increases.
• B. Absorbance decreases as path length increases.
• C. Absorptivity is wavelength specific.
• D. Absorbance spectrums plot absorbance and wavelength.

Spectrophotometry

So in our last lesson video, we reviewed the Lambert Beer law and spectrophotometry. And spectrophotometry data can be plotted onto an absorbance spectrum. An absorbance spectrum plots the absorbance values on the y-axis and the wavelength of light on the x-axis. Looking at our example down below at the absorbance spectrum on the left, notice that we have the absorbance values on the y-axis and the wavelength of light on the x-axis. Also notice that we have two different types of molecules that are being plotted. We have a protein molecule being plotted with the blue curve, and we have a nucleic acid molecule being plotted with the red curve. Notice that these two different molecules absorb light strongly at different wavelengths of light. The nucleic acid molecule, in red, absorbs light strongly at a wavelength of about 260 nanometers, whereas the protein molecule strongly absorbs wavelengths of light at 280 nanometers. It turns out that a peak light absorbance, specifically at 280 nanometers, is a characteristic property. Proteins strongly absorbing wavelengths of light at 280 nanometers is due to just two amino acids, and those two amino acids are tryptophan and tyrosine. Tryptophan strongly absorbs light at wavelengths of 200 nanometers to 280 nanometers, and tyrosine weakly absorbs wavelengths of light at 280 nanometers. Nevertheless, they both absorb wavelengths of light at 280 nanometers, which is a unique characteristic property of these two amino acids. We can clearly see that in the absorbent spectrum on the right, where again, we have the absorbance on the y-axis and the wavelength of light on the x-axis, and we can see that tryptophan strongly and tyrosine weakly absorb wavelengths of light at 280 nanometers. Now, we know that tryptophan and tyrosine are just two of a total of 20 amino acids. So what about all the other amino acids? It turns out that those amino acids do not strongly absorb any characteristic wavelength of light, and so biochemists don't use their light absorbance to quantify the concentration of proteins. But because tryptophan and tyrosine strongly absorb this unique characteristic wavelength at 280 nanometers, they can use their light absorbance to quantify proteins. It turns out that most proteins in nature are going to be quite large and they're going to have a lot of amino acids. And so the chances that they're going to have tryptophan and tyrosine is quite high, and that's why biochemists are able to use a wavelength at 280 nanometers to acquire the absorbance of most proteins and to use that absorbance to determine the concentration of most proteins. But, of course, if the protein does not have any tryptophans or tyrosines in them, then using a wavelength of 280 nanometers is not going to be the best way to quantify the protein and they're going to need to use a different method to do that. And so this concludes our lesson here on why tryptophan and tyrosine absorb light strongly at 280 nanometers, and we'll be able to get some practice in our next video. So I'll see you guys there.

A) Suppose myoglobin's molecular weight is 17,800 g/mole and its extinction coefficient at 280 nm wavelength is 15,000 M-1 cm-1. What is the absorbance of a myoglobin solution (concentration = 1 mg/mL) across a 1-cm path?

Hint: Use Beer's law.

a. 0.49            

b. 0.73            

c. 0.36            

d. 0.84

B) What is the percentage of the incident light that is transmitted through this solution?

a. 14%            

b. 6%

c. 21%

d. 58%

So here's a two-part practice problem that involves a lot of calculations, so if you don't have your calculator, pause the video now and go grab it. Part a says, suppose myoglobin's molecular weight is 17,800 grams per mole and its extinction coefficient at 280 nanometer wavelength is 15,000 with units of inverse molarity and inverse centimeters. It then asks, what is the absorbance of a myoglobin solution that has a concentration of 1 milligram per milliliter across a 1 centimeter path. It gives us the hint to use Beer's Law. Notice above, I've provided Beer's Law from our previous lessons. We are going to need to recognize the portion of Beer's Law that uses the incident light information. That means we are only going to focus on the absorbance and the other portion of Beer's Law that includes the extinction coefficient, the concentration, and the length of the light path. We can rewrite Beer's Law without the incident light and transmitted light portion: A = ε ⋅ c ⋅ l The length here is provided as 1 centimeter, and the molar extinction coefficient is given as 15,000 both in appropriate units. However, the concentration given as 1 milligram per milliliter must be converted to molarity. We convert: 1 milligram = 0.001 grams, using the molecular weight of 17,800 grams per mole, we have: 0.001 / 17800 = 5.618 - 8 moles For conversion from milliliters to liters: 0.001 liters Combining these: 5.618 - 5 moles / liter Now, we have all the variables for our Beer's Law equation, to find the absorbance: A = 15000 ⋅ 5.618 - 5 ⋅ 1 The absorbance is approximately 0.84. Moving on to part b, it asks for the percentage of the incident light that is transmitted through the solution. Using Beer's Law: A = log ⁡ I T With an absorbance of 0.84, we isolate for T/I by taking the antilog: T / I = antilog ⁡ ( - 0.84 ) ≈ 14.36 % The percentage of incident light transmitted through the solution is roughly 14%. This matches option a as our correct answer. This concludes our calculation-heavy practice problem. I'll see you guys in our next video.

A protein solution has an absorbance of 0.1 at 280 nm with a path length of 1 cm. If the protein sequence includes 3 Trp residues but no other aromatic residues, what is the concentration of the protein? (Trp ε = 3,400 M^-1 cm^-1).

• A. 29.4 μM
• B. 5.32 μM
• C. 9.8 μM
• D. 0.7036 μM

An unknown protein has been isolated in your laboratory and determined to have 172 amino acids but does not have tryptophan. You have been asked to determine the possible tyrosine content of this protein. You know from your study of this lesson that there is a relatively easy way to do this. You prepare a pure 50 μM solution of the protein, and you place it in a sample cell with a 1-cm path length, and you measure the absorbance of this sample at 280 nm in a UV-visible spectrophotometer. The absorbance of the solution is 0.398. How many tyrosine residues are there in this protein? (Tyr ε ≈ 1,000 M^-1 cm^-1 ).

Alright. So at first glance, this practice problem looks really, really challenging. But it's not as bad as it looks and really all it's asking is how many tyrosine residues are there in this protein? And another way to ask that same question is, what is the ratio of the number of tyrosine residues per number of protein molecules? So really, to answer this problem, we're going to need to determine what this ratio is here. So really, this is what we're going to look for to answer the problem. And so after reading through the problem, it should be pretty obvious that we're going to need to use Beer's law, because: we're using a spectrophotometer, we're given an absorbance value, a molar extinction coefficient, a concentration, a wavelength of 280 nanometers, and all of those are hints that we're going to need to use Beer's law. So notice that down below in this box, I've provided Beer's law from our previous lesson videos. And so the portion of Beer's law that has the log of the incident light over the transmitted light, we can pretty much ignore in this practice problem. And the reason for that is because we're simply not provided any information about the incident light or the transmitted light. And it's not even asking us about the incident light or transmitted light. And so what that means is we can focus on the relevant portion of Beer's Law, which is that, the absorbance, which is equal to the extinction coefficient times the concentration of the absorbent solute times the length of the light path. Now, the next thing that we're going to need to realize is that because we're measuring the absorbance of the sample at 280 nanometers, we need to recall from our previous lessons that the absorbance at 280 nanometer wavelength is an indicator of the presence of tryptophan and/or tyrosine amino acid residues. And so, that's because tryptophan and tyrosine uniquely absorb wavelengths of light at 280 nanometer wavelengths. And so, notice that up in our problem, it says that our protein has 172 amino acids, but it does not have any tryptophan. And so what that means is that since it doesn't have any tryptophan, any absorbance that's present at 280 nanometers is going to indicate the presence of tyrosine. And so this is something really important that we need to take into account, that there are no tryptophans in our residue in our protein. And so essentially, the strategy for this problem is going to be to use Beer's law to determine the concentration of Tyrosine amino acid residues. Once we determine the concentration of Tyrosine amino acid residues through using Beer's Law, then we can essentially have the top number here of our ratio. And the bottom number of our ratio, the number proteins, is essentially given to us up above here with the 50 micromolar solution of the protein. And so, we have the bottom number given to us, we all we need to do is use Beer's law to get this top number of our ratio. So we can go ahead and plug that right into our equation for the absorbance. So our absorbance is 0.398, and that is equal to our molar extinction coefficient, which is the molar extinction coefficient of Tyrosine here, which is, 1,000 with units of inverse molarity and inverse centimeters. So, we can go ahead and put that in here, 1,000 with units of inverse molarity and inverse centimeters, and that is going to be equal to the concentration here. And, of course, the concentration is given to us above as 50 micromolars. Right? So we can plug in 50 micromolars here for our concentration. Right? No, not right. So remember, this concentration that's up here, the 50 micromolar, is the concentration of tyrosine. Tyrosine. And so remember, because we're using the molar extinction coefficient of tyrosine, that means that the molar extinction coefficient of tyrosine is, going to make this c here the concentration of tyrosine, not the concentration of protein. So this is the concentration of protein, and that's not what we want to plug into our equation. Remember, this c here is representing the length of the path of light. So, the length of the path of light. So, we're told here that we have a 1 centimeter path length, so we can plug in 1 straight in here for our l. And so now, we have all of our variables filled in, we're going to solve for the missing variable here c, which is again the concentration of tyrosine. And so essentially, what we can do is use our algebra skills, and we're going to take 1,000 and multiply it by 1 centimeter. And essentially, what we end up getting is 1,000, inverse molarity times c, and then that's going to be equal to 0.398. And then we can divide, to continue to isolate for the c here, we can divide both sides of the equation by 1,000 with inverse centimeters. And so when we take 0.398 and divide it by 1,000, what we end up getting is an answer of 0.000398, and this is going to be equal to our concentration here. And the units, of course, because we have inverse molarity here, it's going to end up making these units of molarity. And so now we have the concentration here, and again, this is the concentration of tyrosine. And so, essentially, this is the top number in our number of tyrosine residues. And so when we're writing this out here, we can essentially take this number right here and plug it in up above. So what we've got is 0.000398 molar. And so, now all we need to do is take our number of proteins, this bottom number here, which again is given to us up above as 50 micromolar for the protein concentration. So we can just plug that right in, 50 micromolar. And so again, what we need to recognize is that there, the units here are not matching. So here we have units of molarity, and down below, we have units of micromolar. So what we're going to need to do is convert this number down here into units of micromolar so that they match. So what we can do is we can get rid of this number, and we can essentially take this same number here and convert it. So we have 0.000398 molar. And we know that in 1 molar, there are 1,000, I'm sorry, 10 There are 10 to the 6 micromolar. And so all we need to do is take our calculators and do 0.000398 molar and multiply it by 10 to the 6. And so when we do that, what we get is an answer of 398 micromolar. And again, this is still our concentration of Tyrosine. It's just in units of micromolar now. So now, we can take this number and plug it right up into our equation, so 398 micromolar. And so now, what we can do is, now that everything is in the same units, we can just take our calculators and do 398 divided by 50. And the answer comes out to 7.96. And so, essentially, this rounds off to about 8. And so the units of this are going to be Tyrosine residues per protein. So Tyrosine residues per protein. And this here is essentially our answer. So how many tyrosine residues are there in the protein? There are 8 tyrosine residues per protein. And so that concludes this challenging practice problem, and I'll see you guys in our next video.

Here’s what students ask on this topic:

What is Beer's Law and how is it used in spectrophotometry?

Beer's Law, also known as the Lambert-Beer Law, is a linear relationship between the absorbance (A) of a solution and the concentration (c) of the absorbing solute, the path length (l) of the light through the solution, and the molar extinction coefficient (ε). The law is mathematically expressed as:

$A=\epsilon cl$

In spectrophotometry, Beer's Law is used to determine the concentration of a solute in a solution by measuring the absorbance of light at a specific wavelength. By knowing the path length and the extinction coefficient, the concentration can be calculated from the absorbance value.

What is the extinction coefficient and why is it important in spectrophotometry?

The extinction coefficient, symbolized as ε, is a specific property of a chemical that measures how strongly it absorbs light at a particular wavelength (λ). It is crucial in spectrophotometry because it allows for the quantification of solute concentration in a solution. The extinction coefficient varies with different wavelengths, so selecting the appropriate wavelength is essential for accurate measurements. The units of the extinction coefficient are typically inverse molarity (M^-1) and inverse centimeters (cm^-1).

Why do proteins absorb light at 280 nm in spectrophotometry?

Proteins absorb light at 280 nm primarily due to the presence of the amino acids tryptophan and tyrosine. Tryptophan strongly absorbs light at this wavelength, while tyrosine absorbs it weakly. This characteristic absorption is used to quantify protein concentration because most proteins contain these amino acids. If a protein lacks tryptophan and tyrosine, alternative methods must be used for quantification.

How does the path length affect absorbance in spectrophotometry?

The path length (l) in spectrophotometry is the distance that light travels through the sample. It directly affects the absorbance (A) of the solution, as described by Beer's Law:

$A=\epsilon cl$

A longer path length increases the absorbance because the light interacts with more solute molecules, leading to more light being absorbed. Conversely, a shorter path length results in lower absorbance. Path length is typically measured in centimeters (cm).

What factors influence the absorbance of a protein sample in spectrophotometry?

Several factors influence the absorbance of a protein sample in spectrophotometry:

• Concentration (c): Higher protein concentration increases absorbance.
• Path Length (l): Longer path length increases absorbance.
• Extinction Coefficient (ε): Specific to the protein and wavelength, higher ε means higher absorbance.
• Wavelength (λ): Absorbance varies with wavelength; proteins typically absorb at 280 nm due to tryptophan and tyrosine.

These factors are incorporated into Beer's Law to quantify protein concentration accurately.