Calculating Radical Yields: Videos & Practice Problems

In radical halogenation, the stability of radicals influences product distribution, with tertiary radicals being the most stable. Chlorination is non-selective, favoring tertiary carbons only slightly more than primaries, while bromination is highly selective, favoring tertiary carbons 1600 times more than primaries. The selectivity decreases with increased temperature. Understanding these rates is crucial for predicting major and minor products in reactions. The relative rates of halogenation at room temperature are essential for calculations, and variations in values may occur across different sources.

Explaining relative rates of halogenation.

All right, guys. So in these videos, I'm going to be going through a much more rigorous explanation of how to calculate the major product for radical halogenation reaction. Now the reason that I'm even recording these videos is because your textbook goes through this more in-depth explanation and I want to make sure that we have all our bases covered. Now understand that this might be beyond the scope of what many professors require for their students, so I'm going to leave it up to you to check with your professor to see if they want you to calculate these ratios or not. So let's just move right into the lesson.

Everyone knows by now the general trend of radical stability which is that tertiary radicals are more stable than secondaries and secondaries are more stable than primaries. And that's been enough for us so far. We've been able to get by and just predict the major product that way. But if we want to calculate the exact percentages of major and minor products, we're going to need equations. We're going to need some kind of method, quantitative method to do that. And It turns out that we can calculate that knowing the relative rate of halogenation at a certain temperature.

Here you see this is a very important little table here. These are the relative rates of different types of halogenations at 25 degrees Celsius or room temperature. Let's just go through these numbers really quick so you understand what it's meaning. So remember how we discussed how chlorination is very unselective, kind of makes bad decisions everywhere and bromination makes these awesome decisions? Well, this can be quantified and the difference has to do with these halogenation rates. Notice that chlorination actually does prefer tertiaries. It has good intentions. The problem is that it doesn't prefer tertiaries very much, only slightly. It likes to halogenate tertiaries about 5 times more than primaries and only a little bit more than secondaries. So you can see how chlorination you're going to get a lot of products everywhere.

Now if you look at bromination, bromination is much more selective because bromination likes to brominate tertiary carbons 1600 times more than pprimary. So you can imagine that that's why we call bromination highly selective versus chlorination which we basically call non-selective. It has to do with the fact that the difference between the relative rates is much bigger when you get to bromination. Here we can go back to our definitions and we can state that chlorination is non-selective because the difference between the relative rates is very small. Whereas bromination is highly selective because the difference between the relative rates is very large.

Now these ratios that I'm giving you here are only valid at one temperature and that's room temperature because that's the temperature that these experiments were conducted under. If we increase the temperature for this reaction, the ratios between the different types of selectivity become, can you guess? Smaller. Meaning that there's less difference between primary, secondary, tertiary. Why? The more heat you add to any reaction, the more ambient energy there's going to be. So the less selective it's going to be. It's going to wind up even bromination can be coarse since it's some bad decisions at a high enough temperature. Okay. Awesome. It's getting hot in here.

Alright, so that's basically the concept behind this table. Now one note of caution for you guys. You might be flipping through a textbook and you might see slightly different values here like you might see it says 1 and then 4.25, 5. I don't really care about the details. The reason I chose these numbers is because these are the safest roundest numbers that I could find from a combination of sources. I looked online. I looked through a few different textbooks and these numbers just seem to make the most sense. There's no point in teaching you with complicated numbers. But in general, the ranges are correct. It's about 1, 45, and then about 180, 1600. If your professor teaches you different values, by all means, do not argue with him. Just go with his values. Everything that I am saying is still going to pertain to that even if you have to use different values.

Draw all of the monochlorination products and calculate percentage yields.

All right, guys. So let's go through this question. It says draw all of the monochlorination products of butane and calculate the percentage yields of each product. So first of all, I just want to show you this table that I made. This table is going to make it very easy to calculate stuff just by filling in blank spaces. But the point isn't that you should have this at your exam. The point is that you should learn through this and then be able to do it on your own. So we'll take this one as a worked example. First of all, butane looks like that bolded molecule there. And the first thing you have to do is you have to calculate or count up the different types of protons that you have because remember that every type of proton has a different relative rate. So as we can see, I split it up into primary protons and secondary protons. And what we can see is that after counting them up, you actually have 6 primary H's and you have 4 secondary H's. Does that make sense so far? Pretty easy. Now, I noticed that there's no slot for tertiary. Guys, because there's no tertiaries here. But if I did have tertiaries, I'd have to add another row. Makes sense, right? Awesome. So now we're going to plug in the relative rate. Where do I get that number? From my table. From my table. So yeah, so relative rate of primary chlorination, see it says monochlorination. That's where this becomes important. So I'm going to look at the numbers and it's 14. So I'm going to put that in here. 1 and 4. Wait. No, that's right. That's right. Perfect. Awesome. Okay. So I have 6 at a rate of 1, 4 at a rate of 4. Now what I do is I multiply these numbers together. So what I'm going to get is I'm going to get 6 here. So 6 times 1 equals 6. That's the relative reaction. And then 4 times 4 is 16. 16. So that means that literally I'm getting this that ratio. You see 6 over 16? That's going to be the final answer. But I need to put this in a percentage yield way. The way we do that is we add up these two numbers. That means that the sum of these two numbers is 22 and that's going to be the number that I put in my denominator. I'm going to put 22 as the bottom of my fraction for each one. Then for the top, I'm just going to put the actual relative amount. That means that 6 out of 22 went to the primary, so the fraction yield was 622 and the fraction yield of my secondaries was 1622. Now these ratios came up a little bit too difficult to calculate in our heads, so let's use a calculator. You could also use this is pretty simple math. So you could use your iPhone if you wanted to. I'm an iPhone guys. 6 divided by 22 gives me 27.2% or 0.3. Let me round. And then 16 divided by 22 gives me 72.7%. That looks good. All right, so now I draw my products out and what you can see is that for my primary product with where I get a chlorine here, I'm going to get 27.3% of that one. And then for my secondary where I put my chlorine here, I'm going to get 72.7% of that. Now notice that chlorination in this case actually was fairly selective. 72% went for the better option. But still when you talk in chemistry terms, this is not good enough. And this difference what's as a waste. That would be considered a low yield reaction. So even though it does seem kind of selective, it's actually not as selective as we need it to be to make this reaction worthwhile. Got it? Awesome. Hopefully, this little layout that I made helps it to make sense. Eventually, I want you guys to be able to do this without a layout. Just know what the next steps are. But for right now, let's go ahead and do some practice problems where in the first one, I'll help you along and then in the second one, I'll take the training wheels off. Let's go ahead and work on the first problem.

What is the percentage yield of the major product?

• A. 64.43%
• B. 99.44%
• C. 99.93%
• D. 76.25%

Answer: (B)

What is the percentage yield of the major product?

• A. 68.2%
• B. 95.2%
• C. 90.8%
• D. 76.9%

Answer: (D)

Here’s what students ask on this topic:

What is the difference between chlorination and bromination in radical halogenation?

Chlorination and bromination differ significantly in their selectivity during radical halogenation. Chlorination is non-selective, favoring tertiary carbons only about 5 times more than primary carbons. This results in a mixture of products. Bromination, on the other hand, is highly selective, favoring tertiary carbons 1600 times more than primary carbons, leading to a more specific product distribution. The selectivity of both processes decreases with increasing temperature.

How do you calculate the major product in radical halogenation reactions?

To calculate the major product in radical halogenation, you need to know the relative rates of halogenation for different types of carbons (primary, secondary, tertiary) at a given temperature. Multiply the number of each type of hydrogen by its relative rate to get the total reactivity for each type. The major product is the one formed from the most reactive hydrogen. For example, in bromination, tertiary hydrogens are much more reactive than primary or secondary hydrogens.

Why is bromination considered more selective than chlorination?

Bromination is considered more selective than chlorination because the relative rate of bromination for tertiary carbons is 1600 times higher than for primary carbons. In contrast, chlorination favors tertiary carbons only about 5 times more than primary carbons. This large difference in selectivity for bromination results in a more specific product distribution, whereas chlorination produces a mixture of products.

How does temperature affect the selectivity of radical halogenation reactions?

Temperature affects the selectivity of radical halogenation reactions by decreasing the difference in reactivity between different types of carbons. At higher temperatures, the added ambient energy makes the reaction less selective, meaning that even bromination, which is usually highly selective, can produce a wider range of products. Conversely, at lower temperatures, the selectivity is higher, leading to more specific product distributions.

What are the relative rates of halogenation for primary, secondary, and tertiary carbons at room temperature?

At room temperature (25°C), the relative rates of halogenation for primary, secondary, and tertiary carbons differ for chlorination and bromination. For chlorination, the rates are approximately 1:4:5 for primary, secondary, and tertiary carbons, respectively. For bromination, the rates are approximately 1:80:1600 for primary, secondary, and tertiary carbons, respectively. These rates are crucial for predicting the major and minor products in radical halogenation reactions.