# Estimating BDE Values

I'm having trouble understanding how to "estimate" the value of the BDE for the compound shown below (I believe it is a secondary benzylic C-Br value) shown below (the 58 kcal/mol). We are supposed to be able to estimate the value from the table values shown below. My teacher said to use the C-H values and C-Br values from the table below to estimate it, but I don't understand how they are able to indicate the value. Any helpful drawings would be nice since I'm new to organic chemistry and have trouble just understanding the names! Thank you.   • Welcome to ChemSE. We would like to see how you arrived at your values. We like to help but loath doing homework. – user55119 Feb 14 at 22:47
• @user55119 Thanks! Sorry if I wasn't clear, but the red is what I am trying to understand - the values are not mine; it is what the teacher said. Specifically, I am confused about how they got the 58 kcal/mol estimation. – Brian Feb 15 at 4:04
• Adding a reference for the source of that table might help. Also, ask your teacher if possible, it does look off. – Buck Thorn Feb 15 at 7:11
• @BuckThorn All the information I have is that it comes from Pearson Education : / . My teacher wants us to use this table to calculate our BDE values. She said the estimate can have a range of 55-60 – Brian Feb 15 at 17:37

## 1 Answer

What you have shown in red is the second propagation step in the benzylic free radical bromination of ethylbenzene. The bond dissociation energy (BDE) of bromine is +46 kcal/mol while the overall heat of reaction of the step is -12 kcal/mol. Thus, the formation of the C-Br bond must be -58 kcal/mol. The BDE for the C-Br bond in (1-bromoethyl)benzene is +58 kcal/mol.

However, the BDE for bromine is not listed in your tables. So how can one estimate the BDE of the C-Br bond in (1-bromoethyl)benzene using the data in the tables? A simple ratio and proportion will suffice. In equation A compare the primary C-H bond of ethane to that of toluene. This ratio is compared to the ratio of the BDE of the secondary C-H bond of propane and its counterpart in ethylbenzene, which is the unknown "x". An estimated value of 82 kcal/mol is obtained. In equation B, this ratio compares secondary C-H bonds with secondary C-Br bonds. The estimate for the BDE of the C-Br bond in (1-bromoethyl)benzene is the value of "y" which is equal to 59 kcal/mol. Pretty close, wouldn't you say? • thank you so much for the response! this technique definitely works. Just a clarifying question, how did you know how to make the fractions? For instance, why did you choose to put CH3CH2H on top of PhCh2H? – Brian Feb 15 at 20:10
• Doesn't matter as long as the two ratios are in the same order. 2:4::1:x. So, x=2. But for 4:2::x:1, the answer is still 2. – user55119 Feb 15 at 22:56