The following observations are made about two hypothetical elements A and B: The A¬A and B¬B bond lengths in the elemental forms of A and B are 236 and 194 pm, respectively. A and B react to form the binary compound AB2, which has a linear structure (that is B-A-B = 180°). Based on these statements, predict the separation between the two B nuclei in a molecule of AB2.

Video transcript

hey everyone in this example, we have the molecule, Y Z two. It's a hypothetical molecule with a Leonard geometry of 1 80 degrees. And we need to calculate the distance between two Z atoms in the molecule. If the bond length of a Y Y bond is 189 nanometers and the bond length of a Zz bond is 175 nanometers. So let's go ahead and write out how this reaction to form our hypothetical molecule would appear as. What we should have is we would have a Y. Y molecule reacting with a Z. Z molecule and this is going to produce a Y. Z molecule, but we should recognize that we're given Y Z two, meaning we have two Z atoms. So we're going to place a coefficient of two in front of our Y Z. Here, meaning to balance this equation out, we would have to place a coefficient of two in front of our yy bonds as well as a two in front of our Zz bonds. Now, according to the prompt, the bond length of a Y Y bond is 189 nanometers. So we'll just represent that in red below here and we should recognize that if we break this bond length in half, this is going to allow us to divide this bond length value by two to give us our atomic radius of a Y adam we can do the same thing for ours. Easy bond were given in the prompt, the bond length of 175 nanometers for the Zz bond. And if we break this bond length and two, we would divide this value by two. To give us our atomic radius of a Zz bond. Or rather of adam. So when we go ahead and divide our bond length of the Y Y bond divided by two, we would have 11 89 divided by two. And this is going to equal a value equal to 94. nanometers as the atomic radius of a Y atom. So, following the same steps for the atomic radius of a Z atom, we would divide the bond length of Azizi bond by two. So we have 1 75 divided by two. And this equals a value of 87.5 as the atomic radius for Az atom. So based on the question, we need to give the distance between hours. Easy bonds here. Or sorry, ours. Easy atoms in our molecule. And because we know our individual atomic radius values for a Y. Adam and a Z. Adam, that means we can therefore say that 87.5 nanometers plus 94.5 nanometers for our Why adam adding these two atomic radius is up for Y. And Z would give us our Bond length of AYZ bond. Which is going to equal a value of 182 nanometers. And again this is for a Y Z bond. And as you can see in our given molecule we have two YZ bonds. We have one here and then we have another here. And so this means because we know the bond length of a Y. Z bond. We can go ahead and recognize that we would multiply this by two, not only because of our equation here, but because we recognize that we have two of these bonds. So we would have two times 182 nanometers, which is our bond length of one Y Z bond. And this is going to equal a value of 364 nanometers. Which is going to give us our distance between our Z. Z atoms in the molecule. Our first C atom here to our second Z atom here have a distance between each other of 364 nanometers. So we can actually rewrite this and just say that this is our atomic distance between our Z atoms in our Z Y Z molecule. And so this is actually our final answer here. To complete this example. If you have any questions, please leave them down below. Otherwise, I will see everyone in the next practice video