Question

use the references to access important values if needed for this question.
the bond lengths of the cl-x bonds in clf, clbr, and cli are 1.63, 2.14, and 2.32 å, respectively. estimate the length of the cl-cl bond in cl₂.
cl-cl bond length =
å
which of these four halides has the weakest cl-x bond?
(express your answer as a chemical formula.)

Explanation:

Part 1: Estimate Cl-Cl bond length

Step1: Recall covalent radius concept

The covalent bond length between two atoms (A - B) is approximately the sum of their covalent radii (\(r_A + r_B\)). For a homonuclear diatomic molecule like \(Cl_2\) (Cl - Cl), the bond length is twice the covalent radius of Cl (\(2r_{Cl}\)). We can also use the trend in Cl - X bond lengths (X = F, Br, I) to estimate \(r_{Cl}\), but a known value or standard method: the covalent radius of Cl is about 0.99 Å, so Cl - Cl bond length is \(2\times0.99 = 1.98\) Å (or using the fact that in Cl₂, the experimental bond length is approximately 1.99 Å, and from the Cl - X bonds, we can think about the radius of Cl. Alternatively, the Cl - Cl bond length can be estimated by knowing that the covalent radius of Cl is ~1.0 Å, so 2*1.0 = 2.0 Å, but more accurately, from standard data, Cl - Cl bond length is approximately 1.99 Å (or 2.0 Å as a close estimate). Wait, actually, the covalent radius of Cl is 0.99 Å, so Cl - Cl bond length is \(2\times0.99 = 1.98\) Å, which is approximately 2.0 Å (or more precisely, experimental value is ~1.98 Å). Let's confirm: the covalent radius of Cl is \(r_{Cl}\), so \(Cl - Cl\) bond length \(= 2r_{Cl}\). From Cl - F (1.63 Å): \(r_{Cl}+r_F = 1.63\), \(r_F = 0.72\) Å (covalent radius of F), so \(r_{Cl}=1.63 - 0.72 = 0.91\) Å? Wait, no, maybe better to use the fact that in Cl₂, the bond length is known to be approximately 1.99 Å (or 2.0 Å for estimation). Wait, maybe the problem expects using the idea that the Cl - Cl bond length is twice the covalent radius of Cl, and from the Cl - X bonds, we can find \(r_{Cl}\). Let's take Cl - F: 1.63 Å, Cl - Br: 2.14 Å, Cl - I: 2.32 Å. The covalent radius of F is ~0.72 Å, so \(r_{Cl}=1.63 - 0.72 = 0.91\) Å. Then Cl - Cl bond length is \(2\times0.91 = 1.82\) Å? Wait, no, maybe I messed up. Wait, the covalent radius of Cl is actually ~0.99 Å, so Cl - Cl is ~1.98 Å. Let's check standard values: the bond length of Cl₂ is approximately 1.98 Å. So we can say the Cl - Cl bond length is approximately 2.0 Å (or 1.98 Å).

Step2: Calculate or recall

Using the covalent radius of Cl (\(r_{Cl} \approx 0.99\) Å), so \(Cl - Cl\) bond length \(= 2\times r_{Cl} = 2\times0.99 = 1.98\) Å (or ~2.0 Å).

The strength of a bond is inversely related to its length (longer bonds are weaker, as the atoms are farther apart, so the attraction between nuclei and shared electrons is less). Among Cl - F (1.63 Å), Cl - Br (2.14 Å), Cl - I (2.32 Å), and Cl - Cl (1.98 Å), the longest Cl - X bond is Cl - I (2.32 Å), so the weakest Cl - X bond is in ClI (chemical formula \(ClI\)).

Answer:

(for Cl - Cl bond length):
\boxed{1.99} (or 2.0, but more accurately 1.98 - 2.0 Å; the experimental value is ~1.98 Å, so we can put 1.99 or 2.0)

Part 2: Weakest Cl - X bond