In molecular bonding theory, which of the following statements about bond order, bond length and stability is false?

Introduction / Context:
Bond order is a useful concept in chemical bonding that gives a rough idea of the number of bonding electron pairs between two atoms. It is related to bond length, bond strength and molecular stability. Understanding these relationships is important in predicting molecular properties and comparing different chemical bonds. This question asks you to identify the false statement among several that describe how bond order connects with bond strength, bond length and stability.

Given Data / Assumptions:

• Bond order is defined as the number of chemical bonds between a pair of atoms, for example single, double or triple bonds.
• Bonds with higher bond order are generally shorter and stronger.
• Negative bond order values obtained from some calculations indicate that a molecule is not stable.
• We assume standard textbook relationships between bond order, bond length and bond energy.

Concept / Approach:
In simple terms, when bond order increases from a single bond to a double bond to a triple bond, the bond becomes stronger and the bond length decreases. This means bond order is directly related to bond strength but inversely related to bond length. If molecular orbital calculations give a negative bond order, it usually means that antibonding interactions dominate and the molecule is not stable. Therefore, any statement that claims bond order is directly proportional to bond length contradicts the usual understanding and is false.

Step-by-Step Solution:
Step 1: Recall that a single bond has bond order 1, a double bond has bond order 2 and a triple bond has bond order 3. Step 2: Note that triple bonds are generally stronger and shorter than double bonds, which in turn are stronger and shorter than single bonds. Step 3: Conclude that as bond order increases, bond strength increases and bond length decreases. Step 4: Examine each statement and compare it with this relationship between bond order, bond length and bond strength. Step 5: Identify the statement that claims bond order is proportional to bond length as false, since the relationship is actually inverse.

Verification / Alternative check:
You can verify by checking examples such as carbon carbon single, double and triple bonds. Typical bond lengths decrease from the single bond to the triple bond, while bond energies increase. This pattern matches the idea that bond order is inversely related to bond length. None of the standard examples or tables support a direct proportional relationship between bond order and bond length. Therefore, the statement that bond order is proportional to bond length is clearly incorrect.

Why Other Options Are Wrong:
The statement that bond strength increases with bond order is true and supported by many examples of double and triple bonds.
The claim that molecules with negative bond order are highly unstable or do not exist reflects the usual interpretation of molecular orbital calculations.
The statement that bond order is inversely proportional to bond length correctly summarises the trend that higher bond order corresponds to shorter bonds.
Higher bond order generally means higher bond energy and therefore stronger bonds, so that statement is also correct.

Common Pitfalls:
A common mistake is to mix up direct and inverse proportionality when comparing bond order and bond length. Students may also forget that trends are general and may have small exceptions, but for basic questions it is safe to rely on the standard rule that higher bond order produces shorter, stronger bonds. Carefully reading each statement and matching it with known examples helps avoid confusion.

Final Answer:
The false statement is that bond order is proportional to the bond length.