Problem 4 - Introductory Chemistry Atoms First

Question

In chloroform, \(\mathrm{CHCl}_{3}\) (a) Assign an oxidation state to each atom in the molecule. (Hint: Draw a dot diagram first.) (b) How many electrons does the \(\mathrm{C}\) atom own by oxidation-state electron bookkeeping? (c) How many more or fewer valence electrons are assigned to the \(\mathrm{C}\) atom here than are present in a free \(C\) atom? (d) Is it correct or incorrect to say that the \(\mathrm{C}\) atom in \(\mathrm{CHCl}_{3}\) has a complete octet of valence electrons? Explain.

Step-by-Step Solution

Answer

(a) In CHCl3, the oxidation state of H is +1, C is +2, and each Cl is -1. (b) The Carbon atom in CHCl3 owns 2 electrons by oxidation-state electron bookkeeping. (c) The Carbon atom in CHCl3 has 2 fewer valence electrons than in its free state. (d) The Carbon atom in CHCl3 does not have a complete octet of valence electrons, as it only has 6 electrons in its outer shell.

Step 1: (a) Determine the oxidation state of each atom in CHCl3

For each atom, we'll first draw a dot diagram based on its bonds to other atoms and then use these diagrams to deduce the oxidation states. Remember that Hydrogen has 1 valence electron, Carbon has 4 valence electrons, and Chlorine has 7 valence electrons. In CHCl3, Carbon is bonded to 1 Hydrogen and 3 Chlorine atoms. To determine the oxidation states, we'll assign electrons according to their electronegativity followed by the rules of calculating the oxidation state for each atom. - Hydrogen has an oxidation state of +1. - Carbon is less electronegative than Chlorine, so Chlorine will have a negative oxidation state. Since there are 3 Chlorine atoms, they will each have an oxidation state of -1. - Sum of oxidation states in a molecule should equal to 0, so in this case: \(x + 1 - 1 - 1 - 1 = 0\) Solving for x, we get x = 2. So, Carbon has an oxidation state of +2.

Step 2: (b) Calculate the number of owned electrons by the carbon atom (by oxidation-state electron bookkeeping)

To calculate the number of owned electrons by the Carbon atom using oxidation-state bookkeeping, we'll subtract the number of valence electrons in the free atom from the oxidation state we determined (Carbon has 4 valence electrons in a free atom). Owned electrons = Valence electrons in a free atom - Oxidation state Owned electrons = 4 - 2 Owned electrons = 2 The Carbon atom owns 2 electrons by oxidation-state electron bookkeeping.

Step 3: (c) Determine the difference in valence electrons between the carbon atom in CHCl3 and a free carbon atom

We have already determined the owned electrons by the Carbon atom in CHCl3 (which is 2). A free Carbon atom has 4 valence electrons. Now, we will determine the difference between these two values. Difference in valence electrons = Valence electrons in CHCl3 - Valence electrons in a free Carbon atom Difference in valence electrons = 2 - 4 Difference in valence electrons = -2 So, in CHCl3, the Carbon atom has 2 fewer valence electrons than it does in its free state.

Step 4: (d) Determining if the carbon atom in CHCl3 has a complete octet of valence electrons and providing an explanation

In CHCl3, Carbon is bonded to 1 Hydrogen and 3 Chlorine atoms. According to the octet rule, an atom is considered to have a complete octet when it is surrounded by 8 electrons in its outer shell. In chloroform, the Carbon atom is sharing 1 electron from Hydrogen and 3 electrons from the Chlorine atoms, which is a total of 4 shared electrons. Additionally, the Carbon atom already has 2 own valence electrons, as we previously calculated. Total owned and shared electrons by Carbon in CHCl3 = Shared electrons + Owned electrons Total owned and shared electrons = 4 (shared) + 2 (owned) So, the Carbon atom in CHCl3 has a total of 6 electrons in its outer shell (not 8), which means that it does not have a complete octet of valence electrons.

Key Concepts

Electron Bookkeeping

Electron bookkeeping is a useful method for analyzing the electron distribution within a molecule. In the context of oxidation states, it helps us understand how electrons are assigned to each atom in a compound. This approach involves calculating the total number of electrons that an atom "owns" compared to its neutral state.

In oxidation-state electron bookkeeping, we follow a few simple rules:

• Electrons in a bond are assigned to the more electronegative atom.
• If two atoms have similar electronegativity, electrons are split equally.
• The electron count is adjusted based on the oxidation state of the molecule.

For chloroform (\(\mathrm{CHCl}_{3}\)), the carbon atom is calculated to own 2 electrons after accounting for the bonds with hydrogen and chlorine. Even though carbon naturally has 4 valence electrons, in this molecule, it effectively manages with 2 due to its interactions with more electronegative chlorine atoms.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial as they participate in chemical bonding. Generally, the chemical properties of an element are chiefly determined by the number of valence electrons, making them essential in the formation of molecules.

Consider carbon in chloroform (\(\mathrm{CHCl}_{3}\)):

• Carbon normally has 4 valence electrons.
• But in \(\mathrm{CHCl}_{3}\), it instead "owns" fewer due to sharing electrons in bonds.
• The calculation showed carbon with 2 electrons, thus depicting it has 2 fewer valence electrons than a free carbon atom.

This difference arises as valence electrons are shared with neighboring atoms, adjusting the electron count of each atom in the compound.

Octet Rule

The Octet Rule is a straightforward guideline stating that atoms strive to surround themselves with 8 electrons in their outer shell, achieving a stable electron arrangement similar to noble gases. It's a key rule for understanding chemical bonding and molecule stability, yet there are exceptions.

In chloroform (\(\mathrm{CHCl}_{3}\)), carbon is involved in four bonds: one with hydrogen and three with chlorine. The electrons shared with these atoms can be counted towards the octet:

• Carbon shares 1 electron from hydrogen.
• It shares 3 additional electrons with chlorine atoms.

When these shared electrons are combined with the 2 valence electrons that carbon already manages in its electron bookkeeping, it only has a total of 6 electrons.

Thus, carbon in chloroform does not have a full octet, highlighting how the octet rule sometimes encounters exceptions in real chemical scenarios.