Chapter 1, Problem 1.50P

Interpretation Introduction

(a)

Interpretation:

The Lewis structure of the ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}$ anion is to be drawn, and the atom which has a non-zero formal charge is to be determined.

Concept introduction:

Lewis structure of a molecule or ion is drawn considering only the valence electrons of the atoms. In case of ions, for each negative charge an electron is added while for each positive charge an electron is subtracted on the ion. Each bond shows a shared pair of electrons. Single, double, and triple bonds are represented by one, two, and three lines, respectively, connecting the two atoms. Non-bonding electrons are shown as dots, generally as lone pairs. Atoms in a Lewis structure should not exceed their valency. The atoms from the 2^nd row must not exceed an octet of valence electrons. Atoms from the 3^rd row onward may exceed an octet by up to four electrons if they are central atoms.

The formal charge (FC) on an atom is determined as the difference between its group number and the actual number of electrons it possesses in the molecule or ion. The formula to calculate formal charge is as below.

$\text{FC = Group number - (number of unshared electrons + }\frac{1}{2}\times \text{bonding electrons)}$

Answer to Problem 1.50P

The Lewis structure of the ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}$ anion is

The atom that bears a non-zero formal charge is the carbon atom on the right, bonded to only two hydrogens.

Explanation of Solution

The total of valence electrons based on the formula ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}$ anion is $\text{2(4) + 1(5) + 1 = 14}$. Based on the rules for drawing Lewis structures, the structure of the anion is

The formal charge on each hydrogen atom is zero:

$\text{FC = 1 - (0 + }\frac{1}{2}\times \text{2) = 0}$

The formal charge on the first carbon (on the left) is zero:

$\text{FC = 4 - (0 + }\frac{1}{2}\times 8\text{) = 0}$

The formal charge on the second carbon is

$\text{FC = 4 - (2 + }\frac{1}{2}\times 6\text{) = -1}$

Therefore, it is the carbon atom on the right, bearing only two hydrogen atoms, that has a non-zero formal charge.

Conclusion

The formal charge on an atom is the difference in its group number and the actual number of electrons it possesses in the molecule or ion.

Interpretation Introduction

(b)

Interpretation:

The Lewis structure of the ${\text{CH}}_{\text{3}}\text{O}$ cation is to be drawn, and the atom which has a non-zero formal charge is to be determined.

Concept introduction:

Lewis structure of a molecule or ion is drawn considering only the valence electrons of the atoms. Each bond shows a shared pair of electrons. Single, double, and triple bonds are represented by one, two, and three lines, respectively, connecting the two atoms. Non-bonding electrons are shown as dots, generally as lone pairs. Atoms in a Lewis structure should not exceed their valency. The atoms from the 2^nd row must not exceed an octet of valence electrons. Atoms from the 3^rd row onward may exceed an octet by up to four electrons if they are central atoms.

The formal charge on an atom is determined as the difference between its group number and the actual number of electrons it possesses in the molecule or ion. The formula to calculate formal charge is as below.

$\text{FC = Group number - (number of unshared electrons + }\frac{1}{2}\times \text{bonding electrons)}$

Answer to Problem 1.50P

The Lewis structure of the ${\text{CH}}_{\text{3}}\text{O}$ cation is

The carbon atom is the one that has a non-zero formal charge.

Explanation of Solution

Carbon is the central atom in this cation, with two hydrogen atoms and the oxygen atom bonded to it. The third hydrogen atom is bonded to the oxygen as shown below:

The formal charges on the atoms are calculated as below:

Hydrogen atoms:

$\text{FC = 1 - (0 + }\frac{1}{2}\times \text{2) = 0}$

Carbon atom:

$\text{FC = 4 - (0 + }\frac{1}{2}\times 6\text{) = +1}$

Oxygen atom:

$\text{FC = 6 - (4 + }\frac{1}{2}\times 4\text{) = 0}$

An alternate structure can be drawn with all three hydrogen atoms and the oxygen atom bonded to the central carbon. However, this will put the positive charge on a highly electronegative oxygen, making it unstable. Therefore, the above mentioned structure is the most likely structure.

Therefore, the carbon atom has a non-zero formal charge.

Conclusion

The formal charge on an atom is the difference in its group number and the actual number of electrons it possesses in the molecule or ion.

Interpretation Introduction

(c)

Interpretation:

The Lewis structure of the ${\text{CH}}_6\text{N}$ cation is to be drawn, and the atom which has a non-zero formal charge is to be determined.

Concept introduction:

Lewis structure of a molecule or ion is drawn considering only the valence electrons of the atoms. Each bond shows a shared pair of electrons. Single, double, and triple bonds are represented by one, two, and three lines, respectively, connecting the two atoms. Non-bonding electrons are shown as dots, generally as lone pairs. Atoms in a Lewis structure should not exceed their valency. The atoms from the 2^nd row must not exceed an octet of valence electrons. Atoms from the 3^rd row onward may exceed an octet by up to four electrons if they are central atoms.

The formal charge on an atom is determined as the difference between its group number and the actual number of electrons it possesses in the molecule or ion. The formula to calculate formal charge is as below.

$\text{FC = Group number - (number of unshared electrons + }\frac{1}{2}\times \text{bonding electrons)}$

Answer to Problem 1.50P

The Lewis structure of the ${\text{CH}}_6\text{N}$ cation is

The atom with a non-zero formal charge is the nitrogen.

Explanation of Solution

Carbon usually forms four bonds; therefore, it is a central atom. Three of the hydrogen atoms and the nitrogen atom must be bonded to it. The nitrogen atom in turn is also a central atom, with the remaining three hydrogen atoms bonded to it. Normally nitrogen forms only three bonds, but it can use its lone pair to form another bond, generally to a hydrogen ion. Therefore, the Lewis structure of the cation must be

The formal charges on the atoms are calculated as follows:

Hydrogen atoms:

$\text{FC = 1 - (0 + }\frac{1}{2}\times \text{2) = 0}$

Carbon atom:

$\text{FC = 4 - (0 + }\frac{1}{2}\times 8\text{) = 0}$

Nitrogen atom:

$\text{FC = 5 - (0 + }\frac{1}{2}\times 8\text{) = +1}$

Therefore, it is the nitrogen atom that has a non-zero formal charge.

Conclusion

The formal charge on an atom is the difference in its group number and the actual number of electrons it possesses in the molecule or ion.

Interpretation Introduction

(d)

Interpretation:

The Lewis structure of the ${\text{CH}}_5\text{O}$ cation is to be drawn, and the atom which has a non-zero formal charge is to be determined.

Concept introduction:

Lewis structure of a molecule or ion is drawn considering only the valence electrons of the atoms. Each bond shows a shared pair of electrons. Single, double, and triple bonds are represented by one, two, and three lines, respectively, connecting the two atoms. Non-bonding electrons are shown as dots, generally as lone pairs. Atoms in a Lewis structure should not exceed their valency. The atoms from the 2^nd row must not exceed an octet of valence electrons. Atoms from the 3^rd row onward may exceed an octet by up to four electrons if they are central atoms.

The formal charge on an atom is determined as the difference between its group number and the actual number of electrons it possesses in the molecule or ion. The formula to calculate formal charge is as below.

$\text{FC = Group number - (number of unshared electrons + }\frac{1}{2}\times \text{bonding electrons)}$

Answer to Problem 1.50P

The Lewis structure of ${\text{CH}}_5\text{O}$ cation is

The atom with non-zero formal charge is the oxygen atom.

Explanation of Solution

The ${\text{CH}}_5\text{O}$ cation can be considered as a protonated methanol molecule. Carbon can form four bonds. Therefore, it is bonded to three hydrogen atoms and the oxygen atom. Oxygen usually forms only two bonds, but it can utilize one of its lone pairs to form another bond to a hydrogen ion. Therefore, the oxygen atom must also be bonded to two hydrogen atoms:

The formal charges on the atoms are calculated as follows:

Hydrogen atoms:

$\text{FC = 1 - (0 + }\frac{1}{2}\times \text{2) = 0}$

Carbon atom:

$\text{FC = 4 - (0 + }\frac{1}{2}\times 8\text{) = 0}$

Oxygen atom:

$\text{FC = 6 - (2 + }\frac{1}{2}\times 6\text{) = +1}$

Therefore, the oxygen has a non-zero formal charge.

Conclusion

The formal charge on an atom is the difference in its group number and the actual number of electrons it possesses in the molecule or ion.

Interpretation Introduction

(e)

Interpretation:

The Lewis structure of the ${\text{C}}_3{\text{H}}_3$ anion with all three hydrogen atoms on the same carbon is to be drawn, and the atom which has a non-zero formal charge is to be determined.

Concept introduction:

Lewis structure of a molecule or ion is drawn considering only the valence electrons of the atoms. Each bond shows a shared pair of electrons. Single, double, and triple bonds are represented by one, two, and three lines, respectively, connecting the two atoms. Non-bonding electrons are shown as dots, generally as lone pairs. Atoms in a Lewis structure should not exceed their valency. The atoms from the 2^nd row must not exceed an octet of valence electrons. Atoms from the 3^rd row onward may exceed an octet by up to four electrons if they are central atoms.

The formal charge on an atom is determined as the difference between its group number and the actual number of electrons it possesses in the molecule or ion. The formula to calculate formal charge is as below.

$\text{FC = Group number - (number of unshared electrons + }\frac{1}{2}\times \text{bonding electrons)}$

Answer to Problem 1.50P

The Lewis structure of the ${\text{C}}_3{\text{H}}_3$ anion with all three H atoms on the same carbon is

The carbon atom at the right end of the chain has a non-zero formal charge.

Explanation of Solution

The total of the valence electrons for this anion is $\text{3(4) + 3(1) + 1 = 16}$.

The carbon atoms have capacity to form up to four bonds. If all three hydrogen atoms are on the same carbon, this carbon must be at the end of a chain of three carbon atoms. The other two carbon atoms must be triply bonded to each other in order to complete their octets. The carbon atom at the other end of the chain must have a lone pair so that all the valence electrons are accounted for.

The Lewis structure of the ${\text{C}}_3{\text{H}}_3$ anion with all three hydrogen atoms on the same carbon is

The formal charges on the atoms are calculated as follows:

Hydrogen atoms:

$\text{FC = 1 - (0 + }\frac{1}{2}\times \text{2) = 0}$

Carbon atom on the left and in the center of the chain:

$\text{FC = 4 - (0 + }\frac{1}{2}\times 8\text{) = 0}$

Carbon atom at the right end of the chain:

$\text{FC = 4 - (2 + }\frac{1}{2}\times 6\text{) = -1}$

Therefore, it is the carbon atom at the right end of the chain that has a non-zero formal charge.

Conclusion

The formal charge on an atom is the difference in its group number and the actual number of electrons it possesses in the molecule or ion.