Chapter 20, Problem 20.143MP

a)

Interpretation Introduction

Interpretation:

The half-life of the reaction has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of ${}^{12}\text{C}$ and ${}^{14}\text{C}$ that takes in. when the living organism dies, the intake of ${}^{14}\text{C}$ stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{where,}\text{k}\text{is rate constant}\text{.}\\ \left(\text{or}\right)\\ {\text{ln[N]}}_{\text{t}}{\text{- ln[N]}}_0\text{= -kt}\end{array}$

b)

Interpretation Introduction

Interpretation:

The molarity of the reaction after $1\text{6}\text{.5}\text{hour}$ has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of ${}^{12}\text{C}$ and ${}^{14}\text{C}$ that takes in. when the living organism dies, the intake of ${}^{14}\text{C}$ stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{where,}\text{k}\text{is rate constant}\text{.}\\ \left(\text{or}\right)\\ {\text{ln[N]}}_{\text{t}}{\text{- ln[N]}}_0\text{= -kt}\end{array}$

c)

Interpretation Introduction

Interpretation:

The possible reaction mechanism with a unimolecular rate-determining step has to be devised.

Concept Introduction:

Molecularity: Depending on how many molecules come together to react, a reaction can be said as unimolecular, bimolecular or trimolecular. The kinetic order of any elementary reaction is equal to its molecularity.

Rate determining step: The overall rate of a reaction is determined by the rate of the slowest step, called the rate-determining step.

d)

Interpretation Introduction

Interpretation:

The reaction product is either chiral or achiral has to be explained.

Concept Introduction:

Achiral: A molecule is achiral if it is superimposable on its mirror image. Most achiral molecules do have a plane of symmetry or a center of symmetry.

Chiral: A molecule is chiral if it is not superimposable on its mirror image. Most chiral molecules can be identified by their lack of a plane of symmetry.

e)

Interpretation Introduction

Interpretation:

The crystal field energy level diagrams for ${\left[\text{Co}{\left(\text{en}\right)}_{\text{2}}{\text{Cl}}_{\text{2}}\right]}^{\text{+}}$ has to be drawn, the electron to orbitals has to be assigned, and number of unpaired electrons has to be predicted.

Concept Introduction:

Coordination compounds: The compounds having coordination covalent bonds which form when metal ions react with polar molecules or anions.

Ligands: The ions or molecules that forms coordination covalent bond with metal ions in a coordination compound. Ligands should have minimum one lone pair of electron, where it donates two electrons to the metal. Metal atom accepts the electron pair from a ligand forming a coordination bond.

$Monodentate$ Ligand is ligand which donates only one pair of electrons to form bond with metal. It only makes one bond with metal. Polydentate ligand forms two or more coordination bond with metal ions to form a complex.

The strong-field ligands results in pairing of electrons present in the complex and leads to diamagnetic species , while the low-field ligand do not have tendency to pair up the electrons therefore forms paramagnetic species.

Ligand field theory: It is used to explain the bonding between metal and ligand in a coordination complex. Ligand field theory is explained in terms of electrostatic interaction of between metal ion and ligands.

$Spectrochemical$ Series: The list of ligands arranged in an ascending order of $\text{(Δ)}$(the splitting of d-orbitals in presence of various ligands).

$\begin{array}{l}\stackrel{{}^{{\text{I}}^{\text{-}}\text{<}{\text{Br}}^{\text{-}}\text{<}{\text{SCN}}^{\text{-}}\text{<}{\text{Cl}}^{\text{-}}\text{<}{\text{S}}^{\text{2-}}\text{<}{\text{F}}^{\text{-}}\text{<}{\text{OH}}^{\text{-}}\text{<}{\text{O}}^{\text{2-}}\text{<}{\text{H}}_{\text{2}}\text{O}\text{<}{\text{NCS}}^{\text{-}}\text{<}{\text{edta}}^{\text{4-}}\text{<}{\text{NH}}_{\text{3}}\text{< en}\text{<}{\text{NO}}^{\text{2-}}\text{<}{\text{CN}}^{\text{-}}\text{<}\text{CO}}}{\to }\\ {}_{{}^{{}^{\begin{array}{l}\text{weak-field}\text{increasing(Δ)}\text{strong-field}\\ \text{ligands}\text{ligands}\end{array}}}}\end{array}$ The strong field ligands lead to splitting to a higher extent than the weak field ligands and the wavelength of light absorbed depends on the energy gap that is produced by a particular ligand.

The five d orbitals get divided into two sets that are ${\text{d}}_{\text{xy}}{\text{, d}}_{\text{yz}}{\text{ and d}}_{\text{xz}}$ orbitals forms one set and ${\text{d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}{\text{and d}}_{{\text{z}}^{\text{2}}}$ forms another set. The first set are oriented between the x, y and z axes whereas the second set gets oriented along the axis.