Chapter 20, Problem 20.90P

(a)

Interpretation Introduction

Interpretation:

For the following haemoglobin reaction, the $\text{K}$ value should be calculated at ${37}^{o}C$, using the given $\Delta G^o$ value.

Concept introduction:

Equilibrium constant$\left({\text{K}}_{\text{c}}\right)$: A system is said to be in equilibrium when all the measurable properties of the system remains unchanged with the time.  Equilibrium constant is the ratio of the rate constants of the forward and reverse reactions at a given temperature.  In other words it is the ratio of the concentrations of the products to concentrations of the reactants.  Each concentration term is raised to a power, which is same as the coefficients in the chemical reaction.

Consider the reaction where the reactant A is giving product B.

    $\text{A}\rightleftharpoons \text{B}$

$\begin{array}{l}\text{Rate of forward reaction = Rate of reverse reaction}\\ \\ {\text{k}}_{\text{f}}\left[\text{A}\right]{\text{=k}}_{\text{r}}\left[\text{B}\right]\end{array}$

On rearranging, $\frac{\left[\text{A}\right]}{\left[\text{B}\right]}\text{=}\frac{{\text{k}}_{\text{f}}}{{\text{k}}_{\text{r}}}={\text{K}}_{\text{c}}$

Where,

${\text{k}}_f$ is the rate constant of the forward reaction.

${\text{k}}_r$ is the rate constant of the reverse reaction.

$K_c$ is the equilibrium constant.

Free energy change$\text{ΔG}$: change in the free energy takes place while reactants convert to product where both are in standard state. It depends on the equilibrium constant $\text{K}$,

  $\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{o}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ \\ {\text{ΔG}}^{\text{o}}\text{=- RT}\ln \left(\text{K}\right)\end{array}$

(b)

Interpretation Introduction

Interpretation:

Using the Le Chatelier’s principle treating $CO$ poisoning has to be explained.

Concept introduction:

Equilibrium pressure$\left({\text{K}}_{\text{p}}\right)$: For gaseous substances the concentration will be proportional to its partial pressure.  The equilibrium constant for gaseous reactions can be expressed in terms of the partial pressures of the gaseous products and reactants, and it is called equilibrium constant ${\text{K}}_{\text{p}}$.  The value of ${\text{K}}_{\text{p}}$ is different from ${\text{K}}_c$.  The relation between ${\text{K}}_{\text{p}}$ and ${\text{K}}_c$ is given below.

    ${\text{K}}_{\text{p}}={\text{K}}_{\text{c}}{\text{RT}}^{\text{Δn}}$

Le Chatelier’s principle:  When a system at equilibrium is disturbed, the system will adjust itself to nullify the effect and maintain the equilibrium.