The correct comparison of $pK_a$'s of $[Fe(H_2O)_6]^{2+}$, $[Fe(H_2O)_6]^{3+}$, $V_2O_5$ and $N_2O_5$ is
Metal Aqua Ion Acidity Comparison
The acidity of metal aqua ions, such as $[Fe(H_2O)_6]^{3+}$ and $[Fe(H_2O)_6]^{2+}$, depends on the charge density of the central metal ion. A higher charge on the metal ion increases its attraction for the electrons in the O-H bonds of the coordinated water molecules, making it easier to release a proton ($H^+$).
- $[Fe(H_2O)_6]^{3+}$ contains $Fe^{3+}$ (charge +3).
- $[Fe(H_2O)_6]^{2+}$ contains $Fe^{2+}$ (charge +2).
- $Fe^{3+}$ has a higher charge density than $Fe^{2+}$.
- Consequently, $[Fe(H_2O)_6]^{3+}$ is a stronger acid than $[Fe(H_2O)_6]^{2+}$.
- Stronger acids have lower $pK_a$ values. Therefore, $pK_a([Fe(H_2O)_6]^{3+}) < pK_a([Fe(H_2O)_6]^{2+})$.
Acidic Oxide Acidity Comparison
The acidity of oxides like $N_2O_5$ and $V_2O_5$ depends on the nature of the central atom and its oxidation state. Generally, non-metal oxides are more acidic than metal oxides, especially when comparing elements in similar oxidation states.
- $N_2O_5$ is the oxide of nitrogen (a non-metal) in the +5 oxidation state. It is a potent acidic oxide, forming nitric acid ($HNO_3$) upon reaction with water.
- $V_2O_5$ is the oxide of vanadium (a transition metal) in the +5 oxidation state. It acts as an acidic oxide, forming vanadic acid, but is considerably weaker than nitric acid.
- Non-metal oxides are typically more acidic than metal oxides. Thus, $N_2O_5$ is a stronger acid than $V_2O_5$.
- Therefore, $pK_a(N_2O_5) < pK_a(V_2O_5)$.
Overall $pK_a$ Comparison
Combining the findings for both pairs:
- For metal aqua ions: $pK_a([Fe(H_2O)_6]^{3+}) < pK_a([Fe(H_2O)_6]^{2+})$.
- For acidic oxides: $pK_a(N_2O_5) < pK_a(V_2O_5)$.
The correct comparison statement is $[Fe(H_2O)_6]^{3+} < [Fe(H_2O)_6]^{2+}$ and $N_2O_5 < V_2O_5$.
Important Questions from Chemical Biology {p}K_a Henderson Hasselbalch
- The equilibrium dissociation constant of acetic acid is $1.74 \times 10^{-5}$ $M$. The $pK_a$ of acetic acid (rounded off to one decimal place) is ________.
- The ionic product of water at $40$ °C is $2.92 \times 10^{-14}$ $M^2$. The pH of water at $40$ °C is ________ (rounded off to 2 decimal places).
- In a lactic acid solution at pH $4.8$, the concentrations of lactic acid and lactate are $0.01$ M and $0.087$ M, respectively. The calculated pKa of lactic acid is ________ (Round off to one decimal place)
An aqueous solution of aspirin (HA) is prepared at pH 7.4. The ratio of concentration of $A^-$ and HA at equilibrium is ________ (round off to the nearest integer).
Given: $K_a$ of aspirin is $3.98 \times 10^{-4}$
- If 50 mL of 0.02 M HCl is added to 950 mL of $H_2O$, then the pH of the final solution will be _________
