Question

Predict the stronger acid in each pair: (a) HNO \(_{3}\) or HNO \(_{2};\) \((\mathbf{b})\mathrm{H}_{2} \mathrm{S}\) or \(\mathrm{H}_{2} \mathrm{O} ;(\mathbf{c}) \mathrm{H}_{2} \mathrm{SO}_{4}\) or \(\mathrm{H}_{2} \mathrm{SeO}_{4}(\mathbf{d}) \mathrm{CH}_{3} \mathrm{COOH}\) or \(\mathrm{CCl}_{3}\) \(\mathrm{COOH}.\)

Short answer

The stronger acids in each pair are: (a) HNO$_{3}$, (b) H$_{2}$S, (c) H$_{2}$SeO$_{4}$, and (d) CCl$_{3}$COOH.

Step-by-step solution

Determine the conjugate base for each acid

To find the conjugate base, remove one proton (H+ ion) from each acid. Pair (a): HNO3 -> NO3- | HNO2 -> NO2- Pair (b): H2S -> HS- | H2O -> OH- Pair (c): H2SO4 -> HSO4- | H2SeO4 -> HSeO4- Pair (d): CH3COOH -> CH3COO- | CCl3COOH -> CCl3COO-

Analyze the stability of the conjugate bases

We will now consider the factors that stabilize the conjugate bases. Pair (a): NO3- is resonance-stabilized while NO2- has only one possible resonance structure. Resonance stabilization indicates a more stable conjugate base. Pair (b): Sulfur (S) within HS- is large and more polarizable than oxygen (O) within OH-, which means that the negative charge can be spread across the atom better in HS-. Pair (c): Compare the electronegativities of sulfur (S) in HSO4- and selenium (Se) in HSeO4-. Selenium is less electronegative than sulfur, hence it can hold the negative charge on the conjugate base better. Pair (d): CCl3COO- has electron-withdrawing chlorine atoms, providing an inductive effect that stabilizes the negative charge on the conjugate base. In CH3COO-, methoxy (CH3) group is less electron-withdrawing compared to the chlorine.

Determine the stronger acid in each pair

Now we can use the stability of the conjugate bases to determine the stronger acid in each pair. Pair (a): HNO3 is the stronger acid as NO3- is more stable due to resonance stabilization. Pair (b): H2S is the stronger acid as HS- is more stable due to sulfur's larger size and polarizability when compared to oxygen in OH-. Pair (c): H2SeO4 is the stronger acid as HSeO4- is more stable due to lower electronegativity of selenium. Pair (d): CCl3COOH is the stronger acid since CCl3COO- is more stable because of the electron-withdrawing chlorine atoms.

Key concepts

Conjugate Base Stability

Understanding the stability of a conjugate base is crucial in determining the strength of an acid. After deprotonation, a stable conjugate base implies a stronger parent acid. The stability of conjugate bases can be influenced by several factors such as size, polarizability, electronegativity, and resonance.

To illustrate, let's take the comparison of HNO₃ and HNO₂. Removing a proton forms their respective conjugate bases: NO3- and NO2-. The NO3- ion is stabilized by resonance—it has multiple equivalent structures that distribute the negative charge evenly. On the other hand, NO2- has less resonance stabilization. Consequently, the greater stability of NO3- indicates that HNO₃ is the stronger acid compared to HNO₂.

In summary, a conjugate base that is more capable of dispersing or bearing a negative charge will generally come from a stronger acid. Analyzing the conjugate base stability can therefore be an effective method for predicting acid strength.

Resonance Stabilization

Resonance stabilization is a molecule's ability to distribute electron density across different atoms through overlapping π orbitals, creating what are known as resonance structures. This delocalization of electrons helps to stabilize the molecule, or in our context, the conjugate base of an acid.

For instance, the nitrate ion (NO3-), the conjugate base of nitric acid (HNO₃), can distribute its negative charge over three oxygen atoms equally. This delocalization through resonance structures contributes significantly to the stabilization of the ion, making HNO₃ a stronger acid compared to acids with less resonance stabilization in their conjugate bases, such as nitrous acid (HNO₂).

Thus, the presence of resonance in a conjugate base is an essential factor that correlates with a decrease in energy and an increase in stability—attributes that are typically associated with a stronger parent acid.

Electronegativity

Electronegativity refers to the tendency of an atom to attract electron density towards itself. When assessing acid strength, understanding electronegativity can be quite informative. Atoms with higher electronegativity can accommodate negative charges more effectively, making their conjugate bases more stable and therefore the parent compounds stronger acids.

Comparing sulfuric acid (H₂SO₄) and selenic acid (H₂SeO₄), we look at the electronegativity of sulfur and selenium. Sulfur has a higher electronegativity than selenium which suggests that the conjugate base of sulfuric acid (HSO₄-) would be less stable than that of selenic acid (HSeO₄-) as it is less capable of stabilizing the negative charge. However, this direct comparison might have exceptions due to other influencing factors which need to be considered alongside electronegativity, such as atomic radius and the inductive effect.

Inductive Effect

The inductive effect is the shift of electron density in a molecule due to the electronegativity of atoms. It plays a pivotal role in the stabilization of conjugate bases and thus the acid strength. Atoms or groups of atoms can pull electron density through sigma bonds, stabilizing nearby negative charges.

A classic example can be observed in the acids acetic acid (CH3COOH) and trichloroacetic acid (CCl₃COOH). The conjugate base of trichloroacetic acid (CCl₃COO-) is highly stabilized by the inductive effect of the electron-withdrawing chlorine atoms. These chlorine atoms are highly electronegative and pull electron density towards themselves, effectively dispersing the negative charge of the conjugate base and making it more stable. Comparatively, the methyl group in the acetate ion (CH3COO-) is not electronegative and therefore does not contribute significantly to the stabilization of the conjugate base. Hence, the acid with the conjugate base experiencing the inductive effect (CCl₃COOH) is the stronger acid.