Problem 68 - Chemistry: The Central Science in SI Units, Global Edition

Question

The hypochlorite ion, \(\mathrm{ClO}^{-}\), acts as a weak base. (a) Is ClO a stronger or weaker base than hydroxylamine? (b) When \(\mathrm{ClO}^{-}\) acts as a base, which atom, \(\mathrm{Cl}\) or \(\mathrm{O}\), acts as the proton acceptor? (c) Can you use formal charges to rationalize your answer to part (b)?

Step-by-Step Solution

Answer

(a) The hypochlorite ion, \(\mathrm{ClO}^{-}\), is a weaker base than hydroxylamine because its conjugate acid, \(\mathrm{HClO}\), has a higher acid dissociation constant (Ka) value than that of hydroxylamine's conjugate acid, \(\mathrm{NH_3OH^+}\). (b) When \(\mathrm{ClO}^{-}\) acts as a base, the oxygen atom is the proton acceptor because it has a lone pair of electrons capable of forming a bond with a proton. (c) The calculated formal charges for \(\mathrm{Cl}\) and \(\mathrm{O}\) in the hypochlorite ion show that the oxygen atom bears a negative formal charge, making it more electron-rich and available for accepting a proton, supporting the identification of oxygen as the proton acceptor in part (b).

Step 1: (a) Comparing Basicity of Hypochlorite Ion and Hydroxylamine

To determine if the hypochlorite ion, \(\mathrm{ClO}^{-}\), is a stronger or weaker base than hydroxylamine (\(\mathrm{NH_2OH}\)), we need to analyze the acid dissociation constant (Ka) of their conjugate acids. The conjugate acid of \(\mathrm{ClO}^{-}\) is \(\mathrm{HClO}\) (hypochlorous acid) and the conjugate acid of hydroxylamine is \(\mathrm{NH_3OH^+}\) (hydroxylammonium ion). A lower Ka value indicates a weaker acid (and stronger conjugate base), while a higher Ka value indicates a stronger acid (and weaker conjugate base). So, we can compare the Ka values for the conjugate acids: - Ka of \(\mathrm{HClO}\): \(2.9 \times 10^{-8}\) - Ka of \(\mathrm{NH_3OH^+}\): \(7.5 \times 10^{-10}\) Since the Ka value of \(\mathrm{HClO}\) is greater than the Ka value of \(\mathrm{NH_3OH^+}\), it means that \(\mathrm{HClO}\) is a stronger acid than \(\mathrm{NH_3OH^+}\), and its conjugate base \(\mathrm{ClO}^{-}\) is a weaker base than hydroxylamine.

Step 2: (b) Identifying the Proton Acceptor in \(\mathrm{ClO}^{-}\)

A base is a proton acceptor. This is, when a base reacts with an acid, it accepts a proton (H+) to form its conjugate acid. In the hypochlorite ion, \(\mathrm{ClO}^{-}\), the oxygen atom has a lone pair of electrons, which can be used to form a bond with a proton. Thus, when \(\mathrm{ClO}^{-}\) acts as a base, it is the oxygen atom that acts as the proton acceptor.

Step 3: (c) Using Formal Charges to Rationalize the Proton Acceptor Atom in \(\mathrm{ClO}^{-}\)

To analyze the hypochlorite ion (\(\mathrm{ClO}^{-}\)) using formal charges, we will calculate the formal charges on both the \(\mathrm{Cl}\) and \(\mathrm{O}\) atoms: Formal charge of \(\mathrm{Cl}\): - Valence electrons of Cl: 7 - Number of bonding electrons: 1 - Number of non-bonding electrons: 6 Formal charge = 7 - 0.5(1) - 6 = +0.5 Formal charge of \(\mathrm{O}\): - Valence electrons of O: 6 - Number of bonding electrons: 1 - Number of non-bonding electrons: 6 Formal charge = 6 - 0.5(1) - 6 = -0.5 The negatively charged oxygen atom is more likely to act as a proton acceptor (as a base) since it has a formal charge of -0.5. This means that the oxygen atom is electron-rich and available for accepting a proton. This rationalizes the identification of the oxygen atom as the proton acceptor in part (b).

Key Concepts

Conjugate Acids

In acid-base chemistry, conjugate acids and bases are paired up to help us understand how substances behave when they gain or lose protons. The conjugate acid is what you get when a base gains a proton (H+). Conversely, a conjugate base is what remains after an acid has donated a proton.

Consider the hypochlorite ion (\(\mathrm{ClO}^{-}\)). When it acts as a base and accepts a proton, it forms its conjugate acid, hypochlorous acid (\(\mathrm{HClO}\)). This concept is crucial for comparing the strengths of bases and their conjugate acids. The weaker the conjugate acid, the stronger its base counterpart.

This is analyzed through the acid dissociation constant, \( K_a \). For example:

• Hypochlorous acid (\(\mathrm{HClO}\)): \( K_a = 2.9 \times 10^{-8} \)
• Hydroxylammonium ion (\(\mathrm{NH_3OH^+}\)): \( K_a = 7.5 \times 10^{-10} \)

This shows that hypochlorous acid is a stronger acid than hydroxylammonium ion, indicating that \(\mathrm{ClO}^{-}\) is a weaker base compared to hydroxylamine.

Formal Charges

Understanding formal charges helps identify how atoms within a molecule are likely to behave in reactions. Formal charge is a theoretical charge assigned to an atom, which helps predict molecular structure and reactivity.

To calculate formal charges, use the formula:\[\text{Formal Charge} = \text{Valence Electrons} - \text{Non-bonding Electrons} - \frac{1}{2}\text{Bonding Electrons}\]Apply this to the hypochlorite ion (\(\mathrm{ClO}^{-}\)):

• Chlorine (\(\mathrm{Cl}\)): Valence electrons: 7, Non-bonding: 6, Bonding: 1
  Formal Charge = 7 - 6 - 0.5(1) = +0.5
• Oxygen (\(\mathrm{O}\)): Valence electrons: 6, Non-bonding: 6, Bonding: 1
  Formal Charge = 6 - 6 - 0.5(1) = -0.5

Oxygen has a negative formal charge, suggesting it is more electron-rich. This makes it more likely to engage in bonds, such as accepting a proton when acting as a base. Recognizing these charges helps us rationalize reaction pathways and sites.

Proton Acceptor

A key concept in base behavior is the ability to accept protons. In the context of the Bronsted-Lowry theory, a base is defined as a proton acceptor. Understanding which atom in a molecule acts as a proton acceptor is crucial for predicting reaction outcomes.

In hypochlorite ion (\(\mathrm{ClO}^{-}\)), the oxygen atom will likely play this role. Oxygen is known for having lone pairs of electrons. These are used to form a bond with a proton, transforming the base into its conjugate acid.

In this case:

• The oxygen atom in \(\mathrm{ClO}^{-}\) readily accepts protons because it possesses a negative formal charge.
• These electrons are what allow it to act as a proton acceptor effectively.

This ability to accept protons is fundamental in determining the substance's role as a base in chemical reactions. Recognizing the oxygen as the reactive site clarifies why it becomes the proton acceptor in this scenario.