Question

Choose pairs in which the species listed first is the conjugate base of the species listed second. a. \(\mathrm{S}^{2-}, \mathrm{HS}^{-}\) b. \(\mathrm{H}^{+}, \mathrm{OH}^{-}\) c. \(\mathrm{HBr}, \mathrm{Br}^{-}\) d. \(\mathrm{NO}_{2}^{-}, \mathrm{HNO}_{2}\)

Short answer

The correct pairs in which the first species is the conjugate base of the second species are: a. \(\mathrm{S}^{2-}, \mathrm{HS}^{-}\) c. \(\mathrm{HBr}, \mathrm{Br}^{-}\) d. \(\mathrm{NO}_{2}^{-}, \mathrm{HNO}_{2}\)

Step-by-step solution

Comparison of each pair

: First, let's explain the concept of a conjugate base. A conjugate base is the species that remains after an acid (a compound which donates a proton) donates a proton. Recall that a proton is represented by H+. So, in each given pair, we will compare the species and see if removing an H+ from the second species results in the formation of the first species.

Analyze Pair A

: In pair A, we have \(\mathrm{S}^{2-}\) and \(\mathrm{HS}^{-}\). If we remove a proton (H+) from \(\mathrm{HS}^{-}\), we get \(\mathrm{S}^{2-}\): \(\mathrm{HS}^{-} - \mathrm{H}^{+} \rightarrow \mathrm{S}^{2-}\) Therefore, in pair A, the species \(\mathrm{S}^{2-}\) is the conjugate base of the species \(\mathrm{HS}^{-}\).

Analyze Pair B

: In pair B, we have \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\). If we remove a proton (H+) from \(\mathrm{OH}^{-}\), we do not get \(\mathrm{H}^{+}\): \(\mathrm{OH}^{-} - \mathrm{H}^{+} \nrightarrow \mathrm{H}^{+}\) Therefore, in pair B, the species \(\mathrm{H}^{+}\) is not the conjugate base of the species \(\mathrm{OH}^{-}\).

Analyze Pair C

: In pair C, we have \(\mathrm{HBr}\) and \(\mathrm{Br}^{-}\). If we remove a proton (H+) from \(\mathrm{HBr}\), we get \(\mathrm{Br}^{-}\): \(\mathrm{HBr} - \mathrm{H}^{+} \rightarrow \mathrm{Br}^{-}\) Therefore, in pair C, the species \(\mathrm{Br}^{-}\) is the conjugate base of the species \(\mathrm{HBr}\).

Analyze Pair D

: In pair D, we have \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{HNO}_{2}\). If we remove a proton (H+) from \(\mathrm{HNO}_{2}\), we get \(\mathrm{NO}_{2}^{-}\): \(\mathrm{HNO}_{2} - \mathrm{H}^{+} \rightarrow \mathrm{NO}_{2}^{-}\) Therefore, in pair D, the species \(\mathrm{NO}_{2}^{-}\) is the conjugate base of the species \(\mathrm{HNO}_{2}\).

Conclusion

: To conclude, the correct pairs in which the first species is the conjugate base of the second species are: a. \(\mathrm{S}^{2-}, \mathrm{HS}^{-}\) c. \(\mathrm{HBr}, \mathrm{Br}^{-}\) d. \(\mathrm{NO}_{2}^{-}, \mathrm{HNO}_{2}\)

Key concepts

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept in chemistry and deals with the interactions between acids and bases. In essence, acids are substances that release hydrogen ions ( H^+ ) when dissolved in water, while bases are substances that can accept hydrogen ions or donate a pair of electrons. A straightforward example is hydrochloric acid ( HCl ), which dissociates into hydrogen ( H^+ ) and chloride ions ( Cl^- ).
This branch of chemistry also introduces the concept of conjugate acid-base pairs:

• An acid becomes its conjugate base after it donates a proton.
• Conversely, a base becomes its conjugate acid after accepting a proton.

Understanding these pairs helps predict the direction of proton transfer reactions. Acid-base chemistry is a cornerstone of chemical reactions, vital in processes like digestion, pharmaceutical formulations, and even environmental chemistry.

Proton Transfer

Proton transfer is the mechanism by which acids and bases interact. During this process, a proton from an acidic species is transferred to a basic species. This is key to acid-base reactions and defines the core behavior of acids and bases.
To determine conjugate bases in given pairs, like HNO_2 and NO_2^- , you identify the species that results from the loss of a proton from the acid (here, HNO_2 ), making NO_2^- the conjugate base.
Key points in proton transfer include:

• Acids must have one or more hydrogen atoms to donate as protons.
• Bases must have lone pairs of electrons to accept the protons.

Ensuring an understanding of this transfer is crucial for mastering complex reactions in organic and inorganic chemistry.

Chemical Equilibrium

Chemical equilibrium refers to the balance in a chemical reaction where the forward and reverse reactions occur at the same rate. In the context of acid-base chemistry, equilibrium plays a crucial role.
Consider the equilibrium that exists when an acid donates a proton to a base. Once established, this balance implies that both the concentration of acids and bases, and their conjugates, remain unchanged despite ongoing reactions.
This understanding leads to the development of the equilibrium constant ( K_ ext{eq} ), which quantifies the relationship between the concentrations of the reactants and products. It is especially applicable in determining whether reactions lie more heavily on the products or reactants side.

• If K_ ext{eq} > 1 , products are favored.
• If K_ ext{eq} < 1 , reactants are favored.

Grasping chemical equilibrium is vital for balancing reactions and predicting the rates and extents of acid-base reactions.