Write equations that show \(\mathrm{NH}_{3}\) as both a conjugate acid and a conjugate base.

Understanding ammonia as a conjugate acid requires a grasp of what happens during acid-base reactions. When ammonia (H_3) accepts a proton (H^+), it transforms into the ammonium ion (H_4^+). This proton acceptance is fundamental to the Brønsted-Lowry acid-base theory, where a conjugate acid is defined as the species formed when a base gains a proton. The chemical equation that illustrates ammonia acting as a conjugate acid is: \[H_{3} + H^+ \rightarrow H_{4}^+\].
By becoming an ammonium ion, ammonia gains a positive charge and one additional hydrogen, proving it can indeed function as a conjugate acid in this context. It's key to note that in this role, ammonia is not an acid by itself; rather, it becomes an acid after accepting a proton.

Conversely, when considering ammonia as a conjugate base, we look at its capacity to donate a proton. In chemical terms, a base is a substance that can donate an electron pair to bond with a proton. Ammonia (H_3) itself is a weak base, and when it donates a proton, it becomes an amide ion (H_2^-). The scenario can be visualized through the reaction: \[H_{3} \rightarrow H_{2}^- + H^+\].
In this reaction, ammonia releases a hydrogen ion, which carries a positive charge and leaves behind a negatively charged amide ion. This demonstrates the dual characteristics of ammonia, capable of both gaining and losing a proton, thereby identifying it as a conjugate acid and base, respectively. The ability to act as both makes ammonia an important participant in acid-base chemistry.

Acid-base reactions are fundamental chemical processes where an acid and base interact to form a conjugate base and a conjugate acid, respectively. These reactions are governed by the principles of the Brønsted-Lowry theory, which states that acids are proton donors and bases are proton acceptors. A simple representation of an acid-base reaction is given by the general equation: \[AH + B \rightarrow A^- + BH^+\].
Here, AH is the acid donating a proton to become the conjugate base (A^-), and B is the base accepting the proton to become the conjugate acid (BH^+). It is through these types of reactions that we can appreciate the role of substances like ammonia that have the versatility to act as both a base and an acid, depending on the reaction context.

Chemical equations are pivotal for understanding chemical reactions as they provide a symbolic representation of what occurs during the reaction. A well-balanced chemical equation ensures the law of conservation of mass is upheld, indicating that the number of atoms for each element is equal on both sides of the reaction. For instance, in the reaction that shows ammonia acting as a base, the chemical equation is balanced as follows: \[H_{3} + H^+ \rightarrow H_{4}^+\] for ammonia as a conjugate acid, and \[H_{3} \rightarrow H_{2}^- + H^+\] for ammonia as a conjugate base.
These equations reflect the simple yet precise nature of acid-base reactions involving ammonia. When studying chemistry, mastery of writing and balancing chemical equations is crucial, as it allows students to predict the outcomes of reactions and understand the transformations of materials at a molecular level.