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Liquid ammonia undergoes autoionization similar to that of water: $$ \mathrm{NH}_{3}(l)+\mathrm{NH}_{3}(l) \rightleftharpoons \mathrm{NH}_{4}^{+}(l)+\mathrm{NH}_{2}^{-}(l) $$ How would you define an acid and a base similar to the way these terms are defined by the Br酶nsted-Lowry concept for aqueous solutions? Write the expression for the ionproduct constant, \(K_{a m},\) for this autoionization. The value of \(K_{a m}\) is \(5.1 \times 10^{-27}\). What is the concentration of \(\mathrm{NH}_{4}^{+}\) in a neutral solution of liquid ammonia? Suppose you dissolve \(\mathrm{NH}_{4} \mathrm{I}\) in liquid ammonia to give \(\mathrm{NH}_{4}{ }^{+}\) and \(\mathrm{I}^{-}\) ions. Similarly, you dissolve \(\mathrm{KNH}_{2}\) (potassium amide) in liquid ammonia to give a solution of \(\mathrm{K}^{+}\) and \(\mathrm{NH}_{2}^{-}\) ions. Which of these two solutions is acidic and which basic according to your definitions? Now, suppose you add the two solutions together. Write an equation for the neutralization reaction.

Step by step solution

01

Define Acid and Base

In the context of liquid ammonia, an acid is a substance that donates a proton (\(\mathrm{NH}_4^+\) is the conjugate acid), while a base is a substance that accepts a proton (\(\mathrm{NH}_2^-\) is the conjugate base). This mirrors the Br酶nsted-Lowry acid-base concept used in aqueous solutions.

02

Write the Ion-Product Constant Expression

For the autoionization of liquid ammonia, the ion-product constant \(K_{am}\) is expressed as: \[ K_{am} = [\mathrm{NH}_4^+][\mathrm{NH}_2^-] \] This quantifies the concentrations of ions in pure liquid ammonia at a given temperature.

03

Calculate \(\mathrm{NH}_4^+\) Concentration

For neutrality in liquid ammonia, the concentrations of \(\mathrm{NH}_4^+\) and \(\mathrm{NH}_2^-\) must be equal, i.e., \(x = [\mathrm{NH}_4^+] = [\mathrm{NH}_2^-]\). Thus, \[ K_{am} = [\mathrm{NH}_4^+][\mathrm{NH}_2^-] = x^2 = 5.1 \times 10^{-27} \] Solving for \(x\), \[ x = \sqrt{5.1 \times 10^{-27}} = 7.14 \times 10^{-14} \text{ M} \] This is the concentration of \(\mathrm{NH}_4^+\) in a neutral solution of liquid ammonia.

04

Determine Acidity and Basicity of Solutions

The solution containing \(\mathrm{NH}_4^+\) ions from \(\mathrm{NH}_4\mathrm{I}\) is acidic because \(\mathrm{NH}_4^+\) can donate a proton. The solution containing \(\mathrm{NH}_2^-\) ions from \(\mathrm{KNH}_2\) is basic because \(\mathrm{NH}_2^-\) can accept a proton.

05

Neutralization Reaction Equation

When you mix the acidic and basic solutions, \(\mathrm{NH}_4^+\) and \(\mathrm{NH}_2^-\) react to form neutral ammonia. The neutralization reaction is: \[ \mathrm{NH}_4^+ (l) + \mathrm{NH}_2^- (l) \rightarrow 2\ \mathrm{NH}_3 (l) \] This results in the formation of neutral \(\mathrm{NH}_3\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Br酶nsted-Lowry Acid-Base Concept

In chemistry, understanding how substances interact with protons is crucial. The Br酶nsted-Lowry acid-base concept provides a framework for this. According to this concept, an acid is defined as a proton donor, meaning it gives up a hydrogen ion (H鈦�) to another substance. Meanwhile, a base is a proton acceptor, meaning it takes in a proton from another substance.
In the context of liquid ammonia, we see similar interactions as in water. When ammonia undergoes autoionization, it forms \ \( NH_4^+ \ \) (ammonium) and \ \( NH_2^- \ \) (amide) ions. Here, \ \( NH_4^+ \ \) acts as the acid because it is willing to donate a proton, whereas \ \( NH_2^- \ \) acts as the base because it is ready to accept a proton. This definition parallels the Br酶nsted-Lowry definition used in aqueous solutions, making it widely applicable.

Ion-Product Constant

The ion-product constant, often symbolized as \ \( K_{am} \ \) for liquid ammonia, helps quantify ion concentrations in a solution. In the autoionization of liquid ammonia, the ion-product constant is expressed as: \ \[ K_{am} = [NH_4^+][NH_2^-] \ \]
This formula indicates how the product of the concentrations of \ \( NH_4^+ \ \) and \ \( NH_2^- \ \) ions is constant at a given temperature in pure liquid ammonia. The given value of \ \( K_{am} = 5.1 \times 10^{-27} \ \) is very small, indicating that both ions form in very low concentrations, signifying that ammonia doesn't strongly autoionize.

• Knowing \ \( K_{am} \ \) helps predict the concentrations of ions.
• This concept is vital in understanding the equilibrium state of a solute in solvent interactions, especially in solvent systems beyond water.

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form a neutral substance, typically water in aqueous solutions. However, in liquid ammonia, this reaction results in the formation of neutral ammonia molecules.
When you mix a solution containing \ \( NH_4^+ \ \), an acidic ion, with a solution containing \ \( NH_2^- \ \), a basic ion, they react in the following way: \ \[ NH_4^+ (l) + NH_2^- (l) \rightarrow 2\ NH_3 (l) \ \]

• The \ \( NH_4^+ \ \) donates a proton to the \ \( NH_2^- \ \), effectively neutralizing each other.
• This creates liquid ammonia, a neutral and stable substance formed by balancing acidic and basic properties.

Acid-Base Definitions in Ammonia

In ammonia, acid-base interactions slightly differ from those in traditional aqueous environments. Upon dissolution, \ \( NH_4^+ \ \) ions from compounds like \ \( NH_4I \ \) are considered acidic because they can donate a proton to form ammonia.
Similarly, \ \( NH_2^- \ \) ions from \ \( KNH_2 \ \) are basic as they are capable of accepting a proton.

• Simplified, the substance that can release a proton in ammonia becomes an acid, and the one that can capture a proton becomes a base.
• This interpretation helps classify substances in non-water-based systems according to their reactivity regarding proton exchange.

Understanding these basic definitions aids in recognizing how neutralization can occur in various chemical environments.