Problem 56 - Chemistry: An Atoms-Focused Approach

Question

Nitric acid (HNO \(_{3}\) ) is a strong acid that is essentially completely ionized in aqueous solutions of concentrations ranging from \(1 \%\) to \(10 \%(1.5 \mathrm{M}) .\) However, in more concentrated solutions, part of the nitric acid is present as un-ionized molecules of HNO \(_{3} .\) For example, in a \(50 \%\) solution \((7.5 \mathrm{M})\) at \(25^{\circ} \mathrm{C},\) only \(33 \%\) of the molecules of HNO \(_{3}\) dissociate into \(\mathrm{H}^{+}\) and \(\mathrm{NO}_{3}^{-} .\) What is the \(K_{\mathrm{a}}\) value of HNO \(_{3} ?\)

Step-by-Step Solution

Answer

Answer: The Ka value for HNO3 in a 50% (7.5 M) aqueous solution at 25°C is approximately 1.215.

Step 1: Write the dissociation equation

Write the dissociation equation for HNO3 in an aqueous solution: HNO3 (aq) <-> H+ (aq) + NO3- (aq)

Step 2: Determine the initial concentration of HNO3

We are given that the initial concentration of HNO3 is a 50% solution, which is 7.5 M. This will be our starting point to calculate the change in concentrations after dissociation.

Step 3: Calculate the change in concentrations after dissociation

We are given that 33% of the HNO3 molecules dissociate. Determine the concentration change of the species involved in the dissociation: ΔHNO3 = -0.33 x 7.5 M = -2.475 M ΔH+ = +0.33 x 7.5 M = +2.475 M ΔNO3- = +0.33 x 7.5 M = +2.475 M

Step 4: Determine the concentrations after dissociation

Now, we can calculate the final concentrations of each species after the dissociations has occurred: [HNO3] = 7.5 M - 2.475 M = 5.025 M [H+] = 0 M + 2.475 M = 2.475 M [NO3-] = 0 M + 2.475 M = 2.475 M

Step 5: Write the Ka expression

Write the Ka expression for the dissociation of HNO3: Ka = ([H+][NO3-])/[HNO3]

Step 6: Calculate Ka

Plug in the final concentrations calculated in Step 4 into the Ka expression and solve for the Ka value: Ka = (2.475 x 2.475) / 5.025 Ka ≈ 1.215 The Ka value for HNO3 in a 50% (7.5 M) aqueous solution at 25°C is approximately 1.215.

Key Concepts

Nitric Acid

Nitric acid, with the chemical formula HNO₃, is a very strong acid commonly used in laboratories and industries. It is highly reactive and can easily give up its proton (H⁺) in a chemical reaction. Because of its strength, nitric acid almost fully ionizes in water at lower concentrations, typically between 1% to 10%.

This acid is known for its strong oxidizing properties, making it useful in manufacturing processes such as fertilizers and explosives.

When nitric acid is at higher concentrations, such as in a 50% solution, some of it remains as un-ionized HNO₃ molecules. Understanding the behavior of nitric acid across different concentrations is crucial to predict its reactivity and the extent of ionization in various environments. This is particularly important in chemical reaction calculations, which rely on knowing which forms of the acid are present.

Ionization

Ionization refers to the process where a molecule or compound splits into its ions. For nitric acid, ionization occurs when the HNO₃ dissociates in water to form hydrogen ions (H⁺) and nitrate ions (NO₃⁻). This splitting is representative of its acidic nature.

The degree of ionization can depend on several factors:

• Concentration of the solution: At lower concentrations, nitric acid tends to be mostly ionized.
• Temperature: Affects the kinetic energy of molecules, which can influence the extent of ionization.

When calculating the ionization of nitric acid, the dissociation equation is essential:
\[ \text{HNO}_3 (\text{aq}) \leftrightarrow \text{H}^+ (\text{aq}) + \text{NO}_3^- (\text{aq}) \]
This equation helps determine how much of the acid remains intact and how much absorbs into the solution as ions, aiding in the calculation of the acid dissociation constant, \(K_a\).

Aqueous Solutions

An aqueous solution is any solution where water is the solvent. In the context of nitric acid, water helps facilitate its ionization by breaking down the compound into ions.

The properties of aqueous solutions are vital in understanding chemical reactions involving acids like HNO₃ because water's polar nature aids this dissociation process. The presence of water as a medium allows for greater mobility of ions, enhancing reactivity.

Additionally, the behavior of acids in aqueous solutions can affect the measurements and calculations in an experiment, such as pH and concentration. It is necessary to account for the state of the acid in solution, especially its ionized and un-ionized forms, to predict the chemical dynamics accurately.

Concentration

Concentration refers to the amount of solute present in a specific volume of solution. In chemistry, it is usually expressed as molarity (M), which is moles per liter.

Using nitric acid as an example, different concentrations can significantly alter its properties and the extent of ionization. At low concentrations (1.5 M or below), HNO₃ is almost entirely ionized. However, in a more concentrated form (e.g., 50% or 7.5 M), a portion remains un-ionized.

Understanding concentration is crucial because it impacts:

• Reactions rates
• Equilibrium positions
• The calculation of the acid dissociation constant \(K_a\)

Knowing the specific concentration allows chemists to control reactions more efficiently and predict the outcomes. For instance, determining the changes in ion concentration after nitric acid dissociation helps calculate its \(K_a\), giving insights into its acidic strength under specific conditions.