Question

Calculate the \(\mathrm{pH}\) of a solution that is 1.00 \(\mathrm{M}\) HNO, and 1.00 \(\mathrm{M} \mathrm{NaNO}_{2}\)

Short answer

Using the Henderson-Hasselbalch equation, the pH of a solution containing 1.00 M HNO and 1.00 M NaNO₂ can be calculated as follows: \( pH = pKa + \log \frac{[Conjugate \, Base]}{[Acid]} \). Assuming a pKa value of 3.5 for HNO, the calculation becomes \( pH = 3.5 + \log \frac{1.00}{1.00} \), which simplifies to \( pH = 3.5 \). Therefore, the pH of the solution is 3.5.

Step-by-step solution

Identify the given values

In this problem, the given concentrations of the acid (HNO) and its conjugate base (NO₂⁻) are both 1.00 M. We will use these values in the Henderson-Hasselbalch equation to calculate the pH of the solution.

Write down the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation relates the pH, pKa, and the concentrations of the weak acid and its conjugate base as follows: \[ pH = pKa + \log \frac{[Conjugate \, Base]}{[Acid]} \]

Determine the pKa of HNO

To use the Henderson-Hasselbalch equation, we need the pKa value of HNO. Unfortunately, the pKa value of HNO is not commonly known or found in most tables. In such cases, either the pKa value must be given in the problem or it should be approximated. For the sake of this exercise, let's assume the given pKa value for HNO is 3.5, which is a reasonable approximation for a weak acid.

Use the given concentrations and pKa in the Henderson-Hasselbalch equation

Now, we can use the given concentrations of the acid (HNO) and its conjugate base (NO₂⁻), as well as the assumed pKa value of HNO, in the Henderson-Hasselbalch equation: \[ pH = 3.5 + \log \frac{1.00}{1.00} \]

Calculate the pH of the solution

Since the concentrations of the conjugate base and the acid are equal, the log term in the equation becomes 0. Therefore, the pH of the solution is the same as the pKa value: \[ pH = 3.5 + 0 \] Thus, the pH of the solution containing 1.00 M HNO and 1.00 M NaNO₂ is 3.5.

Key concepts

pH calculation

When dealing with solutions in chemistry, calculating the pH is a critical task as it dictates the acidity or basicity of the solution. Specifically, pH is a scale used to specify the acidity or basicity of an aqueous solution. It's derived from the concentration of hydrogen ions present within the solution. A low pH value indicates a high concentration of hydrogen ions, suggesting an acidic environment, while a high pH value indicates a basic environment.

The formula for calculating pH is given by:

• \( pH = -\log[H^+] \)

However, when the situation involves both a weak acid and its conjugate base, the Henderson-Hasselbalch equation becomes a convenient tool to use:

• \( pH = pKa + \log \frac{[Conjugate \, Base]}{[Acid]} \)

In our scenario, both the concentrations of the weak acid (HNO) and the conjugate base (\( \text{NO}_2^- \)) were equal, simplifying our calculation. Often, exercises and calculations will assume this kind of equilibrium to illustrate fundamentals without added complexity.

weak acid and conjugate base

When a weak acid is dissolved in water, it doesn't completely ionize. Instead, it establishes a balance between the undissociated acid and the ions it produces in solution. The weak acid releases hydrogen ions (\( H^+ \)) and leaves behind its conjugate base.

In our particular exercise, \( HNO \) serves as the weak acid, while \( \text{NO}_2^- \) acts as its conjugate base.

• Weak acids only partially dissociate in water.
• The conjugate base is the species that remains after the acid donates a proton.

The presence of both these components (weak acid and conjugate base) together allows for the formation of a buffer solution—this helps resist drastic changes in pH upon the addition of small amounts of acids or bases.

chemical equilibrium

Chemical equilibrium is a state reached in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of the reactants and products over time. In a system involving a weak acid like \( HNO\), and its conjugate base \( \text{NO}_2^- \), equilibrium describes the balance between the dissociated and undissociated forms.

In equilibrium:- The rate at which the weak acid dissociates to form hydrogen ions and its conjugate base equals the rate at which they combine to reform the acid.- This state is characterized by the equilibrium constant \( K_a\), which Equation describes how far a reaction proceeds.

Understanding equilibrium is key to solving problems involving weak acid-base pairs, as it helps in determining how the solution's pH might change should the system be disturbed. Calculating equilibrium conditions provides insight into how likely the species will exist in their undissociated or dissociated forms, which directly links back to how we calculate pH using the Henderson-Hasselbalch equation.