Problem 35 - Chemistry: An Atoms-Focused Approach

Question

A buffer consists of \(0.120 \mathrm{MHNO}_{2}\) and \(0.150 \mathrm{MNaNO}_{2}\) at \(25^{\circ} \mathrm{C}\) a. What is the pH of the buffer? b. What is the pH after the addition of 1.00 mL of \(11.6 M\) HCl to 1.00 L of the buffer solution?

Step-by-Step Solution

Answer

Answer: The method used to find the pH of a buffer solution and the pH after adding HCl to the buffer solution is the Henderson-Hasselbalch equation. The steps to follow are: 1. Find the pKa of the weak acid (HNO₂) by calculating -log(Ka). 2. Calculate the pH of the buffer solution using the Henderson-Hasselbalch equation with the given concentrations of the weak acid and its conjugate base. 3. Determine the new concentrations of the weak acid and its conjugate base after adding HCl by adjusting the initial concentrations. 4. Calculate the new pH after adding HCl using the Henderson-Hasselbalch equation with the new concentrations of the weak acid and its conjugate base.

Step 1: Finding the pKa of the weak acid (HNO\(_{2}\))

To find the pKa, we must first determine the Ka, which is the acid dissociation constant for HNO\(_{2}\). The Ka value for HNO\(_{2}\) is 4.5 × 10\(^{-4}\). Next, we can calculate our pKa using the formula: pKa = -log(Ka). pKa = -log(4.5 × 10\(^{-4}\))

Step 2: Calculating the pH of the buffer solution using the Henderson-Hasselbalch equation

Now, we can use the pKa and given concentrations of the weak acid and its conjugate base to find the pH of our buffer solution. pH = pKa + log([NO\(_{2}^{-}\)]/[HNO\(_{2}\)]) pH = pKa + log([0.150]/[0.120])

Step 3: Calculate the new concentrations after adding HCl

First, let's determine the moles of HCl added to the solution: moles HCl = Volume × Concentration of HCl = (1.00 mL) × (11.6 M) Since we're working in a liter of buffer, we can calculate the new concentrations by adjusting the initial concentrations of the weak acid and its conjugate base. HCl reacts with the conjugate base, decreasing the [NO\(_{2}^{-}\)] concentration and increasing the [HNO\(_{2}\)] concentration. New [NO\(_{2}^{-}\)] = Initial [NO\(_{2}^{-}\)] - moles HCl New [HNO\(_{2}\)] = Initial [HNO\(_{2}\)] + moles HCl

Step 4: Calculating the new pH after adding HCl

We now have the new concentrations of the weak acid and its conjugate base. Let's plug these values into the Henderson-Hasselbalch equation to find the new pH: New pH = pKa + log([New NO\(_{2}^{-}\)]/[New HNO\(_{2}\)])

Key Concepts

pH calculation

Calculating the pH of a solution is an essential step in understanding its acidity or basicity. A solution's pH is a numeric scale used to specify how acidic or basic an aqueous solution is. It typically ranges from 0 to 14 at 25°C. A pH of 7 is considered neutral, below 7 indicates acidity, and above 7 indicates basicity.

For buffer solutions like the one described in the exercise, pH calculation requires knowing the concentrations of the weak acid and its conjugate base. The buffer system resists changes in pH upon the addition of small amounts of acid or base.

To find the pH, we use the Henderson-Hasselbalch equation, which connects the pH to the acid dissociation constant (Ka) and the concentrations of the acid ( [HNO_{2}] ) and its conjugate base ( [NO_{2}^{-}] ). This equation provides a straightforward method to calculate pH in an equilibrium state and during chemical reactions that slightly alter concentration.

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is an invaluable tool in chemistry, particularly useful for pH calculation of buffer solutions. It is expressed as: \[ pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right) \]

In this equation, \(A^-\) represents the conjugate base, and \([HA]\) is the weak acid. \(pKa\) is derived from the negative logarithm of the acid dissociation constant \(Ka\), which measures the strength of the acid.

When we apply this equation to a buffer system, it allows us to predict how the pH will respond to changes within the solution. With even small amounts of added acid or base, a buffer utilizes its equilibrium between the weak acid and conjugate base to maintain a relatively stable pH. This equation thus illustrates the relationship between chemical equilibrium and pH stability in buffers.

acid-base reactions

Acid-base reactions are fundamental processes in chemistry where an acid donates a proton (H⁺) to a base. This proton exchange forms the basis of many chemical reactions, determining the pH and reactivity of solutions.

In the context of buffer solutions, such as the one in the exercise, the addition of strong acids like HCl into the solution involves a classic acid-base reaction. The H^+ ions from HCl react with the conjugate base NO_{2}^{-} , reducing its concentration while converting it back to the weak acid HNO_{2} .

These reactions serve to consume the extra H^+ , thus softening changes in pH and showcasing the buffer's ability to stabilize pH despite acid addition. This balance is crucial for many biological and chemical systems which require a constant pH to function optimally.