Problem 79 - Chemistry: Structure and Properties

Question

Methyl red has a pKa of 5.0 and is red in its acid form and yellow in its basic form. If several drops of this indicator are placed in a 25.0-mL sample of 0.100 M HCl, what color does the solution appear? If 0.100 M NaOH is slowly added to the HCl sample, in what pH range will the indicator change color?

Step-by-Step Solution

Answer

The solution appears red initially. Methyl red will change color from red to yellow as the pH of the solution is increased from pH 4.4 to pH 6.2 upon gradual addition of NaOH.

Step 1: Determine the initial pH of the HCl solution

To find the initial color of the methyl red in the HCl solution, calculate the pH of a 0.100 M HCl solution. This strong acid completely dissociates in water, so the pH is given by the negative logarithm of its concentration: $$\text{pH} = -\log[H^+] = -\log(0.100)$$

Step 2: Find the initial color of the indicator

With a pKa of 5.0, methyl red transitions from red to yellow as the pH goes from below to above this value. Since the pH of 0.100 M HCl is lower than the pKa, the indicator will initially be in its acid form, which is red.

Step 3: Identify the color change range

Methyl red has a pH transition range typically around the pKa value, usually within a range of pH 4.4 to 6.2. This is the range over which the color will change from red to yellow when NaOH is added.

Key Concepts

Understanding pKa

The concept of pKa is fundamental in the study of acid-base chemistry. It represents the acidity of a substance by indicating the pH at which half of the molecules of an acid are deprotonated. In simpler terms, pKa is the pH level where an acid and its conjugate base are in equilibrium. The lower the pKa value, the stronger the acid because it has a greater tendency to lose its proton. For an indicator like methyl red with a pKa of 5.0, this implies that at pH 5.0, the molecule exists in a 50:50 mixture of its acid (protonated) and base (deprotonated) forms.

Knowing the pKa can help predict the behavior of an acid in different pH environments, which is crucial for understanding the color changes of acid-base indicators during titration.

Calculating pH

The pH of a solution is a measure of its acidity or alkalinity on a logarithmic scale. Specifically, pH is the negative logarithm of the hydrogen ion concentration (\( -\log[H^+] \)). When calculating the pH of strong acids like HCl, it's important to remember they fully dissociate in water. This means the concentration of hydrogen ions is equal to the acid's initial concentration.For a 0.100 M HCl solution, the pH calculation becomes a straightforward logarithmic operation: \( \text{pH} = -\log(0.100) \), leading to a pH close to 1. This very low pH indicates a high acidity level.

Characteristics of Strong Acids

Strong acids such as hydrochloric acid (HCl) are defined by their complete dissociation in aqueous solutions. This full dissociation releases a significant concentration of hydrogen ions (\( H^+ \)), which defines the strength of the acid. HCl, sulfuric acid (\( H_2SO_4 \)), and nitric acid (\( HNO_3 \)) are common examples of strong acids. Their high dissociation constant is reflected in their low pH levels when in solution, typically well below the pKa of most acid-base indicators. This characteristic makes them ideal for titrations when determining the acidity of a given sample.

Color Change of Indicators

Acid-base indicators are compounds that display a color change within a specific pH range, which is intrinsically related to their pKa value. The visible shift in color marks the transition of pH across the pKa, where the proportion of acid and conjugate base forms of the indicator change significantly. Methyl red, for instance, is red in its acidic form and yellow in its basic form.The color change occurs over a pH range, not a precise value, allowing some leeway when observing the transition. The theoretical range is approximately \( pKa \pm 1 \), which, for methyl red, translates into a pH range of about 4.4 to 6.2. Within this interval, as the pH increases from acidic to basic, the color change from red to yellow will be noticeable, thus providing a visual cue during titration processes.