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 will the solution appear? If 0.100 M NaOH is slowly added to the HCl sample, in what pH range will the indicator change color?

Verified step by step guidance

1. 1. Methyl red changes color based on the pH of the solution it is in. In acidic solutions (pH < 5.0), it appears red, and in basic solutions (pH > 5.0), it appears yellow. The solution of 0.100 M HCl is a strong acid, so its pH will be less than 5.0. Therefore, the solution will appear red when methyl red is added.
2. 2. When 0.100 M NaOH, a strong base, is added to the HCl solution, it will neutralize the HCl and increase the pH of the solution. The pH at which the color change occurs is around the pKa of the indicator, which is 5.0 for methyl red.
3. 3. However, the color change is not instantaneous and occurs over a range of pH values. For most indicators, this range is approximately ±1 around the pKa value. So, for methyl red, the color change will start to occur around pH 4.0 and will be complete by pH 6.0.
4. 4. Therefore, the pH range in which the indicator will change color when 0.100 M NaOH is added to the HCl solution is approximately 4.0 to 6.0.

Key Concepts

pKa and Acid-Base Indicators

The pKa value of an acid is the pH at which half of the acid is dissociated into its conjugate base. Methyl red, with a pKa of 5.0, serves as an acid-base indicator, changing color based on the pH of the solution. Below its pKa, it appears red (acidic form), and above it, it turns yellow (basic form). This property is crucial for determining the color of the solution in different pH environments.

Strong Acids and pH Calculation

Strong acids, like HCl, completely dissociate in solution, meaning that the concentration of hydrogen ions [H⁺] equals the concentration of the acid. In a 0.100 M HCl solution, the pH can be calculated using the formula pH = -log[H⁺], resulting in a pH of 1. This low pH indicates that the solution will appear red when methyl red is added, as it is below the pKa of 5.0.

Titration and Color Change Range

During a titration, as a strong base like NaOH is added to a strong acid like HCl, the pH of the solution gradually increases. The color change of methyl red occurs around its pKa, specifically between pH 4.4 (red) and pH 6.2 (yellow). Therefore, as NaOH is added, the indicator will transition from red to yellow as the pH crosses this range, indicating the point at which the solution becomes neutral to slightly basic.