Problem 39 - Chemistry: Principles and Reactions

Question

Metacresol purple is an indicator that changes from yellow to purple at \(\mathrm{pH} 8.2\). (a) What is \(K_{\mathrm{a}}\) for this indicator? (b) What is its \(\mathrm{pH}\) range? (c) What is the color of a solution with \(\mathrm{pH} 9.0\) and a few drops of metacresol purple?

Step-by-Step Solution

Answer

Based on the given information, the \(K_a\) value for metacresol purple is approximately \(10^{-8.2}\), its \(\mathrm{pH}\) range is \(7.5 - 9.2\), and its color in a \(\mathrm{pH} 9.0\) solution would be purple.

Step 1: Calculate \(K_a\) from \(\mathrm{pH}\)

We are given that metacresol purple changes color at \(\mathrm{pH} 8.2\). When the color change occurs, the ratio of the concentrations of the conjugate base (\(CB\)) and the weak acid form (\(WA\)) is equal to 1. To determine \(K_a\), use the \(\mathrm{pH}\) formula: \(\mathrm{pH} = -\log_{10}(K_a \times \frac{[WA]}{[CB]})\) At the color change point, \([WA] = [CB]\), so the ratio is 1: \(\mathrm{pH} = -\log_{10}(K_a)\) Now, solve for \(K_a\): \(K_a = 10^{-\mathrm{pH}}\) Plug in the given \(\mathrm{pH}\) value: \(K_a = 10^{-8.2}\)

Step 2: Determine the \(\mathrm{pH}\) range of the indicator

The \(\mathrm{pH}\) range is the range within which the indicator changes color, and it is typically within one \(\mathrm{pH}\) unit above and below the \(\mathrm{pH}\) at which the color change occurs: Lower \(\mathrm{pH}\) limit: \(8.2 - 1 = 7.2\) Upper \(\mathrm{pH}\) limit: \(8.2 + 1 = 9.2\) So, the \(\mathrm{pH}\) range of metacresol purple is \(7.2 - 9.2\).

Step 3: Determine the color of metacresol purple in a \(\mathrm{pH} 9.0\) solution

In a solution with \(\mathrm{pH} 9.0\), we need to determine if the indicator is in its acidic (yellow) or its basic (purple) form. Since \(\mathrm{pH} 9.0\) is within the \(\mathrm{pH}\) range of metacresol purple and it is closer to the upper limit, the indicator will be in its basic form, with the color purple.

Key Concepts

Acid-Base Chemistry

Acid-base chemistry is an essential part of understanding how indicators like metacresol purple work. At its core, this branch of chemistry deals with acids, which donate protons, and bases, which accept them.
In any solution, there are balances between these two entities, often leading to a measurable property called the pH level.
Indicators are substances that help visually signal these balances through color changes. A simple way to remember this is:

• Acids increase the concentration of hydrogen ions, and have a lower pH.
• Bases decrease this concentration, resulting in a higher pH.

Acid-base reactions often involve an equilibrium state. This state is where acids convert into their conjugate bases and vice versa. This dynamic process is what makes indicators practical; they can show changes as the equilibrium shifts, and the pH changes.

Dissociation Constant (Ka)

The dissociation constant, abbreviated as \(K_a\), is a crucial concept in acid-base chemistry. It describes the strength of an acid in solution. In simple terms, \(K_a\) quantifies how completely an acid dissociates into its ions. The formula used is: \[K_a = \frac{[H^+][A^-]}{[HA]}\]Here, \([H^+]\) is the concentration of hydrogen ions, \([A^-]\) is the conjugate base, and \([HA]\) is the undissociated acid. A higher \(K_a\) indicates a stronger acid because it dissociates more completely, whereas a lower \(K_a\) shows a weaker acid.
For metacresol purple, its \(K_a\) can be determined at the pH where it changes color. The pH of 8.2 leads to solving the equation:
\(K_a = 10^{-8.2}\).
This value gives insights into the behavior of the indicator and its transition from one color to another.

pH Range

The pH range is a vital property of an indicator, showing where it effectively changes color to signal an acid-base transition. Most indicators have a range of about two pH units, spanning one unit above and below their transition pH. This is when they can noticeably change color.
For metacresol purple, the transition pH is 8.2. Thus, its effective pH range is between 7.2 and 9.2. Within this span:

• Below 7.2, the solution would predominantly exhibit the color associated with the acidic form.
• Above 9.2, it displays the color related to the basic form.
• Between 7.2 and 9.2, there's a visible shift from acidic to basic depending on the exact pH.

Understanding the pH range helps in choosing the right indicator for monitoring specific reactions or solutions.

Color Change in Indicators

Color change is the most noticeable aspect of pH indicators and is crucial for visualizing acidity changes. When using indicators like metacresol purple, this change occurs due to the shifting equilibrium between their acid and base forms. As the pH changes, the concentration ratios of these forms alter, leading to a distinct visible change.
Each indicator has a unique set of colors it transitions through. Metacresol purple changes:

• Yellow, in its acidic form at lower pH levels.
• Purple, in its basic form as the pH rises above its transition point.

In practice, if a solution has a pH of 9.0, which lies within metacresol purple's range, the indicator would show a purple color. This indicates that the solution is closer to the base form, reflecting the typical behavior of indicators in slightly basic solutions.