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Chapter 14: Problem 39

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?

Short Answer

Expert verified
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 by step solution

01

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: \(K_a = 10^{-8.2}\)
02

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 \(7.2 - 9.2\).
03

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.

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