Question

Thymol blue indicator has \(t w o\) pH ranges. It changes color from red to yellow in the pH range from 1.2 to 2.8, and from yellow to blue in the pH range from 8.0 to 9.6. What is the color of the indicator in each of the following situations? (a) The indicator is placed in \(350.0 \mathrm{mL}\) of \(0.205 \mathrm{M} \mathrm{HCl}\) (b) To the solution in part (a) is added \(250.0 \mathrm{mL}\) of \(0.500 \mathrm{M} \mathrm{NaNO}_{2}\) (c) To the solution in part (b) is added \(150.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\) (d) To the solution in part (c) is added \(5.00 \mathrm{g} \mathrm{Ba}(\mathrm{OH})_{2}\)

Short answer

So, color of the solution would be: (a) Red, (b) Yellow, (c) Blue, (d) Blue.

Step-by-step solution

Calculate the HCl solution pH

(a) For this, calculate the moles of HCl to find out the concentration. \(0.205M \cdot 350.0mL = 71.75 mmol\) of HCl. The HCl solution is strong acid, so the pH will less than 1. Since the pH of the solution is less than 1.2, the thymol blue indicator would be red according to the pH range of thymol blue.

Determine the pH after adding NaNO2 for solution (b)

To the above solution is added 250.0 ml of 0.500 M NaNO2. The HNO2 produces from NaNO2 will neutralize the HCl. The number of moles of HNO2 is calculated as follow: \(0.500M \cdot 250.0mL = 125 mmol\). Now, Moles of HCL in excess: \(71.75 mmol - 125 mmol = -53.25 mmol\) indicating that NaNO2 is limiting and will be completely consumed. The solution now contains HNO2 which a weak acid. Do the calculation of pH using Henderson–Hasselbalch equation. The pH turns out be greater than 1 but less than 2.8. As such, solution (b) will be yellow.

Determine the pH after adding NaOH for solution (c)

Add 150.0 ml of 0.100 M NaOH to solution (b). First calculate the moles of NaOH: \(0.100M \cdot 150.0ml = 15 mmol\). NaOH is a strong base, so it completely dissociates. Since there is NaOH in excess, the solution becomes basic. Again, calculate the pH using the ion product of water expression and concentration of OH-. The pH turns out be greater than 7.0 but less than 9.6. So, the color of solution (c) will be blue in color.

Determine the pH after adding Ba(OH)2 for solution (d)

Adding 5.00g of Ba(OH)2 to solution (c). The molar mass of Ba(OH)2 is approximately 171.341g/mol. Calculate the moles of Ba(OH)2: \(5.00g \div 171.341g/mol =0.029 mol\). Ba(OH)2 is a strong base and it produces 2 mole of OH- for every mole which makes the solution more basic than previous. The pH would be greater than 9.6. Therefore, solution (d) would also be blue.

Key concepts

Thymol Blue Indicator

Understanding pH indicators is crucial for visualizing the acidity or basicity of a solution. The thymol blue indicator is a chemical compound that changes color based on the pH level of the solution it is in. Specifically, it has two color-transition pH ranges: from red to yellow between pH 1.2 and 2.8, and from yellow to blue between pH 8.0 and 9.6.

This indicator is typically used in titration experiments to determine the point of acid-base neutralization. For instance, when thymol blue is added to a highly acidic solution (pH less than 1.2), it will appear red. Conversely, in a basic solution with a pH above 9.6, it turns blue. If the pH is between 1.2 and 2.8, the indicator will show a yellow color, and this is the point where you're likely to observe the indicator transitioning between red and yellow as the solution's pH changes.

Acid-Base Neutralization

Acid-base neutralization is a fundamental chemical reaction where an acid and a base react to form water and a salt. This process is integral to understanding how the color change of thymol blue occurs in the given textbook problem. When a strong acid like hydrochloric acid (HCl) reacts with a strong base, such as sodium hydroxide (NaOH), they neutralize each other's properties, leading to a change in the pH of the solution.

In the exercise when sodium nitrite (NaNO2), which can act as a base, is added to the HCl solution, it reacts to form nitrous acid (HNO2), a weak acid. This acid-base reaction leads to a less acidic solution, hence a rise in pH. Consequently, the color of the thymol blue indicator shifts from red towards yellow. This exemplifies acid-base neutralization's role in changing the pH and thus, the indicator's color.

pH Calculation

The calculation of pH is a quantitative measure of the acidity or basicity of a solution. It is the negative logarithm of the hydrogen ion concentration in a solution. In simpler terms, pH tells us whether a solution is acidic, neutral, or basic.

A pH less than 7 is acidic, a pH of 7 is neutral, and a pH greater than 7 is basic. For strong acids and bases, the pH can be calculated directly from the concentration of the acid or base. However, for weak acids or bases or when dealing with buffer solutions, calculations become more complex and often require the use of the Henderson–Hasselbalch equation. This is demonstrated in the problem solutions where the pH must be determined at different stages of mixing various chemicals.

Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation is a mathematical formula used to estimate the pH of a buffer solution, which resists changes in pH upon the addition of small amounts of acid or base. The equation relates the pH of a solution to the pKa (acid dissociation constant) and the ratio of the concentrations of the conjugate base and acid present in the solution.

The equation is given by: \[ pH = pKa + \log\left(\frac{\text{[Conjugate Base]}}{\text{[Acid]}}\right) \] This equation comes into play particularly in steps 2 and 3 of the given problem where the pH needs to be calculated after the addition of HNO2 and NaOH. The Henderson–Hasselbalch equation enables the calculation of pH when weak acids or bases are involved, which is essential for predicting the color change of the thymol blue indicator in these more complex scenarios.