Question

Methyl red has a \(\mathrm{pK}_{2}\) 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 \(\mathrm{mL}\) sample of \(0.100 \mathrm{M} \mathrm{HCl},\) what color does the solution appear? If 0.100 \(\mathrm{M} \mathrm{NaOH}\) is slowly added to the HCl sample, in what \(\mathrm{pH}\) range will the indicator change color?

Short answer

The solution will initially appear red because it is in an acidic environment (pH of 1.0). Methyl red would change color from red to yellow when the pH of the solution is raised to its transition range, which is between pH 4.0 and 6.0.

Step-by-step solution

Determine the color of the indicator in 0.100 M HCl

First, notice that HCl is a strong acid and will significantly lower the pH of the solution. Given that methyl red is red in its acid form and the solution is acidic due to HCl, the color of the solution should be red.

Calculating the pH of the initial HCl solution

Calculate the pH of the 0.100 M HCl using the formula for pH: \(\text{pH} = -\log[\text{H}^+]\). Since HCl is a strong acid and fully dissociates, its concentration equals the concentration of \(\text{H}^+\): \(\text{pH} = -\log(0.100) = 1.0\).

Determine the pH range for color change

Methyl red changes color around its \(\mathrm{pK}_{2}\) value of 5.0. The color change typically occurs within the pH range of \(\mathrm{pK}_{2} \pm 1\), which for methyl red is between pH 4.0 and 6.0.

Key concepts

Methyl Red

Understanding Methyl Red is crucial for performing certain chemistry experiments, particularly acid-base titrations. Methyl Red is a type of pH indicator commonly used to visibly signal changes in pH level within a solution. It exhibits a clear color transition from red in its acidic form to yellow in its basic form, which makes it easy to detect the endpoint of a titration. Practically, when added to an acidic solution like hydrochloric acid (HCl), the solution appears red. This is because the indicator reacts with the hydrogen ions present and adopts its acid form.

In the context of the exercise, adding Methyl Red to a 0.100 M HCl solution, it will absolutely appear red due to the high concentration of hydrogen ions from the complete dissociation of HCl, which is what defines a strong acid. Knowing this behavior helps interpret and predict outcomes in laboratory experiments and understanding the chemistry behind it reinforces critical thinking in scientific practices.

pH Calculation

The pH calculation is an essential tool for chemists to quantify the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with 7 serving as the neutral midpoint. Acids have a pH less than 7; bases have a pH greater than 7. The formula for calculating pH is \( \text{pH} = -\log[\text{H}^+] \), where \( [\text{H}^+] \) is the concentration of hydrogen ions in the solution. In our exercise, for a 0.100 M solution of HCl (a strong acid that dissociates completely), the pH is calculated to be 1.0, a highly acidic solution.

It's important for students to grasp that pH is a logarithmic scale, meaning that each whole pH value below 7 is ten times more acidic than the next higher value. For instance, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4. This fundamental knowledge is crucial in understanding the scale of acidity or basicity reflected during pH calculation.

Acid-Base Titration

Acid-base titration is an analytical procedure used to determine the concentration of an unknown acid or base by neutralizing it with a known counterpart. The concept revolves around the reaction between acids and bases, where the moles of hydrogen ions from the acid equate to the moles of hydroxide ions from the base. The point at which neutralization occurs is known as the equivalence point and is where the moles of acid equal the moles of base.

During the process, an indicator like Methyl Red is used to visually mark the end of the titration by changing color. When adding 0.100 M NaOH to the HCl sample, the pH will gradually increase until reaching the pH range where Methyl Red changes color, which acts as an approximation for the equivalence point. In this exercise, the color change signifies that we've approached a pH range that nears neutrality, but is slightly acidic, typically between pH 4.0 and 6.0.

pH Indicators

pH indicators are substances that display different colors at different pH levels, thus they are pivotal in visually determining the pH of a solution. Choosing the right indicator for a particular reaction is based on the expected pH range at the equivalence point of the titration. Methyl Red, for example, has a transition range between pH 4.0 and 6.0, meaning it changes color within this range, suitable for reactions where the equivalence point falls within these values.

pH indicators like Methyl Red are weak acids or bases themselves, which dissociate to form ions that show different colors. This dual-colored nature allows chemists to identify the pH endpoint of a titration visually. The exercise demonstrates this with the Methyl Red indicator discerning the acidic environment created by HCl and later the gradual shift toward a less acidic environment as NaOH is added.