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Chapter 13: Problem 26

Ramsing and co-workers developed an FIA method for acid-base titrations using a carrier stream that is \(2.0 \times 10^{-3} \mathrm{M} \mathrm{NaOH}\) and that contains the acid-base indicator bromothymol blue. \({ }^{25}\) Standard solutions of \(\mathrm{HCl}\) were injected, and the following values of \(\Delta t\) were measured from the resulting fiagrams. $$ \begin{array}{cccc} {[\mathrm{HCl}](\mathrm{M})} & \Delta t(s) & {[\mathrm{HCl}](\mathrm{M})} & \Delta t(s) \\ \hline 0.008 & 3.13 & 0.080 & 7.71 \\ 0.010 & 3.59 & 0.100 & 8.13 \\ 0.020 & 5.11 & 0.200 & 9.27 \\ 0.040 & 6.39 & 0.400 & 10.45 \\ 0.060 & 7.06 & 0.600 & 11.40 \end{array} $$ A sample with an unknown concentration of \(\mathrm{HCl}\) is analyzed five times, giving values of \(7.43,7.28,7.41,7.37,\) and \(7.33 \mathrm{~s}\) for \(\Delta t .\) Determine the concentration of \(\mathrm{HCl}\) in the sample.

Short Answer

Expert verified
The concentration of HCl in the sample is approximately 0.060 M.

Step by step solution

01

Summary of Given Data

We need to determine the concentration of an unknown HCl solution using the provided data of known HCl concentrations and their corresponding time values (\(\Delta t\)) after injection. The measured times for the unknown samples are: 7.43, 7.28, 7.41, 7.37, and 7.33 seconds.
02

Average Calculation of Unknown 螖t

Calculate the average \(\Delta t\) from the given times for the unknown sample: \(\Delta t_{avg} = \frac{7.43 + 7.28 + 7.41 + 7.37 + 7.33}{5}\).
03

Linear Relationship Identification

From the provided data, note that there is likely a linear relationship between the concentration of \(\mathrm{HCl}\) and \(\Delta t\). We will use this relationship to find the unknown concentration once the average \(\Delta t\) is calculated.
04

Determine the Equation of the Line

Using the known pairs \([\mathrm{HCl}](M)\) and \(\Delta t\), plot the points to determine the best line or calculate using linear regression if necessary. The equation of the line will have the form \(y = mx + b\), where \(y\) is \(\Delta t\) and \(x\) is \([\mathrm{HCl}]\).
05

Substitute Average 螖t to Find Concentration

Using the line equation from Step 4, substitute the average \(\Delta t\) found in Step 2 to solve for the concentration \([\mathrm{HCl}]\) in the unknown sample.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid-Base Titration
Acid-base titration is a method for determining the concentration of an acid or base in a solution. This process involves the gradual addition of a titrant (a solution with a known concentration) to a sample (analyte) until a reaction completion point is reached, often indicated by a color change of an indicator. In this experiment, HCl (hydrochloric acid) is the analyte, and NaOH (sodium hydroxide) is used as part of the carrier stream in flow injection analysis.

Flow injection analysis (FIA) is a technique where the sample is injected into a continuous flowing carrier stream containing the indicator and titrant. The advantage of flow injection is the rapid and automatic analysis of numerous samples with minimized reagent use.
  • The goal is to determine the concentration of an unknown sample by comparing it against a standard curve developed from known concentrations.
  • The titration curve is constructed by plotting the reaction time (\( \Delta t\)) at each known concentration.
For precise results, proper preparation and experimental execution are vital. Also, selecting an appropriate indicator and setting up the right conditions ensures accurate titration endpoints.
Bromothymol Blue
Bromothymol blue is a widely used pH indicator that changes color over a specific pH range. It is often used in titrations because its color transition straddles neutral pH, which is convenient for detecting endpoint in acid-base reactions.

In the context of acid-base titrations using FIA, bromothymol blue serves as the visual cue to ascertain the completion of the reaction.
  • The color change from yellow to blue occurs as the pH shifts from acidic to basic.
  • This indicator is primarily effective for strong acid-strong base titrations, where the pH at the endpoint is near neutral.
As the acid reacts with the base in the carrier stream, bromothymol blue transitions through shades that are distinctly visible, marking the titration's endpoint. This reliable color change makes it a suitable choice for the continuous flow setting, as visual observation verifies when equilibrium is reached.
Linear Relationship
Understanding the linear relationship in acid-base titrations allows for the determination of unknown concentrations. This relationship involves plotting the known concentrations of the acid against their respective time differences (\( \Delta t\)) upon reaction.

Let's delve into why this linearity is important:
  • A direct proportionality exists because the reaction time should increase steadily as the acid concentration increases.
  • By plotting these values, a linear tendency appears, which can be described using the equation of a line:\( y = mx + b \), where \( y \) is the time differential, \( m \) the slope, \( x \) the concentration, and \( b \) the y-intercept.
Through linear regression or a graphical method, derive this equation from the set of known data points.
The calculated average \( \Delta t \)of the unknown sample is substituted into this equation, turning the \( x \) variable into a solvable concentration value. Accurately identifying this linear relationship is crucial as it simplifies complex titration data into a clear, interpretable form.

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Most popular questions from this chapter

To improve the sensitivity of a FIA analysis you might do any of the following: inject a larger volume of sample, increase the flow rate, decrease the length and the diameter of the manifold's tubing, or merge separate channels before injecting the sample. For each action, explain why it leads to an improvement in sensitivity.

The enzyme urease catalyzes the hydrolysis of urea. The rate of this reaction is determined for a series of solutions in which the concentration of urea is changed while maintaining a fixed urease concentration of \(5.0 \mu \mathrm{M}\). The following data are obtained. $$ \begin{array}{cc} \text { [urea }](\mu \mathrm{M}) & \text { rate }\left(\mu \mathrm{M} \mathrm{s}^{-1}\right) \\ \hline 0.100 & 6.25 \\ 0.200 & 12.5 \\ 0.300 & 18.8 \\ 0.400 & 25.0 \\ 0.500 & 31.2 \\ 0.600 & 37.5 \\ 0.700 & 43.7 \\ 0.800 & 50.0 \\ 0.900 & 56.2 \\ 1.00 & 62.5 \end{array} $$ Determine the values of \(V_{\max }, k_{2}\), and \(K_{m}\) for urease.

The concentration of \(\mathrm{Ni}\) in a new alloy is determined by a neutron activation analysis. A 0.500 -g sample of the alloy and a 1.000 -g sample of a standard alloy that is \(5.93 \% \mathrm{w} / \mathrm{w} \mathrm{Ni}\) are irradiated with neutrons in a nuclear reactor. When irradiation is complete, the sample and the standard are allowed to cool and their gamma ray activities measured. Given that the activity is \(1020 \mathrm{cpm}\) for the sample and \(3540 \mathrm{cpm}\) for the standard, determine the \(\% \mathrm{w} / \mathrm{w} \mathrm{Ni}\) in the alloy.

The vitamin \(\mathrm{B}_{12}\) content of a multivitamin tablet is determined by the following procedure. A sample of 10 tablets is dissolved in water and diluted to volume in a 100 -mL volumetric flask. A 50.00 -mL portion is removed and \(0.500 \mathrm{mg}\) of radioactive vitamin \(\mathrm{B}_{12}\) having an activity of 572 cpm is added as a tracer. The sample and tracer are homogenized and the vitamin \(\mathrm{B}_{12}\) isolated and purified, producing \(18.6 \mathrm{mg}\) with an activity of 361 cpm. Calculate the milligrams of vitamin \(\mathrm{B}_{12}\) in a multivitamin tablet.

To study the effect of an enzyme inhibitor \(V_{\max }\) and \(K_{m}\) are measured for several concentrations of inhibitor. As the concentration of the inhibitor increases \(V_{\max }\) remains essentially constant, but the value of \(K_{m}\) increases. Which mechanism for enzyme inhibition is in effect?
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