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Wang and Taha described an interesting application of potentiometry, which they call batch injection. \({ }^{24}\) As shown in Figure \(11.56,\) an ionselective electrode is placed in an inverted position in a large volume tank, and a fixed volume of a sample or a standard solution is injected toward the electrode's surface using a micropipet. The response of the electrode is a spike in potential that is proportional to the analyte's concentration. The following data were collected using a \(\mathrm{pH}\) electrode and a set of \(\mathrm{pH}\) standards. \begin{tabular}{cc} \(\mathrm{pH}\) & potential (mV) \\ \hline 2.0 & +300 \\ 3.0 & +240 \\ 4.0 & +168 \\ 5.0 & +81 \\ 6.0 & +35 \\ 8.0 & -92 \\ 9.0 & -168 \\ 10.0 & -235 \\ 11.0 & -279 \end{tabular} Determine the \(\mathrm{pH}\) of the following samples given the recorded peak potentials: tomato juice, \(167 \mathrm{mV} ;\) tap water, \(-27 \mathrm{mV} ;\) coffee, \(122 \mathrm{mV}\).

Step by step solution

01

Analyze the Given Data

Review the provided data which consist of pH values and corresponding electrode potentials. The relationship between pH and potentials is crucial for further calculations.

02

Establish the Calibration Curve

Plot the given pH values against their corresponding potentials to create a calibration curve. This graph shows potential (mV) on the Y-axis and pH on the X-axis, which should yield a roughly linear relationship.

03

Determine the Relationship Using Linear Regression

Apply linear regression on the plotted data to find the best-fit line. This will provide the equation of the line, generally in the form of \( V = a \cdot pH + b \), where \( V \) is the potential and \( a \) and \( b \) are constants derived from the regression.

04

Insert Sample Potentials Into the Calibration Equation

Using the equation derived from linear regression in Step 3, insert the recorded peak potentials for each sample (tomato juice: 167 mV, tap water: -27 mV, coffee: 122 mV) to calculate the approximate pH for each.

05

Calculate Probable pH Values

Replace the potential values into the regression equation: - For tomato juice, solve \( 167 = a \cdot pH_{tomato} + b \).- For tap water, solve \( -27 = a \cdot pH_{water} + b \).- For coffee, solve \( 122 = a \cdot pH_{coffee} + b \).

06

Solve for Each Sample's pH

Rearrange and solve the linear equations derived: - Solve for \( pH_{tomato} \), \( pH_{water} \), and \( pH_{coffee} \) by isolating the pH variable in each equation using the constants \( a \) and \( b \) estimated from the calibration curve.

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Key Concepts

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

Ion-Selective Electrode

An ion-selective electrode (ISE) is a key tool in potentiometry. It is designed to be sensitive to specific ions and measure their activity in a solution. The unique feature of an ISE is its specific membrane, which allows selective ion exchange. The electrode generates a potential difference that is directly related to the ion concentration.
ISEs are popular for their use in environments where precise ion concentration readings are essential. These electrodes are commonly used to measure the pH of a solution, where the membrane selectively interacts with hydrogen ions (H鈦�). This interaction causes changes in voltage that can be interpreted to determine pH levels accurately. Understanding how an ion-selective electrode works is integral to using potentiometric methods effectively.

Calibration Curve

Creating a calibration curve is a fundamental step in potentiometric measurements. This curve is essential as it establishes the relationship between the known pH values and their corresponding potential readings.
To create a calibration curve, one would plot the potential (in mV) on the y-axis and the pH on the x-axis. This graph visually represents how changes in pH correspond to changes in electrode potential. The calibration curve is usually a straight line in the case of ion-selective electrodes, reflecting their linear response over a particular range.
This curve is crucial during analysis because it allows the computation of unknown sample pH values by comparing potential measurements against the established line.

Linear Regression

Linear regression is a statistical method used to find the best-fit line through a set of data points. In the context of potentiometry, linear regression helps determine the mathematical equation that represents the relationship between pH and potential.
By applying linear regression to the plotted calibration data, we obtain an equation of the form:\[ V = a \cdot pH + b \]
where \( V \) is the potential in millivolts, \( a \) is the slope of the line, and \( b \) is the y-intercept.
This equation allows for precise determination of unknown pH values by substituting the potential readings from sample measurements. Linear regression provides a mathematical way to interpret the graphical data obtained from the calibration curve, ensuring accurate pH readings.

pH Measurement

pH measurement using potentiometry is a practical application of ion-selective electrodes. It focuses on determining the hydrogen ion concentration, or "power of hydrogen," in various solutions.
The process involves using a pH electrode that reacts with H鈦� ions, producing a potential difference measurable in millivolts. By referencing the calibration curve and using the linear regression equation, one can accurately compute the pH of unknown samples.
This method is widely used in different fields, from laboratory testing to environmental monitoring, due to its precision and adaptability. With an understanding of how pH measurements work, users can confidently analyze the acidity or basicity of various substances and apply this knowledge in practical scenarios.