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How can the concentration of a substance be determined quantitatively in a sample by using polarography? Discuss the experimental setup, mechanism, and factors affecting the results. Provide a practical example of using polarography to determine the concentration of a particular substance in a given sample.

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Polarography is an electroanalytical technique used to determine the concentration of a substance in a sample by measuring the current-voltage relationship. It is based on the principle of electrochemical reduction or oxidation of the analyte at a working electrode  usually a dropping mercury electrode, DME  in an electrochemical cell.Experimental setup:1. Electrochemical cell: The cell consists of a working electrode  DME , a reference electrode  e.g., calomel electrode , and an auxiliary electrode  e.g., platinum wire . The electrodes are immersed in a solution containing the analyte and supporting electrolyte.2. Potentiostat: A potentiostat is used to control the potential between the working and reference electrodes.3. Polarograph: The polarograph records the current flowing between the working and auxiliary electrodes as a function of the applied potential.Mechanism:1. The potential between the working and reference electrodes is gradually increased  in a linear or staircase manner  by the potentiostat.2. When the potential reaches the reduction or oxidation potential of the analyte, electrons are transferred between the analyte and the working electrode, resulting in a current flow.3. The current is proportional to the concentration of the analyte in the solution, and a polarogram  a plot of current vs. potential  is obtained.4. The half-wave potential  E1/2  and limiting current  il  are determined from the polarogram. The concentration of the analyte can be calculated using the limiting current and calibration data.Factors affecting the results:1. Temperature: The rate of electron transfer and diffusion of the analyte to the electrode surface are temperature-dependent, which affects the limiting current and half-wave potential.2. Supporting electrolyte: The presence of a supporting electrolyte helps in maintaining constant ionic strength and reduces the resistance of the solution.3. Stirring: Stirring the solution ensures a constant supply of the analyte to the electrode surface, which affects the limiting current.4. Electrode surface: The cleanliness and condition of the electrode surface can affect the electron transfer process and the resulting polarogram.Practical example:Determination of trace metals, such as lead  Pb , in water samples is a common application of polarography. The procedure involves the following steps:1. Prepare a series of standard solutions containing known concentrations of lead and a supporting electrolyte  e.g., potassium chloride .2. Record polarograms for each standard solution and the water sample using the polarographic setup described above.3. Determine the half-wave potential  E1/2  and limiting current  il  for each standard solution and the water sample.4. Plot a calibration curve of the limiting current vs. concentration for the standard solutions.5. Determine the concentration of lead in the water sample by comparing its limiting current with the calibration curve.In conclusion, polarography is a powerful technique for the quantitative determination of the concentration of a substance in a sample. By understanding the experimental setup, mechanism, and factors affecting the results, accurate and reliable measurements can be obtained.

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