IR spectroscopy can indeed be used to determine the concentration of a sample, utilising the Beer-Lambert law. According to this law, the absorbance of a sample is directly proportional to its concentration and the path length of the sample cell. In practice, a calibration curve is first established using standards of known concentrations. These standards are analysed to create a plot of absorbance versus concentration. Then, the unknown sample’s absorbance is measured using IR spectroscopy, and its concentration is determined by referencing the calibration curve. This method is particularly useful in quantitative analysis of compounds with specific functional groups that exhibit strong and distinct absorption peaks. However, it’s important to note that the sample must be homogeneous, and the IR spectra should be free from interferences caused by overlapping peaks or impurities. The technique is widely used in various fields, including pharmaceuticals, environmental science, and food analysis, for the quantitative determination of specific compounds.

IR spectra are usually plotted with wavenumber (measured in cm⁻¹) rather than wavelength because wavenumber is directly proportional to energy. This makes wavenumbers a more useful and informative measure in vibrational spectroscopy. In contrast, wavelength and energy are inversely related, which can make the interpretation less intuitive. The use of wavenumber simplifies the correlation between the observed spectral features and the vibrational energy levels of the molecule. Moreover, plotting with wavenumber provides a more linear and uniform scale, as the energy differences between vibrational levels in a molecule are more uniform when plotted against wavenumber. This uniformity helps in the clearer differentiation and identification of peaks corresponding to different functional groups. Additionally, chemists and spectroscopists have conventionally used wavenumber for historical and practical reasons, aiding in standardization and comparison of spectra across different studies and instruments.

The presence of impurities in a sample can significantly affect its IR spectrum, potentially complicating the analysis. Impurities may introduce additional absorption peaks or modify the intensity and shape of existing peaks. For example, if a sample containing an alcohol also has water as an impurity, the broad O-H stretching band typical of alcohols may be intensified or broadened due to the overlapping water O-H stretching vibration. Additionally, impurities can create new peaks that might be mistaken for functional groups not actually present in the sample. This can lead to incorrect interpretations unless the impurity is identified and accounted for. Careful sample preparation and purity analysis are crucial to ensure accurate IR spectroscopy results. In a laboratory setting, using purified samples and comparing spectra with reference compounds are common practices to mitigate the effects of impurities.

The different absorption frequencies of functional groups in IR spectroscopy are primarily due to the variations in bond strength and the mass of the atoms involved. Each bond in a molecule, such as C-H, C=O, or O-H, has a specific natural vibrational frequency, which is a function of the mass of the bonded atoms and the stiffness of the bond. This stiffness, or bond strength, is related to the type of bond (single, double, triple) and the electronegativity of the bonded atoms. In simpler terms, heavier atoms and stronger bonds tend to vibrate at lower frequencies, while lighter atoms and weaker bonds vibrate at higher frequencies. For instance, a C=O bond has a different vibrational frequency compared to a C-H bond due to differences in mass (oxygen being heavier than hydrogen) and bond strength (double bonds being stronger than single bonds). This unique vibrational frequency is what IR spectroscopy measures, allowing us to identify the presence of specific functional groups based on their characteristic absorption frequencies.

Temperature and pressure can have noticeable effects on IR spectra. Temperature changes can alter the intensity and position of absorption bands. As temperature increases, the intensity of absorption bands can decrease due to the increased molecular motion, leading to a broadening of the peaks. Additionally, higher temperatures can cause shifts in the peak positions due to changes in the bond vibrational energy. Pressure, on the other hand, may affect the IR spectra of gases more than liquids and solids. In gases, increased pressure can lead to broadening and merging of peaks due to increased collision rates between molecules.

To manage these effects, IR spectroscopic analysis is often conducted under controlled temperature and pressure conditions. In laboratories, samples are typically analysed at room temperature to maintain consistency. When analysing gases, the pressure is usually kept constant and known. In cases where temperature effects are being studied, the analysis is done over a range of temperatures, and the results are interpreted with the understanding of how temperature influences the spectra. Standardization of these conditions is crucial for reproducibility and accuracy in IR spectroscopic analysis.