The equilibrium constant K in the Langmuir isotherm is usually used to calculate the standard Gibbs free energy of adsorption (ΔG°). However, in a strictly theoretical sense, this calculation method is incorrect. The reason is that the K in the Langmuir isotherm has a dimension. According to the provisions of the International Union of Pure and Applied Chemistry (IUPAC), the standard equilibrium constant (K°) for calculating ΔG° must be a dimensionless parameter. We examined four examples from the literature and found that the calculation of ΔG° presented in these four references was incorrect. Based on the fact that this misapplication is very common, this note reviews the related literature and gives a short comment on this problem. Two methods for calculating the thermodynamic equilibrium constant by the Langmuir equation are provided and discussed.

Cadmium (Cd) is documented as one of the most lethal metals and poses a major threat to all life forms in the environment due to its toxic effects. Bioremediation of hazardous metals has received considerable and growing interest over the years. The functional fungi with tolerance to the heavy metal Cd were screened from the mining soil samples. Two fungi isolates from coal mine soil were characterized as Sarocladium sp. M2 and Sarocladium sp. M6 based on morphological and partial ITS sequencing analysis. M2 and M6 exhibited high levels of resistance to cadmium, and they were investigated for their micro-morphology and application in heavy metal removal with different concentration Cd(II) (0, 50, 100, 150 and 200 mg/L). The colony morphology of M2 and M6 gradually become very similar to that of bacteria with the increase of cadmium concentration (150-200 mg/L). Micro-morphological studies showed that Cd(II) exposure caused the disappearance of conidial heads and the occurrence of hyphae breakage (100-200 mg/L Cd(II), which is consistent to the colony morphology results. The surface/volume ratio of the spores decreased with the presence of Cd(II). The removal potential of fungi for cadmium was quantified by atomic absorption spectrometry. M2 and M6 showed great potential as bioremediators for highly Cd(II)-contaminated environment. The highest Cd(II) biosorption capacity was 5.13 ± 0.21 mg/g for M2 and 6.04 ± 0.21 mg/g for M6. The highest heavy metal sorption by M2 removed 57.11% ± 4.45% Cd(II) while that of M6 removed 48.35% ± 1.44% Cd(II) in 200 mg/L initial concentration Cd(II). To the best of our knowledge, this is the first report that cadmium induced the change of reproduction mode of the Sarocladium, from conidia to arthrospores, which made the colony morphological modifications, from the fungi colony morphology to the bacteria colony morphology. The arthrospore-modified (hyphae breakage) seemed to accumulate greater amounts of heavy metals than filamentous hyphae formation.

Accurate calculations and precise results are very important for the dissemination of scientific knowledge, whereas the errors of calculation will diminish the academic value of the paper. This discussion focuses on the calculation of thermodynamics and the determination of the spontaneity of adsorption processes in the paper of Ofudje et al. (2023). Ofudje et al. found that the apatite synthesized by chemical method (CHAp) has excellent adsorption properties for cadmium ions, which is an important contribution to the remediation of cadmium pollution. However, the calculation results of standard Gibbs free energy change (ΔG^o), standard enthalpy change (ΔH^o) and standard entropy change (ΔS^o) of the adsorption of Cd²⁺ onto CHAp surface need to be corrected due to an incorrect calculation. Firstly, the partition coefficient (K_D) with a dimension cannot be used for thermodynamic calculation. Secondly, the adsorbent mass (m) described by Ofudje et al. in different Sections is inconsistent, leading to incorrect results of K^o and ΔG^o. When the appropriate value of the adsorbent mass is selected and the partition coefficient is converted to the standard adsorption equilibrium constant K^o, the calculated ΔG^o is less than zero, which means that the adsorption is spontaneous. This discussion provides the correct calculation method of standard adsorption equilibrium constants and thermodynamic parameters, which can improve the reader's judgment and understanding of adsorption spontaneity.

Quinoa bran is a by-product during quinoa processing, which is not well used due to its high content of antinutritional factors. The nutritional, antinutritional, antioxidative and mineral content were analyzed in quinoa bran from five producing areas (Hebei, Shanxi, Qinghai, Inner Mongolia and Gansu Province) in China. The results showed that the mean values of protein, starch, fat, fiber, reducing sugar, ash, moisture and energy in quinoa bran were 9.35%, 47.37%, 8.26%, 10.74%, 3.68%, 6.25%, 9.29% and 360.2 kcal/100 g, respectively. Although the protein content in quinoa bran is lower than that in quinoa grain, it is comparable to that in other grains (rice, corn, millet and sorghum) and brans (wheat, oat and rice), so it has the commercial potential to be processed into animal feed or other edible food. The contents of antioxidant flavonoids (460.9 mg/100g) and polyphenols (477.8 mg/100 g) in quinoa bran were higher than those in quinoa grain, suggesting that quinoa bran had better antioxidant capacity. The contents of saponins, tannins and phytic acid in quinoa bran were 18.65, 0.30 and 0.73%, respectively. The content of saponins was nearly one times higher than that in quinoa grain, the contents of tannins and phytic acid, however, were lower than those in quinoa grain. Therefore, the removal of saponins is the key to eliminate the antinutritional properties of quinoa bran. The contents of macroelements (sodium, potassium, calcium, magnesium, phosphorus) and microelements (iron, manganese, copper, zinc, cobalt, molybdenum, selenium, barium) in quinoa bran were generally higher than those in quinoa grain, which was consistent with the results of ash determination. In summary, quinoa bran was found to be a rich source of nutritional and bioactive components and minerals. If the antinutritional problem can be overcome, quinoa bran has great potential for application in the food industry.