To determine the Langmuir constant and maximum adsorption capacity of a metal oxide nanoparticle, the student needs to use the Langmuir adsorption isotherm equation:q_e = Q_max * K_L * C_e / 1 + K_L * C_e where:q_e = amount of adsorbate adsorbed at equilibrium mg/g Q_max = maximum adsorption capacity mg/g K_L = Langmuir constant L/mg C_e = equilibrium concentration of adsorbate in the solution mg/L To find the Langmuir constant K_L and maximum adsorption capacity Q_max , the student needs to linearize the equation by taking the reciprocal:1/q_e = 1/Q_max + 1/ Q_max * K_L * C_eNow, the equation is in the form of a straight line y = mx + b , where:y = 1/q_ex = C_em = 1/ Q_max * K_L b = 1/Q_maxThe student should plot the experimental data as 1/q_e vs. C_e and perform a linear regression to find the slope m and intercept b . From these values, the student can calculate Q_max and K_L:Q_max = 1/bK_L = m / bOnce the Langmuir constant and maximum adsorption capacity are determined, the student can plot the experimental data and the Langmuir model on the same graph. The experimental data should be plotted as q_e vs. C_e, and the Langmuir model should be plotted using the equation:q_e = Q_max * K_L * C_e / 1 + K_L * C_e Interpretation of the results:1. If the linear regression shows a good fit high R-squared value , it indicates that the Langmuir model is suitable for describing the adsorption behavior of the metal oxide nanoparticle towards the selected adsorbate.2. The value of Q_max represents the maximum adsorption capacity of the metal oxide nanoparticle. A higher Q_max value indicates a higher adsorption capacity for the given adsorbate.3. The value of K_L represents the affinity of the adsorbate for the metal oxide nanoparticle. A higher K_L value indicates a stronger interaction between the adsorbate and the nanoparticle, suggesting a more favorable adsorption process.4. By comparing the Langmuir constant and maximum adsorption capacity values with those of other adsorbents, the student can evaluate the effectiveness of the metal oxide nanoparticle in adsorbing the selected adsorbate from water.