Consider a solution of gas X in contact with a solid surface at a constant temperature. The Langmuir adsorption isotherm for this system is represented by the equation /= _/(1+), where is the partial pressure of gas X, is the volume of the gas, _ is the saturation pressure of the gas, and is the Langmuir adsorption constant. Suppose a student conducts an experiment to investigate the Langmuir adsorption isotherm for gas X on a particular solid surface. They measure the partial pressure of the gas at various volumes and obtain the following results: (mL/g) : 2.0 2.5 3.0 3.5 4.0 (atm) : 0.2 0.4 0.6 0.8 1.0 Using these values, what is the Langmuir adsorption constant, , for the given system?

Question

Consider a solution of gas X in contact with a solid surface at a constant temperature. The Lang

Answer 1

To find the Langmuir adsorption constant, , we can use the given data points to create a system of linear equations. First, let's rewrite the Langmuir isotherm equation as follows:/ = _/ 1+  => / - _/ = _/Now, let's use the given data points to create a system of linear equations:1  0.2/2.0 - _/2.0 =  0.2 _/2.02  0.4/2.5 - _/2.5 =  0.4 _/2.53  0.6/3.0 - _/3.0 =  0.6 _/3.04  0.8/3.5 - _/3.5 =  0.8 _/3.55  1.0/4.0 - _/4.0 =  1.0 _/4.0To solve this system of linear equations, we can use any method such as substitution, elimination, or matrix inversion. However, it's important to note that this system of equations is not linearly independent, meaning that there is no unique solution for  and _. Instead, we can use a graphical method or a numerical method like the least squares method to find the best-fit values for  and _. Using a graphical method or a numerical method, we can find the best-fit line that represents the relationship between / and , and then use the slope and intercept of this line to determine the values of  and _.