The Langmuir adsorption isotherm is given by the equation: = KP / 1 + KP where is the fractional surface coverage, K is the Langmuir constant 0.25 L/mol in this case , and P is the pressure 1 atm .To find the maximum surface coverage of nitrogen gas on the platinum surface, we can plug in the given values into the equation: = 0.25 L/mol * 1 atm / 1 + 0.25 L/mol * 1 atm = 0.25 / 1 + 0.25 = 0.25 / 1.25 0.20The maximum surface coverage of nitrogen gas on the platinum surface at 25C and a pressure of 1 atm, according to the Langmuir adsorption isotherm data with a Langmuir constant of 0.25 L/mole, is approximately 0.20 or 20%.