To determine the maximum monolayer coverage of nitrogen gas on a silver surface in Langmuir units, we can use the Langmuir adsorption isotherm equation: = P * K / 1 + P * K where is the fractional coverage of the surface in Langmuir units , P is the partial pressure of nitrogen gas 2.5 atm , and K is the Langmuir adsorption constant.First, we need to find the Langmuir adsorption constant K . We can use the area per molecule of nitrogen adsorbed on the silver surface 1.55 10^-19 m^2 and the ideal gas law to find K.The ideal gas law is:PV = nRTwhere P is the pressure 2.5 atm , V is the volume, n is the number of moles, R is the ideal gas constant 0.0821 L atm/mol K , and T is the temperature 298 K .We can rearrange the ideal gas law to find the volume per mole of nitrogen gas:V/n = RT/PV/n = 0.0821 L atm/mol K * 298 K / 2.5 atm = 9.85 L/molNow, we can convert the volume per mole to the area per molecule using Avogadro's number 6.022 10^23 molecules/mol :Area per molecule = 9.85 L/mol / 6.022 10^23 molecules/mol = 1.64 10^-23 m^2/moleculeNow, we can find the Langmuir adsorption constant K using the area per molecule of nitrogen adsorbed on the silver surface 1.55 10^-19 m^2 and the area per molecule in the gas phase 1.64 10^-23 m^2/molecule :K = 1.55 10^-19 m^2 / 1.64 10^-23 m^2/molecule = 9.45 10^3Now that we have the Langmuir adsorption constant K , we can use the Langmuir adsorption isotherm equation to find the maximum monolayer coverage : = P * K / 1 + P * K = 2.5 atm * 9.45 10^3 / 1 + 2.5 atm * 9.45 10^3 1The maximum monolayer coverage of nitrogen gas on a silver surface in Langmuir units is approximately 1, which means the silver surface is fully covered by a monolayer of nitrogen gas under these conditions.